├── .gitignore ├── www ├── FigApp.png ├── favicon.ico ├── logo_covid.png ├── logoestatistica.png └── styles.css ├── STvideos ├── US_n.rds ├── Brazil_n.rds ├── China_n.rds ├── India_n.rds ├── Italy_n.rds └── Spain_n.rds ├── app_v1 ├── www │ ├── FigApp.png │ ├── favicon.ico │ ├── Covid19UFMG.pdf │ ├── event_2105.jpg │ ├── GitHub-Mark-32px.png │ ├── logoestatistica.png │ ├── GitHub-Mark-Light-32px.png │ ├── markdown │ │ ├── CoronaUFMG_MD_en.pdf │ │ ├── CoronaUFMG_MD_pt.pdf │ │ ├── CoronaUFMG_MD.md │ │ └── CoronaUFMG_MD.Rmd │ ├── code.js │ ├── styles.css │ └── CoronaUFMG_MD.Rmd ├── EstadosCov19.csv ├── time_series_covid19_deaths_global.csv ├── time_series_covid19_confirmed_global.csv ├── google-analytics.html ├── README.md ├── global.R ├── CoronaUFMG_MD.md └── CoronaUFMG_MDen.md ├── STpredictions ├── Iraq_d.rds ├── Iraq_n.rds ├── Peru_d.rds ├── Peru_n.rds ├── Brazil_d.rds ├── Brazil_n.rds ├── Canada_d.rds ├── Canada_n.rds ├── Chile_d.rds ├── Chile_n.rds ├── China_d.rds ├── China_n.rds ├── France_d.rds ├── France_n.rds ├── Greece_d.rds ├── Greece_n.rds ├── India_d.rds ├── India_n.rds ├── Italy_d.rds ├── Italy_n.rds ├── Japan_d.rds ├── Japan_n.rds ├── Mexico_d.rds ├── Mexico_n.rds ├── Norway_d.rds ├── Norway_n.rds ├── Panama_d.rds ├── Panama_n.rds ├── Poland_d.rds ├── Poland_n.rds ├── Russia_d.rds ├── Russia_n.rds ├── Spain_d.rds ├── Spain_n.rds ├── Sweden_d.rds ├── Sweden_n.rds ├── Turkey_d.rds ├── Turkey_n.rds ├── Argentina_d.rds ├── Argentina_n.rds ├── Australia_d.rds ├── Australia_n.rds ├── Belgium_d.rds ├── Belgium_n.rds ├── Bolivia_d.rds ├── Bolivia_n.rds ├── Colombia_d.rds ├── Colombia_n.rds ├── Ecuador_d.rds ├── Ecuador_n.rds ├── Ethiopia_d.rds ├── Ethiopia_n.rds ├── Germany_d.rds ├── Germany_n.rds ├── Guatemala_d.rds ├── Guatemala_n.rds ├── Honduras_d.rds ├── Honduras_n.rds ├── Indonesia_d.rds ├── Indonesia_n.rds ├── Ireland_d.rds ├── Ireland_n.rds ├── Morocco_d.rds ├── Morocco_n.rds ├── Paraguay_d.rds ├── Paraguay_n.rds ├── Portugal_d.rds ├── Portugal_n.rds ├── Romania_d.rds ├── Romania_n.rds ├── Ukraine_d.rds ├── Ukraine_n.rds ├── Uruguay_d.rds ├── Uruguay_n.rds ├── Venezuela_d.rds ├── Venezuela_n.rds ├── Brazil_AC_de.rds ├── Brazil_AC_ne.rds ├── Brazil_AL_de.rds ├── Brazil_AL_ne.rds ├── Brazil_AM_de.rds ├── Brazil_AM_ne.rds ├── Brazil_AP_de.rds ├── Brazil_AP_ne.rds ├── Brazil_BA_de.rds ├── Brazil_BA_ne.rds ├── Brazil_CE_de.rds ├── Brazil_CE_ne.rds ├── Brazil_DF_de.rds ├── Brazil_DF_ne.rds ├── Brazil_ES_de.rds ├── Brazil_ES_ne.rds ├── Brazil_GO_de.rds ├── Brazil_GO_ne.rds ├── Brazil_MA_de.rds ├── Brazil_MA_ne.rds ├── Brazil_MG_de.rds ├── Brazil_MG_ne.rds ├── Brazil_MS_de.rds ├── Brazil_MS_ne.rds ├── Brazil_MT_de.rds ├── Brazil_MT_ne.rds ├── Brazil_PA_de.rds ├── Brazil_PA_ne.rds ├── Brazil_PB_de.rds ├── Brazil_PB_ne.rds ├── Brazil_PE_de.rds ├── Brazil_PE_ne.rds ├── Brazil_PI_de.rds ├── Brazil_PI_ne.rds ├── Brazil_PR_de.rds ├── Brazil_PR_ne.rds ├── Brazil_RJ_de.rds ├── Brazil_RJ_ne.rds ├── Brazil_RN_de.rds ├── Brazil_RN_ne.rds ├── Brazil_RO_de.rds ├── Brazil_RO_ne.rds ├── Brazil_RR_de.rds ├── Brazil_RR_ne.rds ├── Brazil_RS_de.rds ├── Brazil_RS_ne.rds ├── Brazil_SC_de.rds ├── Brazil_SC_ne.rds ├── Brazil_SE_de.rds ├── Brazil_SE_ne.rds ├── Brazil_SP_de.rds ├── Brazil_SP_ne.rds ├── Brazil_TO_de.rds ├── Brazil_TO_ne.rds ├── Costa-Rica_d.rds ├── Costa-Rica_n.rds ├── Netherlands_d.rds ├── Netherlands_n.rds ├── New-Zealand_d.rds ├── New-Zealand_n.rds ├── South-Korea_d.rds ├── South-Korea_n.rds ├── Switzerland_d.rds ├── Switzerland_n.rds ├── Saudi-Arabia_d.rds ├── Saudi-Arabia_n.rds ├── South-Africa_d.rds ├── South-Africa_n.rds ├── United-Kingdom_d.rds ├── United-Kingdom_n.rds ├── United-States-of-America_d.rds └── United-States-of-America_n.rds ├── cache ├── EstadosCov19.csv ├── time_series_covid19_deaths_global.csv └── time_series_covid19_confirmed_global.csv ├── app_COVID19.Rproj ├── google-analytics.html ├── R ├── JAGS │ ├── loadData.R │ ├── jags_poisson.R │ ├── posterior_sample.R │ ├── mcmcplot_country.R │ ├── 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-------------------------------------------------------------------------------- 1 | $( document ).ready(function() { 2 | $( ".navbar .container-fluid" ).append( '

Source Code

' ); 3 | }); -------------------------------------------------------------------------------- /app_COVID19.Rproj: -------------------------------------------------------------------------------- 1 | Version: 1.0 2 | 3 | RestoreWorkspace: Default 4 | SaveWorkspace: Default 5 | AlwaysSaveHistory: Default 6 | 7 | EnableCodeIndexing: Yes 8 | UseSpacesForTab: Yes 9 | NumSpacesForTab: 2 10 | Encoding: UTF-8 11 | 12 | RnwWeave: Sweave 13 | LaTeX: pdfLaTeX 14 | -------------------------------------------------------------------------------- /app_v1/www/styles.css: -------------------------------------------------------------------------------- 1 | .fab { 2 | color: black; 3 | } 4 | 5 | .img-with-text { 6 | text-align: center; 7 | max-width: 120px; 8 | max-height: 50px; 9 | margin: 1%; 10 | } 11 | 12 | .img-with-text img { 13 | display: block; 14 | margin: auto; 15 | padding: 1% 16 | } -------------------------------------------------------------------------------- /google-analytics.html: -------------------------------------------------------------------------------- 1 | 2 | 3 | -------------------------------------------------------------------------------- /app_v1/google-analytics.html: -------------------------------------------------------------------------------- 1 | 2 | 3 | -------------------------------------------------------------------------------- /R/JAGS/loadData.R: -------------------------------------------------------------------------------- 1 | ## main function to load the data - GLOBAL 2 | loadData = function(fileName, columnName) { 3 | data = read.csv(file.path(baseURL, fileName), check.names=FALSE, stringsAsFactors=FALSE) %>% 4 | select(-Lat, -Long) %>% 5 | pivot_longer(-(1:2), names_to="date", values_to=columnName)%>% 6 | mutate(date=as.Date(date, format="%m/%d/%y")) %>% 7 | rename(country = `Country/Region`, state = `Province/State`) 8 | save(data, file=fileName) 9 | return(data) 10 | } 11 | -------------------------------------------------------------------------------- /rsconnect/shinyapps.io/dest-ufmg/app_COVID19.dcf: -------------------------------------------------------------------------------- 1 | name: app_COVID19 2 | title: app_COVID19 3 | username: 4 | account: dest-ufmg 5 | server: shinyapps.io 6 | hostUrl: https://api.shinyapps.io/v1 7 | appId: 2008872 8 | bundleId: 3289548 9 | url: https://dest-ufmg.shinyapps.io/app_COVID19/ 10 | when: 1592520228.8867 11 | asMultiple: FALSE 12 | asStatic: FALSE 13 | ignoredFiles: Brazil_n.rds|plot_LTpred.R|README.md|teste_plots_weekend.R|teste_subplot.R|cache/EstadosCov19.csv|app_v1|R|STpredictions|STvideos 14 | -------------------------------------------------------------------------------- /R/pop/pop_BR.csv: -------------------------------------------------------------------------------- 1 | "uf","pop" 2 | "AC",881935 3 | "AL",3337357 4 | "AM",4144597 5 | "AP",845731 6 | "BA",14873064 7 | "CE",9132078 8 | "DF",3015268 9 | "ES",4018650 10 | "GO",7018354 11 | "MA",7075181 12 | "MG",21168791 13 | "MS",2778986 14 | "MT",3484466 15 | "PA",8602865 16 | "PB",4018127 17 | "PE",9557071 18 | "PI",3273227 19 | "PR",11433957 20 | "RJ",17264943 21 | "RN",3506853 22 | "RO",1777225 23 | "RR",605761 24 | "RS",11377239 25 | "SC",7164788 26 | "SE",2298696 27 | "SP",45919049 28 | "TO",1572866 29 | "BR",210147125 30 | -------------------------------------------------------------------------------- /R/getRepofiles.R: -------------------------------------------------------------------------------- 1 | readfiles.repo <- function(){ 2 | req <- GET("https://api.github.com/repos/thaispaiva/app_COVID19/git/trees/master?recursive=1") 3 | stop_for_status(req) 4 | filelist <- unlist(lapply(content(req)$tree, "[", "path"), use.names = F) 5 | files <- grep("STpredictions/", filelist, value = TRUE, fixed = TRUE) 6 | files <- unlist(lapply(strsplit(files, "/"), "[", 2)) 7 | files <- grep(".rds", files, value = TRUE) 8 | 9 | return(files) 10 | } 11 | 12 | #files <- readfiles.repo() 13 | 14 | 15 | #strsplit(files,"_") 16 | -------------------------------------------------------------------------------- /R/STAN/create_cases_BR.R: -------------------------------------------------------------------------------- 1 | library("dplyr") 2 | library("PandemicLP") 3 | library("pracma") 4 | 5 | setwd("/home/marcosop/Covid/R/STAN/") 6 | source("utils.R") 7 | 8 | out <- nwaves(country = FALSE) 9 | nwaves <- out$nwaves 10 | state_list <- out$state_list 11 | 12 | template <- readLines("template_cases_BR.R") 13 | 14 | files <- list.files(pattern="predict_BR_[1,2,3,4,5,6,7,8,9](.*?).R") 15 | file.remove(files) 16 | 17 | for(i in 1:length(nwaves)){ 18 | 19 | states <- paste("c(\"",paste(state_list[[i]],collapse="\",\""),"\")",sep="") 20 | 21 | code <- gsub("_statelist_",states,template) 22 | code <- gsub("_nwaves_",nwaves[i],code) 23 | file.name <- paste0("predict_BR_",nwaves[i],"wave.R") 24 | write(code,file=file.name) 25 | cat("File ", paste0(getwd(),"/",file.name), "written.\n") 26 | } 27 | 28 | 29 | -------------------------------------------------------------------------------- /R/STAN/create_cases_country.R: -------------------------------------------------------------------------------- 1 | library("dplyr") 2 | library("PandemicLP") 3 | library("pracma") 4 | 5 | setwd("/home/marcosop/Covid/R/STAN/") 6 | source("utils.R") 7 | 8 | out <- nwaves() 9 | nwaves <- out$nwaves 10 | country_list <- out$country_list 11 | 12 | template <- readLines("template_cases_countries.R") 13 | 14 | files <- list.files(pattern="predict_[1,2,3,4,5,6,7,8,9](.*?).R") 15 | file.remove(files) 16 | 17 | for(i in 1:length(nwaves)){ 18 | 19 | countries <- paste("c(\"",paste(country_list[[i]],collapse="\",\""),"\")",sep="") 20 | 21 | code <- gsub("_countrynames_",countries,template) 22 | code <- gsub("_nwaves_",nwaves[i],code) 23 | file.name <- paste0("predict_",nwaves[i],"wave_par.R") 24 | write(code,file=file.name) 25 | cat("File ", paste0(getwd(),"/",file.name), "written.\n") 26 | } 27 | -------------------------------------------------------------------------------- /R/STAN/create_deaths_BR.R: -------------------------------------------------------------------------------- 1 | library("dplyr") 2 | library("PandemicLP") 3 | library("pracma") 4 | 5 | setwd("/home/marcosop/Covid/R/STAN/") 6 | source("utils.R") 7 | 8 | out <- nwaves(country = FALSE,new_cases = FALSE) 9 | nwaves <- out$nwaves 10 | state_list <- out$state_list 11 | 12 | template <- readLines("template_deaths_BR.R") 13 | 14 | files <- list.files(pattern="death_BR_[1,2,3,4,5,6,7,8,9](.*?).R") 15 | file.remove(files) 16 | 17 | for(i in 1:length(nwaves)){ 18 | 19 | states <- paste("c(\"",paste(state_list[[i]],collapse="\",\""),"\")",sep="") 20 | 21 | code <- gsub("_statelist_",states,template) 22 | code <- gsub("_nwaves_",nwaves[i],code) 23 | file.name <- paste0("death_BR_",nwaves[i],"wave.R") 24 | write(code,file=file.name) 25 | cat("File ", paste0(getwd(),"/",file.name), "written.\n") 26 | } 27 | -------------------------------------------------------------------------------- /R/STAN/create_deaths_country.R: -------------------------------------------------------------------------------- 1 | library("dplyr") 2 | library("PandemicLP") 3 | library("pracma") 4 | 5 | setwd("/home/marcosop/Covid/R/STAN/") 6 | source("utils.R") 7 | 8 | out <- nwaves(new_cases = FALSE) 9 | nwaves <- out$nwaves 10 | country_list <- out$country_list 11 | 12 | template <- readLines("template_deaths_countries.R") 13 | 14 | files <- list.files(pattern="death_[1,2,3,4,5,6,7,8,9](.*?).R") 15 | file.remove(files) 16 | 17 | for(i in 1:length(nwaves)){ 18 | 19 | countries <- paste("c(\"",paste(country_list[[i]],collapse="\",\""),"\")",sep="") 20 | 21 | code <- gsub("_countrynames_",countries,template) 22 | code <- gsub("_nwaves_",nwaves[i],code) 23 | file.name <- paste0("death_",nwaves[i],"wave_par.R") 24 | write(code,file=file.name) 25 | cat("File ", paste0(getwd(),"/",file.name), "written.\n") 26 | } 27 | 28 | 29 | -------------------------------------------------------------------------------- /footer.html: -------------------------------------------------------------------------------- 1 |
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GitHub
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Website
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E-mail
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-------------------------------------------------------------------------------- /Rver: -------------------------------------------------------------------------------- 1 | classify.flag = function(obs, adj){ 2 | 3 | colnames(obs) = c("date", "y") 4 | 5 | dados = full_join(obs, adj) %>% mutate(y_s = rollmean(y, k = 20, fill = NA) %>% rollmean(k = 10, fill = NA), # suavizando os dados 6 | dif_s = c(NA, y_s %>% diff()) %>% rollmean(k = 50, fill = NA), # diferença suavizada 7 | id = c(NA, dif_s %>% sign() %>% diff()) ) # identificador de mudança de comportamento 8 | 9 | aux = dados %>% filter(id == 2 |id == -2) %>% arrange(desc(date)) 10 | 11 | if(aux$id[1] == -2){ # se o último ponto identificado é um pico, a amplitude é calculada com base na última observação do y suavizado 12 | aux = rbind(tail(dados %>% filter(!is.na(y_s)), 1) %>% mutate(id = 2), aux) 13 | } 14 | 15 | est = (aux %>% mutate(amp_y = c(NA, diff(y_s)), 16 | amp_mu = c(NA, diff(mu)), 17 | id_df = c(NA, diff(id)), 18 | est = (amp_y - amp_mu)^2/max(y_s)^2) %>% 19 | filter(id_df == -4) %>% # amplitudes corretas 20 | summarise(crit = sum(est)))$crit 21 | 22 | #ifelse(est <= 0.2, 0, ifelse(est <= 0.5, 1, 2)) 23 | est 24 | } 25 | -------------------------------------------------------------------------------- /app_v1/README.md: -------------------------------------------------------------------------------- 1 | # Previsão de Curto e Longo Prazo para COVID-19 / DEST-UFMG 2 | 3 | Esse é o repositório com o código utilizado para implementação do aplicativo para previsão de curto e longo prazo para casos de COVID-19. 4 | 5 | O aplicativo pode ser acessado em: [https://dest-ufmg.shinyapps.io/app_COVID19/](https://dest-ufmg.shinyapps.io/app_COVID19/). 6 | 7 | Este projeto está sendo desenvolvido por um grupo de professores e alunos de pós-graduação do [Departamento de Estatística](http://www.est.ufmg.br) da [Universidade Federal de Minas Gerais](http://www.ufmg.br). 8 | 9 | Para mais projetos relacionados aos dados de COVID-19 desenvolvidos no DEST/UFMG, acesse: [est.ufmg.br/portal/extensao/coronavirus](http://www.est.ufmg.br/portal/extensao/coronavirus). 10 | 11 | --- 12 | 13 | ### Short and long term prediction for COVID-19 / DEST-UFMG 14 | This repository contains the source code for the implementation of an app for long and short term prediction of COVID-19 cases. 15 | 16 | The app can be accessed at: [https://dest-ufmg.shinyapps.io/app_COVID19/](https://dest-ufmg.shinyapps.io/app_COVID19/). 17 | 18 | This project is being developed as a group work with professors and graduate students at the [Department of Statistics](http://www.est.ufmg.br) at [UFMG](http://www.ufmg.br) (Federal University of Minas Gerais). 19 | 20 | For more projects related to COVID-19 data being developed at the Statistics Department, visit: [est.ufmg.br/portal/extensao/coronavirus](http://www.est.ufmg.br/portal/extensao/coronavirus). 21 | -------------------------------------------------------------------------------- /R/JAGS/jags_poisson.R: -------------------------------------------------------------------------------- 1 | ############################################################################### 2 | ### M0 (new) 3 | ############################################################################### 4 | mod_string_new <- "model{ 5 | 6 | for(i in 1:t) { 7 | y[i] ~ dpois(mu[i]) 8 | mu[i] = f*a*c*exp(-c*i)/(b+exp(-c*i))^(f+1) 9 | } 10 | 11 | a ~ dgamma(0.1, 0.1) 12 | b ~ dgamma(0.1, 0.1) 13 | c ~ dbeta(2,6) 14 | f = exp(f1) 15 | f1 ~ dnorm(0,.1) 16 | # f ~ dgamma(1,1) 17 | # f ~ dgamma(0.1,0.1) 18 | 19 | # for(j in 1:L){ 20 | # yfut[j] ~ dpois(mu[t+j]) 21 | # mu[t+j] = f*a*c*exp(-c*(t+j))/(b+exp(-c*(t+j)))^(f+1) 22 | # } 23 | 24 | }" 25 | 26 | 27 | 28 | 29 | ############################################################################### 30 | ### M0 (new DM) 31 | ############################################################################### 32 | mod_string_new_dm <- "model{ 33 | 34 | for(i in 1:t) { 35 | y[i] ~ dpois(mu[i]) 36 | a[i] = exp(sum(wa[1:i])) 37 | mu[i] = f*a[i]*c*exp(-c*i)/(b+exp(-c*i))^(f+1) 38 | } 39 | 40 | b ~ dgamma(0.1, 0.1) 41 | c ~ dbeta(2,6) 42 | f = exp(f1) 43 | f1 ~ dnorm(0,.1) 44 | # f ~ dgamma(1,1) 45 | # f ~ dgamma(0.1,0.1) 46 | # f = 1 47 | # Wa = 1e1 48 | # Ka = 1 # 1e1 49 | Wa ~ dgamma(0.01, 0.01) 50 | 51 | # prioris para o inicio da dinamica 52 | wa[1] ~ dnorm(-5, 0.1) 53 | # prioris para as perturbacoes da evolucao 54 | for (i in 2:t){ 55 | # wa[i] ~ dnorm(0, Wa) 56 | wa[i] ~ dnorm(-1/(2*Wa),Wa) 57 | } 58 | for (j in 1:L){ 59 | # wa[t+j] ~ dnorm(0, Wa) 60 | # wa[t+j] ~ dnorm(0, Wa/Ka) 61 | wa[t+j] ~ dnorm(-1/(2*Wa),Wa) 62 | # wa[t+j] ~ dnorm(-Ka/(2*Wa),Wa/Ka) 63 | } 64 | 65 | for(j in 1:L){ 66 | yfut[j] ~ dpois(mu[t+j]) 67 | a[t+j] = exp(sum(wa[1:(t+j)])) 68 | mu[t+j] = f*a[t+j]*c*exp(-c*(t+j))/(b+exp(-c*(t+j)))^(f+1) 69 | } 70 | 71 | }" 72 | 73 | 74 | -------------------------------------------------------------------------------- /R/JAGS/posterior_sample.R: -------------------------------------------------------------------------------- 1 | ## generate a sample from the predictive distribution 2 | # M: sample size for the predictive sample 3 | # L: number of steps in future 4 | # B: baseline time (last t of the fitted model) 5 | # a: samples of parameter a in time t 6 | # b: samples of parameter b in time t 7 | # c: samples of parameter c in time t 8 | # taua : precision of the normal distribution for the future samples of a 9 | # taub : precision of the normal distribution for the future samples of b 10 | # tauc : precision of the normal distribution for the future samples of c 11 | pred <- function(L=100,B,a,b,c,taua,taub,tauc){ 12 | #save sample size 13 | M.save <- M <- length(a) 14 | 15 | mu <- a.fut <- b.fut <- c.fut <- matrix(-Inf, ncol=L+1,nrow=M) 16 | 17 | #initialize process with first information 18 | a.fut[,1] <- a 19 | b.fut[,1] <- b 20 | c.fut[,1] <- c 21 | 22 | mu[,1] <- (a.fut[,1]*exp(c.fut[,1]*(B+1))) / (1+b.fut[,1]*exp(c.fut[,1]*(B+1))) 23 | 24 | #limit attempt for the rejection procedure 25 | limit <- 100 26 | for(t in 2:(L+1)){ 27 | #counter for how many attempts 28 | count <- 1 29 | M <- M.save 30 | pos <- 1:M 31 | while(count <= limit){ 32 | 33 | #generate sample for w's 34 | wa <- rnorm(M,0,sd=sqrt(1/taua)) 35 | wb <- rnorm(M,0,sd=sqrt(1/taub)) 36 | wc <- rnorm(M,0,sd=sqrt(1/tauc)) 37 | 38 | #calculate a,b and c parameters 39 | a.fut[pos,t] <- exp(log(a.fut[pos,t-1]) + wa) 40 | b.fut[pos,t] <- exp(log(b.fut[pos,t-1]) + wb) 41 | c.fut[pos,t] <- exp(log(c.fut[pos,t-1]) + wc) 42 | 43 | #calculate mu 44 | mu[pos,t] <- (a.fut[pos,t]*exp(c.fut[pos,t]*(B+t))) / (1+b.fut[pos,t]*exp(c.fut[pos,t]*(B+t))) 45 | 46 | #check if mu satisify condition 47 | cond <- mu[,t]-mu[,t-1] 48 | pos <- which(cond <= 0) 49 | if(length(pos) != 0){ 50 | M <- length(pos) 51 | count <- count + 1 52 | if(count == limit+1) mu[pos,t] <- mu[pos,t-1] + 1e-7 53 | } 54 | else count <- limit + 1 55 | } 56 | } 57 | 58 | M <- M.save 59 | y.fut <- matrix(-Inf, ncol=L,nrow=M) 60 | #gernate sample from the mu's 61 | for(i in 1:L) y.fut[,i] <- rpois(M,mu[,i+1]-mu[,i]) 62 | 63 | out <- list(y.fut <- y.fut, mu.fut <- mu, a.fut <- a.fut, b.fut <- b.fut, c.fut <- c.fut) 64 | return(out) 65 | } 66 | 67 | -------------------------------------------------------------------------------- /R/STAN/template_cases_countries.R: -------------------------------------------------------------------------------- 1 | rm(list=ls()) 2 | setwd("/home/marcosop/Covid/R/STAN") 3 | 4 | ################################################################### 5 | ### Packages 6 | ################################################################### 7 | library(PandemicLP) 8 | library(foreach) 9 | library(doMC) 10 | library(dplyr) 11 | library(zoo) 12 | source("utils.R") 13 | 14 | Sys.setenv(LANGUAGE='en') 15 | rstan_options(auto_write = TRUE) 16 | 17 | ################################################################### 18 | ### Data sets: https://github.com/CSSEGISandData 19 | ################################################################### 20 | countrylist <- _countrynames_ 21 | 22 | #register cores 23 | #registerDoMC(cores = detectCores()-1) # Alternativa Linux 24 | registerDoMC(cores = min(63,length(countrylist))) # Alternativa Linux 25 | 26 | 27 | obj <- foreach(s = 1:length(countrylist)) %dopar% { 28 | 29 | country_name <- countrylist[s] 30 | covid_country <- load_covid(country_name=country_name) # load data 31 | 32 | nwaves = _nwaves_ 33 | 34 | nom <- c("date","n","d","n_new","d_new") 35 | name.to.save <- gsub(" ", "-", country_name) 36 | results_directory = "/home/marcosop/Covid/chains/" 37 | name.file <- paste0(results_directory,name.to.save,'_',nom[2],'.rds') 38 | old <- readRDS(name.file) 39 | 40 | mod <- pandemic_model(covid_country,case_type = "confirmed", p = 0.08, 41 | n_waves = nwaves, 42 | warmup = 10e3, thin = 3, sample_size = 1e3, 43 | init=old, covidLPconfig = FALSE) # run the model 44 | 45 | names(covid_country$data) <- nom 46 | 47 | pred <- posterior_predict(mod,horizonLong = 1000,horizonShort = 14) # do predictions 48 | 49 | stats <- pandemic_stats(pred) # calculate stats 50 | stats[[1]] <-NULL # removing the data (the app use the data coming from other object) 51 | names(stats) <- c("df_predict","lt_predict","lt_summary","mu_plot") 52 | 53 | names(stats$df_predict) <- c("date", "q25", "med", "q975", "m") 54 | names(stats$lt_predict) <- c("date", "q25", "med", "q975", "m") 55 | names(stats$lt_summary) <- c("NTC25","NTC500","NTC975","high.dat.low","high.dat.med","high.dat.upper","end.dat.low", 56 | "end.dat.med","end.dat.upper") 57 | 58 | #create flag 59 | flag <- try(classify.flag(covid_country$data[,c("date","n_new")],stats$mu_plot)) 60 | 61 | if(class(flag)== "try-error") flag <- -1 62 | 63 | list_out <- list( df_predict = stats$df_predict, lt_predict=stats$lt_predict, lt_summary=stats$lt_summary, 64 | mu_plot = stats$mu_plot, residuals = cbind(mod$nominal_errors, mod$relative_errors), 65 | flag = flag) 66 | 67 | name.to.save <- gsub(" ", "-", country_name) 68 | 69 | ### saveRDS 70 | results_directory = "/home/marcosop/Covid/app_COVID19/STpredictions/" 71 | name.file <- paste0(results_directory,name.to.save,'_',colnames(covid_country$data)[2],'.rds') 72 | saveRDS(list_out, file=name.file) 73 | 74 | ### saveChain 75 | results_directory = "/home/marcosop/Covid/chains/" 76 | name.file <- paste0(results_directory,name.to.save,'_',colnames(covid_country$data)[2],'.rds') 77 | saveRDS(mod, file=name.file) 78 | } 79 | -------------------------------------------------------------------------------- /R/STAN/template_deaths_countries.R: -------------------------------------------------------------------------------- 1 | rm(list=ls()) 2 | setwd("/home/marcosop/Covid/R/STAN") 3 | 4 | ################################################################### 5 | ### Packages 6 | ################################################################### 7 | library(PandemicLP) 8 | library(foreach) 9 | library(doMC) 10 | library(dplyr) 11 | library(zoo) 12 | source("utils.R") 13 | 14 | Sys.setenv(LANGUAGE='en') 15 | rstan_options(auto_write = TRUE) 16 | 17 | ################################################################### 18 | ### Data sets: https://github.com/CSSEGISandData 19 | ################################################################### 20 | countrylist <- _countrynames_ 21 | 22 | #register cores 23 | #registerDoMC(cores = detectCores()-1) # Alternativa Linux 24 | registerDoMC(cores = min(63,length(countrylist))) # Alternativa Linux 25 | 26 | 27 | obj <- foreach(s = 1:length(countrylist)) %dopar% { 28 | 29 | country_name <- countrylist[s] 30 | covid_country <- load_covid(country_name=country_name) # load data 31 | 32 | nwaves = _nwaves_ 33 | 34 | nom <- c("date","n","d","n_new","d_new") 35 | name.to.save <- gsub(" ", "-", country_name) 36 | results_directory = "/home/marcosop/Covid/chains/" 37 | name.file <- paste0(results_directory,name.to.save,'_',nom[3],'.rds') 38 | old <- readRDS(name.file) 39 | 40 | mod <- pandemic_model(covid_country,case_type = "deaths", p = 0.08*.25, 41 | n_waves = nwaves, 42 | warmup = 10e3, thin = 3, sample_size = 1e3, 43 | init=old, covidLPconfig = FALSE) # run the model 44 | 45 | names(covid_country$data) <- nom 46 | 47 | pred <- posterior_predict(mod,horizonLong = 1000,horizonShort = 14) # do predictions 48 | 49 | stats <- pandemic_stats(pred) # calculate stats 50 | stats[[1]] <-NULL # removing the data (the app use the data coming from other object) 51 | names(stats) <- c("df_predict","lt_predict","lt_summary","mu_plot") 52 | 53 | names(stats$df_predict) <- c("date", "q25", "med", "q975", "m") 54 | names(stats$lt_predict) <- c("date", "q25", "med", "q975", "m") 55 | names(stats$lt_summary) <- c("NTC25","NTC500","NTC975","high.dat.low","high.dat.med","high.dat.upper","end.dat.low", 56 | "end.dat.med","end.dat.upper") 57 | 58 | #create flag 59 | flag <- try(classify.flag(covid_country$data[,c("date","d_new")],stats$mu_plot)) 60 | 61 | if(class(flag)== "try-error") flag <- -1 62 | 63 | list_out <- list( df_predict = stats$df_predict, lt_predict=stats$lt_predict, lt_summary=stats$lt_summary, 64 | mu_plot = stats$mu_plot, residuals = cbind(mod$nominal_errors, mod$relative_errors), 65 | flag = flag) 66 | 67 | name.to.save <- gsub(" ", "-", country_name) 68 | 69 | ### saveRDS 70 | results_directory = "/home/marcosop/Covid/app_COVID19/STpredictions/" 71 | name.file <- paste0(results_directory,name.to.save,'_',colnames(covid_country$data)[3],'.rds') 72 | saveRDS(list_out, file=name.file) 73 | 74 | ### saveChain 75 | results_directory = "/home/marcosop/Covid/chains/" 76 | name.file <- paste0(results_directory,name.to.save,'_',colnames(covid_country$data)[3],'.rds') 77 | saveRDS(mod, file=name.file) 78 | } 79 | -------------------------------------------------------------------------------- /global.R: -------------------------------------------------------------------------------- 1 | ## Load packages 2 | library(dplyr) 3 | library(tidyr) 4 | library(httr) 5 | library(lubridate) 6 | library(knitr) 7 | library(shiny) 8 | library(shinyjs) 9 | library(plotly) 10 | library(shinythemes) 11 | library(shinycssloaders) 12 | library(shinyWidgets) 13 | library(shinyBS) 14 | library(markdown) 15 | 16 | ## Load local functions 17 | source("utils.R") 18 | 19 | ## Define font to be used later 20 | f1 <- list(family = "Arial", size = 10, color = "rgb(30, 30, 30)") 21 | 22 | ## colors for observed data 23 | blu <- 'rgb(100, 140, 240)' 24 | dblu <- 'rgb(0, 0, 102)' 25 | red <- 'rgb(200, 30, 30)' 26 | dred <- 'rgb(100, 30, 30)' 27 | 28 | ##-- DATA SOURCES ---- 29 | ## setup data source (Johns Hopkins)- GLOBAL 30 | baseURL <- "https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series" 31 | 32 | allData <- loadData("time_series_covid19_confirmed_global.csv", "CumConfirmed") %>% 33 | inner_join( 34 | loadData("time_series_covid19_deaths_global.csv", "CumDeaths"), 35 | by = c("Province/State", "Country/Region", "date") 36 | ) 37 | 38 | countries <- sort(unique(allData$`Country/Region`)) 39 | 40 | ## Setup data source (MSaude/BR)- BRAZIL 41 | # baseURL.BR = "https://raw.githubusercontent.com/belisards/coronabr/master/dados" 42 | # baseURL.BR = "https://covid.saude.gov.br/assets/files/COVID19_" 43 | baseURL.BR <- "https://raw.githubusercontent.com/covid19br/covid19br.github.io/master/dados" 44 | # baseURL.BR <- "https://raw.githubusercontent.com/thaispaiva/app_COVID19/master/R/STAN" 45 | brData <- loadData.BR("EstadosCov19.csv") 46 | 47 | ## Setup data source - US 48 | baseURL.US = "https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series" 49 | 50 | covid19_confirm <- loadData.US_cases("time_series_covid19_confirmed_US.csv", "confirmed") 51 | covid19_deaths <- loadData.US_deaths("time_series_covid19_deaths_US.csv", "deaths") 52 | usData <- left_join(covid19_confirm,covid19_deaths, by=c('state','date')) %>% 53 | rename(`Province/State`=state, CumConfirmed=confirmed, CumDeaths=deaths) %>% 54 | select(`Province/State`, CumConfirmed, CumDeaths, date) 55 | 56 | ##-- LOAD PREDICTION RESULTS ---- 57 | files <- readfiles.repo() 58 | aux <- sub(pattern = '(\\_n.rds$)|(\\_d.rds$)', replacement = '', x = files) 59 | 60 | ## List of countries for SHORT TERM prediction 61 | countries_STpred <- sort(unique( 62 | unlist(lapply(strsplit(aux, "_"), function(x) x[1])))) 63 | countries_STpred_orig <- gsub("-", " ", countries_STpred) 64 | 65 | ## List of Brazil's states 66 | statesBR_STpred <- unique(unlist(lapply(strsplit(aux, "_"), function(x) if(x[1] == "Brazil") return(x[2])))) 67 | statesBR_STpred[is.na(statesBR_STpred)] <- "" 68 | statesBR_STpred <- sort(statesBR_STpred) 69 | 70 | ## List of countries for LONG TERM prediction 71 | countries_LTpred_orig <- countries_STpred_orig 72 | 73 | ## List of Brazil's states - LONG TERM 74 | statesBR_LTpred <- statesBR_STpred 75 | 76 | ##-- List of countries to hide new cases 77 | # hide_countries_nc <- list('Australia', 'Belgium', 'Canada', 'Greece', 'Japan', 'Korea, South', 78 | # 'Netherlands', 'Peru', 'Poland', 'Portugal', 'Spain', 'Switzerland', 79 | # 'Uruguay', 'US') 80 | hide_countries_nc <- list() 81 | 82 | ##-- List of countries to hide deaths 83 | # hide_countries_d <- list('Australia', 'US') 84 | hide_countries_d <- list() 85 | 86 | ## Read RDS files from github repository 87 | githubURL <- "https://github.com/thaispaiva/app_COVID19/raw/master/STpredictions" 88 | 89 | ##-- Date format 90 | dt_format <- "%d/%b/%y" -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Projeto CovidLP - Previsão de Curto e Longo Prazos para COVID-19 / DEST-UFMG 2 | 3 | Neste repositório, encontram-se todos os arquivos e códigos necessários para implementar o nosso aplicativo de previsões sobre os casos do COVID-19. A versão online do aplicativo está disponível em [http://est.ufmg.br/covidlp](http://est.ufmg.br/covidlp). 4 | 5 | O aplicativo foi criado por um grupo de professores e alunos de pós-graduação do Departamento de Estatística da Universidade Federal de Minas Gerais, com intuito de fazer com que o usuário possa acompanhar e saber o que esperar sobre os casos e mortes confirmadas de COVID-19. Para mais informações sobre o projeto, acesse o site [http://est.ufmg.br/covidlp/home](http://est.ufmg.br/covidlp/home). 6 | 7 | --- 8 | 9 | Abaixo segue uma explicação deste repositório e seus diretórios: 10 | 11 | - Os arquivos na pasta principal são os códigos necessários para a implementação do aplicativo Shiny no R. 12 | - Na pasta "R" encontram-se arquivos com os códigos executados diariamente para ajustar o modelo de estimação para cada país/estado analisados. 13 | - A pasta "STpredictions" contém os resultados mais recentes das previsões de curto e longo prazo para todos os países, além de relatórios sobre a convergência dos parâmetros do modelo. 14 | - A pasta "STvideos" contém as previsões, de alguns países, realizadas em datas anteriores. Os registros ao longo do tempo são necessários para construir a animação com a evolução das análises. Essa função está em desenvolvimento. 15 | - Na pasta "www" estão as figuras estáticas, utilizadas no aplicativo. 16 | - O botão verde "Clonar ou baixar" oferece a opção de baixar todos os arquivos da página, para que o usuário possa fazer um clone do nosso aplicativo na versão atual. Ressaltamos que o trabalho está em desenvolvimento, e recomendamos acompanhar as atualizações deste repositório. 17 | 18 | --- 19 | 20 | # CovidLP - Short and long term predictions for COVID-19 / DEST-UFMG 21 | 22 | In this repository, you will find all the files needed to implement our app of predictions about COVID-19 cases. The online app can be accessed at [http://est.ufmg.br/covidlp](http://est.ufmg.br/covidlp). 23 | 24 | This application was created by a group of faculty and graduate students from the Statistics Department of the Universidade Federal de Minas Gerais, to allow users to follow and know what to expect about the confirmed cases and deaths cause by COVID-19. For more information about this project, check our site [http://est.ufmg.br/covidlp/home](http://est.ufmg.br/covidlp/home). 25 | 26 | --- 27 | 28 | Below is an explanation of this repository and its directories: 29 | - The files on the root folder are the code files needed to implement the shiny app using R. 30 | - In the "R" folder, there are files with the codes executed daily to fit the estimation model for each country/state being analyzed. 31 | - The folder "STpredictions" contains the most recent results of short and long time predictions for all countries, as well as reports on the convergence of the parameters of the model. 32 | - The folder "STvideos" contains the predictions of some countries, made for previous dates. Records over time are necessary to build the animation with the evolution of the analysis. This feature is under development. 33 | - The "www" folder contains the figures that are static, used in the app. 34 | - The green button "Clone or download" offers the option to download all the files of the repository, so that the user can make a clone of our app on its current version. We emphasize that the work is still under development, and we recommend all users to follow the updates of this repository. 35 | -------------------------------------------------------------------------------- /www/styles.css: -------------------------------------------------------------------------------- 1 | #country { 2 | background-color: #fff !important; 3 | } 4 | 5 | .nav { 6 | padding-left: 1%; 7 | } 8 | 9 | .fab { 10 | color: #00b1d8; 11 | font-size: x-large; 12 | } 13 | 14 | .fa, .fas { 15 | color: #00b1d8; 16 | font-size: smaller; 17 | font-size: x-large; 18 | } 19 | 20 | label { 21 | font-weight: 100; 22 | } 23 | 24 | .container-fluid { 25 | padding: 0; 26 | background-color: #f4f4f7; 27 | } 28 | 29 | body { 30 | background-color: #e8e8ea; 31 | } 32 | 33 | .h1, .h2, .h3, .h4, .h5, .h6, h1, h2, h3, h4, h5, h6 { 34 | font-family: Avenir Next, sans-serif; 35 | color: #565656; 36 | } 37 | 38 | .a, a { 39 | color: #00b1d8; 40 | text-decoration: underline; 41 | } 42 | 43 | .row { 44 | margin-right: 0; 45 | margin-left: 0; 46 | } 47 | 48 | /*.btn, .btn-default { 49 | color: #fff; 50 | background-color: #00b1d8; 51 | border-color: #fff; 52 | display: inline; 53 | float: right; 54 | }*/ 55 | 56 | .btn-default, .btn-default:hover { 57 | color: #fff; 58 | background-color: #00b1d8; 59 | border-color: #fff; 60 | } 61 | 62 | .btn-default.active, .btn-default:active, .open>.dropdown-toggle.btn-default { 63 | color: #fff; 64 | background-color: #00b1d8; 65 | background-image: none; 66 | border-color: #ffffff; 67 | } 68 | 69 | .btn-default.active.focus, .btn-default.active:focus, .btn-default.active:hover, .btn-default:active.focus, .btn-default:active:focus, .btn-default:active:hover, .open>.dropdown-toggle.btn-default.focus, .open>.dropdown-toggle.btn-default:focus, .open>.dropdown-toggle.btn-default:hover { 70 | color: #fff; 71 | background-color: #00b1d8; 72 | border-color: #ffffff; 73 | } 74 | 75 | .btn-default.focus, .btn-default:focus { 76 | color: #fff; 77 | background-color: #00b1d8; 78 | border-color: #ffffff; 79 | } 80 | 81 | .bootstrap-select>.dropdown-toggle { 82 | font-size: 1.25em; 83 | } 84 | 85 | #pB2 { 86 | background-color: #00b1d8; 87 | border-color: white; 88 | color: white; 89 | } 90 | 91 | .bttn-material-flat.bttn-default { 92 | float: right; 93 | } 94 | 95 | hr { 96 | border-top: 1px solid #eee0; 97 | } 98 | 99 | .dropdown-menu>.active>a, .dropdown-menu>.active>a:focus, .dropdown-menu>.active>a:hover { 100 | color: #fff !important; 101 | background-color: #00b1d8 !important; 102 | } 103 | 104 | .shiny-input-container:not(.shiny-input-container-inline) { 105 | padding-top: 10px; 106 | } 107 | 108 | .bootstrap-select .dropdown-toggle .filter-option-inner-inner { 109 | text-align: center; 110 | } 111 | 112 | .btn_div { 113 | display: inline-block; 114 | vertical-align: initial; 115 | } 116 | 117 | .well { 118 | margin-bottom: 0px; 119 | } 120 | 121 | .footer { 122 | max-height: 100%; 123 | bottom: 0px; 124 | left: 0px; 125 | right: 0px; 126 | margin-bottom: 0px; 127 | background-color: #FFFFFF; 128 | text-align: center; 129 | } 130 | 131 | .img_footer{ 132 | padding-top: 10px; 133 | padding-right: 100px; 134 | padding-left: 100px; 135 | } 136 | 137 | .imgContainerFooter{ 138 | padding-top: 20px; 139 | float: right; 140 | } 141 | 142 | .imgContainerFooter img { 143 | height: 40px; 144 | padding: 5px 5px 5px 5px; 145 | } 146 | 147 | .logoContainerFooter{ 148 | padding-top: 0px; 149 | float: left; 150 | } 151 | 152 | .logoContainerFooter img { 153 | height: 30px; 154 | } 155 | 156 | .shiny-input-container:not(.shiny-input-container-inline) { 157 | padding-top: 0px; 158 | margin-bottom: 0px; 159 | } 160 | 161 | .column { 162 | float: left; 163 | width: 50%; 164 | } 165 | 166 | .row:after { 167 | content: ""; 168 | display: table; 169 | clear: both; 170 | } -------------------------------------------------------------------------------- /R/JAGS/mcmcplot_country.R: -------------------------------------------------------------------------------- 1 | mcmcplot_country <- function (mcmcout, parms = NULL, regex = NULL, random = NULL, 2 | leaf.marker = "[\\[_]", dir = tempdir(), filename = "MCMCoutput", 3 | extension = "html", title = NULL, heading = title, 4 | col = NULL, lty = 1, xlim = NULL, ylim = NULL, style = c("gray","plain"), 5 | greek = FALSE, 6 | country = NULL, 7 | type = NULL) 8 | { 9 | if (is.null(title)) 10 | title <- paste("MCMC Plots: ", deparse(substitute(mcmcout)), 11 | sep = "") 12 | if (is.null(heading)) 13 | heading <- title 14 | style <- match.arg(style) 15 | current.devices <- dev.list() 16 | on.exit(sapply(dev.list(), function(dev) if (!(dev %in% current.devices)) dev.off(dev))) 17 | mcmcout <- convert.mcmc.list(mcmcout) 18 | nchains <- length(mcmcout) 19 | if (is.null(col)) { 20 | col <- mcmcplotsPalette(nchains) 21 | } 22 | css.file <- system.file("MCMCoutput.css", package = "mcmcplots") 23 | css.file <- paste("file:///", css.file, sep = "") 24 | htmlfile <- .html.begin(dir, filename, extension, title = title, 25 | cssfile = css.file) 26 | if (is.null(varnames(mcmcout))) { 27 | warning("Argument 'mcmcout' did not have valid variable names, so names have been created for you.") 28 | varnames(mcmcout) <- varnames(mcmcout, allow.null = FALSE) 29 | } 30 | parnames <- parms2plot(varnames(mcmcout), parms, regex, random, 31 | leaf.marker, do.unlist = FALSE) 32 | if (length(parnames) == 0) 33 | stop("No parameters matched arguments 'parms' or 'regex'.") 34 | np <- length(unlist(parnames)) 35 | cat("\n
\n", file = htmlfile, append = TRUE) 36 | cat("

", heading, "

", sep = "", 37 | file = htmlfile, append = TRUE) 38 | cat("
\n", file = htmlfile, append = TRUE) 39 | cat("\n

Table of Contents

", file = htmlfile, 40 | append = TRUE) 41 | cat("
    \n", file = htmlfile, append = TRUE) 42 | for (group.name in names(parnames)) { 43 | cat(sprintf("
  • %s
    • \n", 44 | group.name, group.name), file = htmlfile, append = TRUE) 45 | } 46 | cat("
\n", file = htmlfile, append = TRUE) 47 | cat("
\n", file = htmlfile, append = TRUE) 48 | htmlwidth <- 640 49 | htmlheight <- 480 50 | for (group.name in names(parnames)) { 51 | cat(sprintf("

Plots for %s

\n", 52 | group.name, group.name), file = htmlfile, append = TRUE) 53 | for (p in parnames[[group.name]]) { 54 | pctdone <- round(100 * match(p, unlist(parnames))/np) 55 | cat("\r", rep(" ", getOption("width")), 56 | sep = "") 57 | cat("\rPreparing plots for ", group.name, ". ", 58 | pctdone, "% complete.", sep = "") 59 | gname <- paste(country,'_',type,'_', p, ".png", sep = "") 60 | png(file.path(dir, gname), width = htmlwidth, height = htmlheight) 61 | plot_err <- tryCatch({ 62 | mcmcplot1(mcmcout[, p, drop = FALSE], col = col, 63 | lty = lty, xlim = xlim, ylim = ylim, style = style, 64 | greek = greek) 65 | }, error = function(e) { 66 | e 67 | }) 68 | dev.off() 69 | if (inherits(plot_err, "error")) { 70 | cat(sprintf("

%s. %s

", 71 | p, plot_err), file = htmlfile, append = TRUE) 72 | } 73 | else { 74 | .html.img(file = htmlfile, class = "mcmcplot", 75 | src = gname, width = htmlwidth, height = htmlheight) 76 | } 77 | } 78 | } 79 | cat("\r", rep(" ", getOption("width")), 80 | "\r", sep = "") 81 | cat("\n
\n
\n", file = htmlfile, append = TRUE) 82 | .html.end(htmlfile) 83 | full.name.path <- paste("file://", htmlfile, sep = "") 84 | #browseURL(full.name.path) 85 | invisible(full.name.path) 86 | } 87 | 88 | environment(mcmcplot_country) <- environment(mcmcplot) 89 | 90 | -------------------------------------------------------------------------------- /R/STAN/template_cases_BR.R: -------------------------------------------------------------------------------- 1 | rm(list=ls()) 2 | setwd("/home/marcosop/Covid/R/STAN") 3 | 4 | ################################################################### 5 | ### Packages 6 | ################################################################### 7 | library(PandemicLP) 8 | library(foreach) 9 | library(doMC) 10 | library(covid19br) 11 | library(dplyr) 12 | library(zoo) 13 | source("utils.R") 14 | 15 | Sys.setenv(LANGUAGE='en') 16 | rstan_options(auto_write = TRUE) 17 | 18 | ################################################################### 19 | ### Data sets: https://github.com/CSSEGISandData 20 | ################################################################### 21 | covid19 <- downloadCovid19(level = "states") %>% 22 | select(date,n=accumCases,d=accumDeaths,n_new=newCases, d_new=newDeaths,state) %>% 23 | arrange(state,date) 24 | 25 | uf <- distinct(covid19,state) 26 | 27 | br_pop <- read.csv("../pop/pop_BR.csv") 28 | 29 | 30 | state_list <- _statelist_ 31 | 32 | #register cores 33 | #registerDoMC(cores = detectCores()-1) # Alternativa Linux 34 | #registerDoMC(cores = 5) # Alternativa Linux 35 | registerDoMC(cores = min(63,length(state_list))) # Alternativa Linux 36 | 37 | obj <- foreach(s = 1:length(state_list)) %dopar% { 38 | 39 | estado <- state_list[s] 40 | data <- covid19 %>% filter(state== estado) %>% 41 | select(date=date, cases=n, deaths=d, new_cases=n_new, new_deaths=d_new,-state) 42 | 43 | #remove duplicated data 44 | {if(sum(duplicated(data$date)) > 0){ 45 | data <- data[-which(duplicated(data$date)),] 46 | }} 47 | 48 | while(any(data$new_cases <0)){ 49 | pos <- which(data$new_cases <0) 50 | for(j in pos){ 51 | data$new_cases[j-1] = data$new_cases[j] + data$new_cases[j-1] 52 | data$new_cases[j] = 0 53 | } 54 | } 55 | 56 | pop <- br_pop$pop[which(br_pop$uf == estado)] 57 | names <- paste("Brazil",estado,sep="_") 58 | 59 | covid_state <- list(data=as.data.frame(data), name = names, population = pop) 60 | 61 | nwaves = _nwaves_ 62 | 63 | nom <- c("date","n","d","n_new","d_new") 64 | results_directory = "/home/marcosop/Covid/chains/" 65 | file_id <- paste0(state_list[s],'_',nom[2],'e') 66 | old <- readRDS(paste0(results_directory,file_id,'.rds')) 67 | 68 | mod <- pandemic_model(covid_state,case_type = "confirmed", p = 0.08, 69 | seasonal_effect=c("sunday","monday"),n_waves = nwaves, 70 | warmup = 10e3, thin = 3, sample_size = 1e3, 71 | init=old, covidLPconfig = FALSE) # run the model 72 | 73 | names(covid_state$data) <- nom 74 | 75 | pred <- posterior_predict(mod,horizonLong = 1000,horizonShort = 14) # do predictions 76 | 77 | stats <- pandemic_stats(pred) # calculate stats 78 | stats[[1]] <-NULL # removing the data (the app use the data coming from other object) 79 | names(stats) <- c("df_predict","lt_predict","lt_summary","mu_plot") 80 | 81 | names(stats$df_predict) <- c("date", "q25", "med", "q975", "m") 82 | names(stats$lt_predict) <- c("date", "q25", "med", "q975", "m") 83 | names(stats$lt_summary) <- c("NTC25","NTC500","NTC975","high.dat.low","high.dat.med","high.dat.upper","end.dat.low", 84 | "end.dat.med","end.dat.upper") 85 | 86 | #create flag 87 | flag <- try(classify.flag(covid_state$data[,c("date","n_new")],stats$mu_plot, rem_saz = TRUE)) 88 | 89 | if(class(flag)== "try-error") flag <- -1 90 | 91 | list_out <- list( df_predict = stats$df_predict, lt_predict=stats$lt_predict, lt_summary=stats$lt_summary, 92 | mu_plot = stats$mu_plot, residuals = cbind(mod$nominal_errors, mod$relative_errors), 93 | flag = flag) 94 | 95 | ### saveRDS 96 | results_directory = "/home/marcosop/Covid/app_COVID19/STpredictions/" 97 | file_id <- paste0(state_list[s],'_',colnames(covid_state$data)[2],'e') 98 | saveRDS(list_out, file=paste0(results_directory,'Brazil_',file_id,'.rds')) 99 | 100 | 101 | ### saveRDS - THE POSTERIOR PREDICT (posterior_predict object) 102 | results_directory = "/home/marcosop/TMP/STaux/" 103 | file_id <- paste0(state_list[s],'_posterior_predict_',colnames(covid_state$data)[2],'e') 104 | saveRDS(pred,file = paste0(results_directory,file_id,'.rds')) 105 | 106 | ### saveChain 107 | results_directory = "/home/marcosop/Covid/chains/" 108 | file_id <- paste0(state_list[s],'_',colnames(covid_state$data)[2],'e') 109 | saveRDS(mod, file=paste0(results_directory,file_id,'.rds')) 110 | } 111 | -------------------------------------------------------------------------------- /R/STAN/template_deaths_BR.R: -------------------------------------------------------------------------------- 1 | rm(list=ls()) 2 | setwd("/home/marcosop/Covid/R/STAN") 3 | 4 | ################################################################### 5 | ### Packages 6 | ################################################################### 7 | library(PandemicLP) 8 | library(foreach) 9 | library(doMC) 10 | library(covid19br) 11 | library(dplyr) 12 | library(zoo) 13 | source("utils.R") 14 | 15 | Sys.setenv(LANGUAGE='en') 16 | rstan_options(auto_write = TRUE) 17 | 18 | ################################################################### 19 | ### Data sets: https://github.com/CSSEGISandData 20 | ################################################################### 21 | covid19 <- downloadCovid19(level = "states") %>% 22 | select(date,n=accumCases,d=accumDeaths,n_new=newCases, d_new=newDeaths,state) %>% 23 | arrange(state,date) 24 | 25 | uf <- distinct(covid19,state) 26 | 27 | br_pop <- read.csv("../pop/pop_BR.csv") 28 | 29 | 30 | state_list <- _statelist_ 31 | 32 | #register cores 33 | #registerDoMC(cores = detectCores()-1) # Alternativa Linux 34 | #registerDoMC(cores = 15) # Alternativa Linux 35 | registerDoMC(cores = min(63,length(state_list))) # Alternativa Linux 36 | 37 | obj <- foreach(s = 1:length(state_list)) %dopar% { 38 | 39 | estado <- state_list[s] 40 | data <- covid19 %>% filter(state== estado) %>% 41 | select(date=date, cases=n, deaths=d, new_cases=n_new, new_deaths=d_new,-state) 42 | 43 | #remove duplicated data 44 | {if(sum(duplicated(data$date)) > 0){ 45 | data <- data[-which(duplicated(data$date)),] 46 | }} 47 | 48 | while(any(data$new_deaths <0)){ 49 | pos <- which(data$new_deaths <0) 50 | for(j in pos){ 51 | data$new_cases[j-1] = data$new_deaths[j] + data$new_deaths[j-1] 52 | data$new_deaths[j] = 0 53 | } 54 | } 55 | 56 | 57 | pop <- br_pop$pop[which(br_pop$uf == estado)] 58 | names <- paste("Brazil",estado,sep="_") 59 | 60 | covid_state <- list(data=as.data.frame(data), name = names, population = pop) 61 | 62 | nwaves = _nwaves_ 63 | 64 | nom <- c("date","n","d","n_new","d_new") 65 | results_directory = "/home/marcosop/Covid/chains/" 66 | file_id <- paste0(state_list[s],'_',nom[3],'e') 67 | old <- readRDS(paste0(results_directory,file_id,'.rds')) 68 | 69 | 70 | mod <- pandemic_model(covid_state,case_type = "deaths", p = 0.08*0.25, 71 | seasonal_effect=c("sunday","monday"),n_waves = nwaves, 72 | warmup = 10e3, thin = 3, sample_size = 1e3, 73 | init=old, covidLPconfig = FALSE) # run the model 74 | 75 | names(covid_state$data) <- nom 76 | 77 | pred <- posterior_predict(mod,horizonLong = 1000,horizonShort = 14) # do predictions 78 | 79 | stats <- pandemic_stats(pred) # calculate stats 80 | stats[[1]] <-NULL # removing the data (the app use the data coming from other object) 81 | names(stats) <- c("df_predict","lt_predict","lt_summary","mu_plot") 82 | 83 | names(stats$df_predict) <- c("date", "q25", "med", "q975", "m") 84 | names(stats$lt_predict) <- c("date", "q25", "med", "q975", "m") 85 | names(stats$lt_summary) <- c("NTC25","NTC500","NTC975","high.dat.low","high.dat.med","high.dat.upper","end.dat.low", 86 | "end.dat.med","end.dat.upper") 87 | 88 | #create flag 89 | flag <- try(classify.flag(covid_state$data[,c("date","d_new")],stats$mu_plot, rem_saz = TRUE)) 90 | 91 | if(class(flag)== "try-error") flag <- -1 92 | 93 | list_out <- list( df_predict = stats$df_predict, lt_predict=stats$lt_predict, lt_summary=stats$lt_summary, 94 | mu_plot = stats$mu_plot, residuals = cbind(mod$nominal_errors, mod$relative_errors), 95 | flag = flag) 96 | 97 | 98 | ### saveRDS 99 | results_directory = "/home/marcosop/Covid/app_COVID19/STpredictions/" 100 | file_id <- paste0(state_list[s],'_',colnames(covid_state$data)[3],'e') 101 | saveRDS(list_out, file=paste0(results_directory,'Brazil_',file_id,'.rds')) 102 | 103 | 104 | ### saveRDS - THE POSTERIOR PREDICT (posterior_predict object) 105 | results_directory = "/home/marcosop/TMP/STaux/" 106 | file_id <- paste0(state_list[s],'_posterior_predict_',colnames(covid_state$data)[3],'e') 107 | saveRDS(pred,file = paste0(results_directory,file_id,'.rds')) 108 | 109 | ### saveChain 110 | results_directory = "/home/marcosop/Covid/chains/" 111 | file_id <- paste0(state_list[s],'_',colnames(covid_state$data)[3],'e') 112 | saveRDS(mod, file=paste0(results_directory,file_id,'.rds')) 113 | 114 | } 115 | -------------------------------------------------------------------------------- /R/JAGS/predict_BR.R: -------------------------------------------------------------------------------- 1 | rm(list=ls()) 2 | 3 | setwd("/run/media/marcos/OS/UFMG/Pesquisa/Covid/R") 4 | 5 | ################################################################### 6 | ### Packages 7 | ################################################################### 8 | library(dplyr) 9 | library(tidyr) 10 | library("rjags") 11 | library(matrixStats) 12 | library(mcmcplots) 13 | 14 | 15 | 16 | ################################################################### 17 | ### Data sets: https://github.com/CSSEGISandData 18 | ################################################################### 19 | baseURLbr = "https://raw.githubusercontent.com/covid19br/covid19br.github.io/master/dados" 20 | 21 | covid19uf <- read.csv(file.path(baseURLbr,"EstadosCov19.csv"), check.names=FALSE, stringsAsFactors=FALSE) %>% 22 | rename(state = estado, 23 | date = data, 24 | n = casos.acumulados, 25 | d = obitos.acumulados, 26 | n_new = novos.casos, 27 | d_new = obitos.novos) %>% 28 | mutate(date = as.Date(date)) %>% 29 | select(date, n, d, n_new, d_new, state) %>% 30 | arrange(state,date) %>% filter(date>'2020-02-01') 31 | 32 | covid19br <- read.csv(file.path(baseURLbr,"BrasilCov19.csv"), check.names=FALSE, stringsAsFactors=FALSE) %>% 33 | mutate(state = 'BR') %>% 34 | rename(date = data, 35 | n = casos.acumulados, 36 | d = obitos.acumulados, 37 | n_new = novos.casos, 38 | d_new = obitos.novos) %>% 39 | mutate(date = as.Date(date)) %>% 40 | select(date, n, d, n_new, d_new, state) %>% 41 | arrange(date) %>% filter(date>'2020-02-01') 42 | 43 | covid19 <- bind_rows(covid19uf,covid19br) 44 | uf <- distinct(covid19,state) 45 | 46 | # class(covid19) 47 | # covid19 %>% tbl_df %>% print(n=Inf) 48 | 49 | ########################################################################### 50 | ###### JAGS 51 | ########################################################################### 52 | source("jags_poisson.R") 53 | i = 2 # (2: confirmed, 3: deaths) 54 | L = 200 55 | params = c("a","b","c","assint","yfut") 56 | 57 | for ( s in 1:dim(uf)[1] ) { 58 | 59 | #t0 = Sys.time() 60 | 61 | Y = covid19 %>% filter(state==uf$state[s]) 62 | t = dim(Y)[1] 63 | data_jags = list(y=Y[[i]], t=t, L=L) 64 | nc = 3 65 | ni = 5e4 66 | 67 | # set.seed(100) 68 | mod = jags.model(textConnection(mod_string), data=data_jags, n.chains=nc) 69 | update(mod, n.iter=5e3) 70 | mod_sim = try(coda.samples(model=mod, variable.names=params, n.iter=ni)) 71 | 72 | if(class(mod_sim) != "try-error"){ 73 | mod_chain = as.data.frame(do.call(rbind, mod_sim)) 74 | # names(mod_chain) 75 | 76 | npar = 4 77 | mod_chain_y = as.matrix(mod_chain %>% select(-names(mod_chain)[1:npar])) 78 | mod_chain_cumy = rowCumsums(mod_chain_y) + Y[[i]][t] 79 | 80 | 81 | ### list output 82 | L0 = 14 83 | df_predict <- data.frame( date = as.Date((max(Y$date)+1):(max(Y$date)+L0), origin="1970-01-01"), 84 | q25 = colQuantiles(mod_chain_cumy[,1:L0], prob=.025), 85 | med = colQuantiles(mod_chain_cumy[,1:L0], prob=.5), 86 | q975 = colQuantiles(mod_chain_cumy[,1:L0], prob=.975), 87 | m = colMeans(mod_chain_cumy[,1:L0])) 88 | row.names(df_predict) <- NULL 89 | 90 | list_out <- list( df_predict = df_predict ) 91 | 92 | 93 | ### saveRDS 94 | results_directory = "/run/media/marcos/OS/UFMG/Pesquisa/Covid/app_COVID19/STpredictions/" 95 | file_id <- ifelse(uf$state[s]=='BR', colnames(Y)[i] , paste0(uf$state[s],'_',colnames(Y)[i],'e')) 96 | saveRDS(list_out, file=paste0(results_directory,'Brazil_',file_id,'.rds')) 97 | 98 | 99 | ### report 100 | source("mcmcplot_country.R") 101 | report_directory = "/run/media/marcos/OS/UFMG/Pesquisa/Covid/app_COVID19/STpredictions/reports" 102 | #report_directory = 'C:/Users/ricar/Dropbox/covid19/R/predict/report' 103 | mcmcplot_country(mcmcout = mod_chain, parms = c("a", "b", "c", "assint"), 104 | dir = report_directory, 105 | filename = paste0('Brazil_',file_id,'_diagnostics'), 106 | heading = paste0('Brazil_',file_id), 107 | extension = "html", greek = TRUE, 108 | country = 'Brazil', 109 | type = file_id) 110 | 111 | 112 | ### run time 113 | #run_time = round(as.numeric(Sys.time()-t0, units="mins"),2) 114 | #print(noquote(paste(run_time, "minutes to", uf$state[s]))) 115 | } 116 | else print(paste0("ERROR:",country_name)) 117 | 118 | } 119 | 120 | 121 | -------------------------------------------------------------------------------- /app_v1/global.R: -------------------------------------------------------------------------------- 1 | ## Load packages 2 | library(dplyr) 3 | library(tidyr) 4 | library(httr) 5 | library(lubridate) 6 | library(knitr) 7 | library(shiny) 8 | library(shinyjs) 9 | library(plotly) 10 | library(shinythemes) 11 | library(shinycssloaders) 12 | library(markdown) 13 | library(shinyWidgets) 14 | library(shinyBS) 15 | 16 | ############################################################################## 17 | 18 | ## Define font to be used later 19 | f1 = list(family = "Arial", size = 10, color = "rgb(30,30,30)") 20 | 21 | ## Function to measure how old a file is 22 | minutesSinceLastUpdate = function(fileName) { 23 | (as.numeric(as.POSIXlt(Sys.time())) - as.numeric(file.info(fileName)$ctime)) / 60 24 | } 25 | 26 | ## Function to format the dates for better plotting 27 | printDate = function(date){ 28 | # paste0(day(date),"/",month(date, lab=T, locale="us")) 29 | monthsEn=c("Jan","Feb","Mar","Apr","May","Jun","Jul","Aug","Sep","Oct","Nov","Dec") 30 | paste0(day(date),"/",monthsEn[month(date)]) 31 | } 32 | 33 | ## colors for observed data 34 | blu = 'rgb(100,140,240)' 35 | dblu = 'rgb(0,0,102)' 36 | red = 'rgb(200,30,30)' 37 | dred = 'rgb(100,30,30)' 38 | 39 | ############################################################################## 40 | ## DATA SOURCES 41 | 42 | ## setup data source (Johns Hopkins)- GLOBAL 43 | baseURL = "https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series" 44 | 45 | ## Main function to load the data - GLOBAL 46 | loadData = function(fileName, columnName) { 47 | if(!file.exists(fileName) || 48 | minutesSinceLastUpdate(fileName) > 10) { 49 | data = read.csv(file.path(baseURL, fileName), 50 | check.names=FALSE, stringsAsFactors=FALSE) %>% 51 | select(-Lat, -Long) %>% 52 | pivot_longer(-(1:2), names_to="date", values_to=columnName)%>% 53 | mutate( 54 | date=as.Date(date, format="%m/%d/%y"), 55 | `Province/State`= 56 | if_else(`Province/State` == "", "", `Province/State`) 57 | ) 58 | save(data, file=fileName) 59 | } else { 60 | load(file=fileName) 61 | } 62 | return(data) 63 | } 64 | 65 | allData = loadData("time_series_covid19_confirmed_global.csv", "CumConfirmed") %>% 66 | inner_join( 67 | loadData("time_series_covid19_deaths_global.csv", "CumDeaths"), 68 | by = c("Province/State", "Country/Region", "date") 69 | ) # %>% 70 | # inner_join( 71 | # loadData("time_series_covid19_recovered_global.csv","CumRecovered")) 72 | 73 | ############################################################################## 74 | ## Setup data source (MSaude/BR)- BRAZIL 75 | # baseURL.BR = "https://raw.githubusercontent.com/belisards/coronabr/master/dados" 76 | # baseURL.BR = "https://covid.saude.gov.br/assets/files/COVID19_" 77 | baseURL.BR = "https://raw.githubusercontent.com/covid19br/covid19br.github.io/master/dados" 78 | 79 | ## Function to load data - BRAZIL 80 | loadData.BR = function(fileName) { 81 | if(!file.exists(fileName) || minutesSinceLastUpdate(fileName) > 10) { 82 | data = read.csv(file.path(baseURL.BR, fileName), 83 | check.names=FALSE, stringsAsFactors=FALSE) %>% 84 | # select(-c(1,3:8,10:11,14)) %>% # remove unwanted columns 85 | select(-c(1,4,6)) %>% 86 | as_tibble() %>% 87 | mutate(date = as.Date(data) 88 | # date=as.Date(date), # format dates 89 | # `CumRecovered` = NA 90 | ) %>% 91 | rename(`Province/State` = estado, # rename some variables 92 | `CumConfirmed` = casos.acumulados, 93 | `CumDeaths` = obitos.acumulados 94 | ) %>% 95 | select(-2) 96 | # browser() 97 | save(data, file=fileName) 98 | } else { 99 | load(file=fileName) 100 | } 101 | 102 | return(data) 103 | } 104 | 105 | # brData = loadData.BR("corona_brasil.csv") 106 | brData = loadData.BR("EstadosCov19.csv") 107 | 108 | ############################################################################## 109 | ## LOAD PREDICTION RESULTS 110 | 111 | ## Function to return list of countries with available data on github 112 | readfiles.repo <- function() { 113 | req <- GET("https://api.github.com/repos/thaispaiva/app_COVID19/git/trees/master?recursive=1") 114 | stop_for_status(req) 115 | # extract list of files on github 116 | filelist <- unlist(lapply(content(req)$tree, "[", "path"), use.names = F) 117 | files <- grep("STpredictions/", filelist, value = TRUE, fixed = TRUE) 118 | files <- unlist(lapply(strsplit(files,"/"),"[",2)) 119 | files <- grep(".rds",files, value=TRUE) 120 | 121 | return(files) 122 | } 123 | 124 | files = readfiles.repo() # get available results 125 | aux = sub('\\_n.rds$', '', sub('\\_d.rds$', '', files)) 126 | 127 | ############################################## 128 | ## List of countries for SHORT TERM prediction 129 | countries_STpred = sort(unique( # country names without space 130 | unlist(lapply(strsplit(aux,"_"), function(x) x[1])))) 131 | countries_STpred_orig = gsub("-"," ", countries_STpred) # country names with space (original) 132 | 133 | ## List of Brazil's states 134 | statesBR_STpred = unique( 135 | unlist(lapply(strsplit(aux,"_"), function(x) if(x[1]=="Brazil") return(x[2]) ))) 136 | statesBR_STpred[is.na(statesBR_STpred)] = "" 137 | statesBR_STpred = sort(statesBR_STpred) 138 | 139 | ############################################# 140 | ## List of countries for LONG TERM prediction 141 | countries_LTpred_orig = countries_STpred_orig 142 | 143 | ## List of Brazil's states - LONG TERM 144 | statesBR_LTpred = statesBR_STpred 145 | 146 | ## Read RDS files from github repository 147 | githubURL = "https://github.com/thaispaiva/app_COVID19/raw/master/STpredictions" 148 | -------------------------------------------------------------------------------- /R/STAN/utils.R: -------------------------------------------------------------------------------- 1 | classify.flag = function(obs, adj, rem_saz = FALSE){ 2 | 3 | colnames(obs) = c("date", "y") 4 | nn = nrow(obs) 5 | 6 | if(rem_saz){ 7 | 8 | dados.aux = suppressMessages(full_join(obs, adj) %>% 9 | mutate(week_days = weekdays(as.Date(date))) %>% 10 | filter(!(week_days == "domingo" | week_days == "segunda-feira")) %>% 11 | mutate(y_s = rollmean(y, k = 20, fill = NA) %>% rollmean(k = 10, fill = NA), # suavizando os dados 12 | dif_s = c(NA, y_s %>% diff()) %>% rollmean(k = 50, fill = NA), # diferen?a suavizada 13 | s1 = dif_s >= 0, 14 | s2 = dif_s < 0, 15 | id = c(NA, diff(s1 - s2)) )) 16 | 17 | } else{ 18 | 19 | dados.aux = suppressMessages(full_join(obs, adj) %>% 20 | mutate(y_s = rollmean(y, k = 20, fill = NA) %>% rollmean(k = 10, fill = NA), # suavizando os dados 21 | dif_s = c(NA, y_s %>% diff()) %>% rollmean(k = 50, fill = NA), # diferen?a suavizada 22 | s1 = dif_s >= 0, 23 | s2 = dif_s < 0, 24 | id = c(NA, diff(s1 - s2)) )) 25 | 26 | } 27 | 28 | maxx = max(dados.aux$y_s, na.rm = TRUE) 29 | 30 | aux = dados.aux %>% filter(id == 2 |id == -2) %>% arrange(desc(date)) 31 | 32 | if(aux$id[1] == -2){ # se o ?ltimo ponto identificado ? um pico, a amplitude ? calculada com base na ?ltima observa??o do y suavizado 33 | aux = rbind(tail(dados.aux %>% filter(!is.na(y_s)), 1) %>% mutate(id = 2), aux) 34 | } 35 | 36 | est = aux %>% mutate(amp_y = c(NA, diff(y_s)), 37 | amp_mu = c(NA, diff(mu)), 38 | id_df = c(NA, diff(id)), 39 | est = (amp_y - amp_mu)^2/maxx^2) %>% 40 | filter(id_df == -4) # amplitudes corretas 41 | 42 | est1 = (est %>% summarise(crit = sum(est)))$crit 43 | 44 | est1 45 | 46 | } 47 | 48 | classify.flag.old = function(obs, adj){ 49 | 50 | colnames(obs) = c("date", "y") 51 | 52 | dados.aux = suppressMessages(full_join(obs, adj) %>% 53 | mutate(y_s = rollmean(y, k = 20, fill = NA) %>% rollmean(k = 10, fill = NA), # suavizando os dados 54 | dif_s = c(NA, y_s %>% diff()) %>% rollmean(k = 50, fill = NA), # diferença suavizada 55 | id = c(NA, dif_s %>% sign() %>% diff()) ) ) # identificador de mudança de comportamento 56 | 57 | maxx = max(dados.aux$y_s, na.rm = TRUE) 58 | 59 | aux = dados.aux %>% filter(id == 2 |id == -2) %>% arrange(desc(date)) 60 | 61 | if(aux$id[1] == -2){ # se o último ponto identificado é um pico, a amplitude é calculada com base na última observação do y suavizado 62 | aux = rbind(tail(dados.aux %>% filter(!is.na(y_s)), 1) %>% mutate(id = 2), aux) 63 | } 64 | 65 | est = aux %>% mutate(amp_y = c(NA, diff(y_s)), 66 | amp_mu = c(NA, diff(mu)), 67 | id_df = c(NA, diff(id)), 68 | est = (amp_y - amp_mu)^2/maxx^2) %>% 69 | filter(id_df == -4) # amplitudes corretas 70 | 71 | est1 = (est %>% summarise(crit = sum(est)))$crit 72 | 73 | est1 74 | 75 | } 76 | 77 | classify.flag.old2 = function(obs, adj){ 78 | 79 | colnames(obs) = c("date", "y") 80 | 81 | dados = full_join(obs, adj) %>% mutate(y_s = rollmean(y, k = 20, fill = NA) %>% rollmean(k = 10, fill = NA), # suavizando os dados 82 | dif_s = c(NA, y_s %>% diff()) %>% rollmean(k = 50, fill = NA), # diferença suavizada 83 | id = c(NA, dif_s %>% sign() %>% diff()) ) # identificador de mudança de comportamento 84 | 85 | aux = dados %>% filter(id == 2 |id == -2) %>% arrange(desc(date)) 86 | 87 | if(aux$id[1] == -2){ # se o último ponto identificado é um pico, a amplitude é calculada com base na última observação do y suavizado 88 | aux = rbind(tail(dados %>% filter(!is.na(y_s)), 1) %>% mutate(id = 2), aux) 89 | } 90 | 91 | est = (aux %>% mutate(amp_y = c(NA, diff(y_s)), 92 | amp_mu = c(NA, diff(mu)), 93 | id_df = c(NA, diff(id)), 94 | est = (amp_y - amp_mu)^2/max(y_s)^2) %>% 95 | filter(id_df == -4) %>% # amplitudes corretas 96 | summarise(crit = sum(est)))$crit 97 | 98 | #ifelse(est <= 0.2, 0, ifelse(est <= 0.5, 1, 2)) 99 | est 100 | } 101 | 102 | nwaves <- function(country = TRUE, new_cases = TRUE){ 103 | 104 | country_name = c("Argentina", "Australia", "Belgium", "Bolivia", "Canada", "Chile", "China", "Colombia", "Costa Rica", "Ecuador", "Ethiopia", "France", "Germany", "Greece", "Guatemala", "Honduras", "India", "Indonesia", "Iraq", "Ireland", "Italy", "Japan", "South Korea", "Mexico", "Morocco", "Netherlands", "New Zealand", "Norway", "Panama", "Paraguay", "Peru", "Poland", "Portugal", "Romania", "Russia", "Saudi Arabia", "South Africa", "Spain", "Sweden", "Switzerland", "Turkey", "Ukraine", "United Kingdom", "Uruguay", "United States of America", "Venezuela") 105 | state_name = c("AC", "AL", "AM", "AP", "BA", "CE", "DF", "ES", "GO", "MA", "MG", "MS", "MT", "PA", "PB", "PE", "PI", "PR", "RJ", "RN", "RO", "RR", "RS", "SC", "SE", "SP", "TO") 106 | 107 | if(country){ 108 | 109 | data = apply(matrix(country_name), 1, load_covid) 110 | 111 | if(new_cases){ 112 | 113 | npeaks = data %>% lapply(function(x) x$data$new_cases) %>% 114 | lapply(function(x) nrow(findpeaks(x, minpeakdistance = 95))) 115 | 116 | } else{ 117 | 118 | npeaks = data %>% lapply(function(x) x$data$new_deaths) %>% 119 | lapply(function(x) nrow(findpeaks(x, minpeakdistance = 95))) 120 | 121 | } 122 | 123 | waves = npeaks %>% unlist 124 | nwaves = waves %>% unique %>% sort 125 | 126 | country_list = list() 127 | for(i in 1:length(nwaves)){ 128 | pos = which(waves == nwaves[i]) 129 | country_list[[i]] = country_name[pos] 130 | } 131 | names(country_list) = paste("wave", nwaves, sep = "") 132 | 133 | final_list = list(nwaves = nwaves, country_list = country_list) 134 | 135 | } else{ # states 136 | 137 | data = apply(matrix(state_name), 1, function(x) load_covid("Brazil", x)) 138 | 139 | if(new_cases){ 140 | 141 | npeaks = data %>% lapply(function(x) x$data$new_cases) %>% 142 | lapply(function(x) nrow(findpeaks(x, minpeakdistance = 95))) 143 | 144 | } else{ 145 | 146 | npeaks = data %>% lapply(function(x) x$data$new_deaths) %>% 147 | lapply(function(x) nrow(findpeaks(x, minpeakdistance = 95))) 148 | 149 | } 150 | 151 | waves = npeaks %>% unlist 152 | nwaves = waves %>% unique %>% sort 153 | 154 | state_list = list() 155 | for(i in 1:length(nwaves)){ 156 | pos = which(waves == nwaves[i]) 157 | state_list[[i]] = state_name[pos] 158 | } 159 | names(state_list) = paste("wave", nwaves, sep = "") 160 | 161 | final_list = list(nwaves = nwaves, state_list = state_list) 162 | 163 | } 164 | 165 | final_list 166 | 167 | } 168 | -------------------------------------------------------------------------------- /R/pop/pop_WR.csv: -------------------------------------------------------------------------------- 1 | country,code,pop 2 | Aruba,ABW,105845 3 | Afghanistan,AFG,37172386 4 | Angola,AGO,30809762 5 | Albania,ALB,2866376 6 | Andorra,AND,77006 7 | Arab World,ARB,419790588 8 | United Arab Emirates,ARE,9630959 9 | Argentina,ARG,44494502 10 | Armenia,ARM,2951776 11 | American Samoa,ASM,55465 12 | Antigua and Barbuda,ATG,96286 13 | Australia,AUS,24982688 14 | Austria,AUT,8840521 15 | Azerbaijan,AZE,9939800 16 | Burundi,BDI,11175378 17 | Belgium,BEL,11433256 18 | Benin,BEN,11485048 19 | Burkina Faso,BFA,19751535 20 | Bangladesh,BGD,161356039 21 | Bulgaria,BGR,7025037 22 | Bahrain,BHR,1569439 23 | Bahamas,BHS,385640 24 | Bosnia and Herzegovina,BIH,3323929 25 | Belarus,BLR,9483499 26 | Belize,BLZ,383071 27 | Bermuda,BMU,63973 28 | Bolivia,BOL,11353142 29 | Brazil,BRA,209469333 30 | Barbados,BRB,286641 31 | Brunei,BRN,428962 32 | Bhutan,BTN,754394 33 | Botswana,BWA,2254126 34 | Central African Republic,CAF,4666377 35 | Canada,CAN,37057765 36 | Central Europe and the Baltics,CEB,102511922 37 | Switzerland,CHE,8513227 38 | Channel Islands,CHI,170499 39 | Chile,CHL,18729160 40 | China,CHN,1392730000 41 | Cote d'Ivoire,CIV,25069229 42 | Cameroon,CMR,25216237 43 | Congo (Kinshasa),COD,84068091 44 | Congo (Brazzaville),COG,5244363 45 | Colombia,COL,49648685 46 | Comoros,COM,832322 47 | Cabo Verde,CPV,543767 48 | Costa Rica,CRI,4999441 49 | Caribbean small states,CSS,7358965 50 | Cuba,CUB,11338138 51 | Curacao,CUW,159800 52 | Cayman Islands,CYM,64174 53 | Cyprus,CYP,1189265 54 | Czechia,CZE,10629928 55 | Germany,DEU,82905782 56 | Djibouti,DJI,958920 57 | Dominica,DMA,71625 58 | Denmark,DNK,5793636 59 | Dominican Republic,DOM,10627165 60 | Algeria,DZA,42228429 61 | East Asia & Pacific (excluding high income),EAP,2081651801 62 | Early-demographic dividend,EAR,3249140605 63 | East Asia & Pacific,EAS,2328220870 64 | Europe & Central Asia (excluding high income),ECA,417797257 65 | Europe & Central Asia,ECS,918793590 66 | Ecuador,ECU,17084357 67 | Egypt,EGY,98423595 68 | Euro area,EMU,341783171 69 | Eritrea,ERI, 70 | Spain,ESP,46796540 71 | Estonia,EST,1321977 72 | Ethiopia,ETH,109224559 73 | European Union,EUU,446786293 74 | Fragile and conflict affected situations,FCS,743958386 75 | Finland,FIN,5515525 76 | Fiji,FJI,883483 77 | France,FRA,66977107 78 | Faroe Islands,FRO,48497 79 | Micronesia; Fed. Sts.,FSM,112640 80 | Gabon,GAB,2119275 81 | United Kingdom,GBR,66460344 82 | Georgia,GEO,3726549 83 | Ghana,GHA,29767108 84 | Gibraltar,GIB,33718 85 | Guinea,GIN,12414318 86 | Gambia,GMB,2280102 87 | Guinea-Bissau,GNB,1874309 88 | Equatorial Guinea,GNQ,1308974 89 | Greece,GRC,10731726 90 | Grenada,GRD,111454 91 | Greenland,GRL,56025 92 | Guatemala,GTM,17247807 93 | Guam,GUM,165768 94 | Guyana,GUY,779004 95 | High income,HIC,1210312147 96 | Hong Kong SAR; China,HKG,7451000 97 | Honduras,HND,9587522 98 | Heavily indebted poor countries (HIPC),HPC,780234406 99 | Croatia,HRV,4087843 100 | Haiti,HTI,11123176 101 | Hungary,HUN,9775564 102 | IBRD only,IBD,4772284113 103 | IDA & IBRD total,IBT,6412522234 104 | IDA total,IDA,1640238121 105 | IDA blend,IDB,555830605 106 | Indonesia,IDN,267663435 107 | IDA only,IDX,1084407516 108 | Isle of Man,IMN,84077 109 | India,IND,1352617328 110 | Not classified,INX, 111 | Ireland,IRL,4867309 112 | Iran,IRN,81800269 113 | Iraq,IRQ,38433600 114 | Iceland,ISL,352721 115 | Israel,ISR,8882800 116 | Italy,ITA,60421760 117 | Jamaica,JAM,2934855 118 | Jordan,JOR,9956011 119 | Japan,JPN,126529100 120 | Kazakhstan,KAZ,18272430 121 | Kenya,KEN,51393010 122 | Kyrgyzstan,KGZ,6322800 123 | Cambodia,KHM,16249798 124 | Kiribati,KIR,115847 125 | Saint Kitts and Nevis,KNA,52441 126 | "Korea, South",KOR,51606633 127 | Kuwait,KWT,4137309 128 | Latin America & Caribbean (excluding high income),LAC,609013934 129 | Laos,LAO,7061507 130 | Lebanon,LBN,6848925 131 | Liberia,LBR,4818977 132 | Libya,LBY,6678567 133 | Saint Lucia,LCA,181889 134 | Latin America & Caribbean,LCN,641357515 135 | Least developed countries: UN classification,LDC,1009662578 136 | Low income,LIC,705417321 137 | Liechtenstein,LIE,37910 138 | Sri Lanka,LKA,21670000 139 | Lower middle income,LMC,3022905169 140 | Low & middle income,LMY,6383958209 141 | Lesotho,LSO,2108132 142 | Late-demographic dividend,LTE,2288665963 143 | Lithuania,LTU,2801543 144 | Luxembourg,LUX,607950 145 | Latvia,LVA,1927174 146 | Macao SAR; China,MAC,631636 147 | St. Martin (French part),MAF,37264 148 | Morocco,MAR,36029138 149 | Monaco,MCO,38682 150 | Moldova,MDA,2706049 151 | Madagascar,MDG,26262368 152 | Maldives,MDV,515696 153 | Middle East & North Africa,MEA,448912859 154 | Mexico,MEX,126190788 155 | Marshall Islands,MHL,58413 156 | Middle income,MIC,5678540888 157 | North Macedonia,MKD,2082958 158 | Mali,MLI,19077690 159 | Malta,MLT,484630 160 | Burma,MMR,53708395 161 | Middle East & North Africa (excluding high income),MNA,382896715 162 | Montenegro,MNE,622227 163 | Mongolia,MNG,3170208 164 | Northern Mariana Islands,MNP,56882 165 | Mozambique,MOZ,29495962 166 | Mauritania,MRT,4403319 167 | Mauritius,MUS,1265303 168 | Malawi,MWI,18143315 169 | Malaysia,MYS,31528585 170 | North America,NAC,364290258 171 | Namibia,NAM,2448255 172 | New Caledonia,NCL,284060 173 | Niger,NER,22442948 174 | Nigeria,NGA,195874740 175 | Nicaragua,NIC,6465513 176 | Netherlands,NLD,17231624 177 | Norway,NOR,5311916 178 | Nepal,NPL,28087871 179 | Nauru,NRU,12704 180 | New Zealand,NZL,4841000 181 | OECD members,OED,1303529456 182 | Oman,OMN,4829483 183 | Other small states,OSS,30758989 184 | Pakistan,PAK,212215030 185 | Panama,PAN,4176873 186 | Peru,PER,31989256 187 | Philippines,PHL,106651922 188 | Palau,PLW,17907 189 | Papua New Guinea,PNG,8606316 190 | Poland,POL,37974750 191 | Pre-demographic dividend,PRE,919485393 192 | Puerto Rico,PRI,3195153 193 | Korea; Dem. People’s Rep.,PRK,25549819 194 | Portugal,PRT,10283822 195 | Paraguay,PRY,6956071 196 | West Bank and Gaza,PSE,4569087 197 | Pacific island small states,PSS,2457367 198 | Post-demographic dividend,PST,1109997273 199 | French Polynesia,PYF,277679 200 | Qatar,QAT,2781677 201 | Romania,ROU,19466145 202 | Russia,RUS,144478050 203 | Rwanda,RWA,12301939 204 | South Asia,SAS,1814388744 205 | Saudi Arabia,SAU,33699947 206 | Sudan,SDN,41801533 207 | Senegal,SEN,15854360 208 | Singapore,SGP,5638676 209 | Solomon Islands,SLB,652858 210 | Sierra Leone,SLE,7650154 211 | El Salvador,SLV,6420744 212 | San Marino,SMR,33785 213 | Somalia,SOM,15008154 214 | Serbia,SRB,6982604 215 | Sub-Saharan Africa (excluding high income),SSA,1078209758 216 | South Sudan,SSD,10975920 217 | Sub-Saharan Africa,SSF,1078306520 218 | Small states,SST,40575321 219 | Sao Tome and Principe,STP,211028 220 | Suriname,SUR,575991 221 | Slovakia,SVK,5446771 222 | Slovenia,SVN,2073894 223 | Sweden,SWE,10175214 224 | Eswatini,SWZ,1136191 225 | Sint Maarten (Dutch part),SXM,40654 226 | Seychelles,SYC,96762 227 | Syria,SYR,16906283 228 | Turks and Caicos Islands,TCA,37665 229 | Chad,TCD,15477751 230 | East Asia & Pacific (IDA & IBRD countries),TEA,2056064424 231 | Europe & Central Asia (IDA & IBRD countries),TEC,459865205 232 | Togo,TGO,7889094 233 | Thailand,THA,69428524 234 | Tajikistan,TJK,9100837 235 | Turkmenistan,TKM,5850908 236 | Latin America & the Caribbean (IDA & IBRD countries),TLA,625569713 237 | Timor-Leste,TLS,1267972 238 | Middle East & North Africa (IDA & IBRD countries),TMN,378327628 239 | Tonga,TON,103197 240 | South Asia (IDA & IBRD),TSA,1814388744 241 | Sub-Saharan Africa (IDA & IBRD countries),TSS,1078306520 242 | Trinidad and Tobago,TTO,1389858 243 | Tunisia,TUN,11565204 244 | Turkey,TUR,82319724 245 | Tuvalu,TUV,11508 246 | Tanzania,TZA,56318348 247 | Uganda,UGA,42723139 248 | Ukraine,UKR,44622516 249 | Upper middle income,UMC,2655635719 250 | Uruguay,URY,3449299 251 | US,USA,326687501 252 | Uzbekistan,UZB,32955400 253 | Saint Vincent and the Grenadines,VCT,110210 254 | Venezuela,VEN,28870195 255 | British Virgin Islands,VGB,29802 256 | Virgin Islands (U.S.),VIR,106977 257 | Vietnam,VNM,95540395 258 | Vanuatu,VUT,292680 259 | World,WLD,7594270356 260 | Samoa,WSM,196130 261 | Kosovo,XKX,1845300 262 | Yemen,YEM,28498687 263 | South Africa,ZAF,57779622 264 | Zambia,ZMB,17351822 265 | Zimbabwe,ZWE,14439018 266 | -------------------------------------------------------------------------------- /R/JAGS/death_BR_par.R: -------------------------------------------------------------------------------- 1 | rm(list=ls()) 2 | 3 | setwd("/run/media/marcos/OS/UFMG/Pesquisa/Covid/R/JAGS") 4 | 5 | ################################################################### 6 | ### Packages 7 | ################################################################### 8 | library(dplyr) 9 | library(tidyr) 10 | library("rjags") 11 | library(matrixStats) 12 | library(mcmcplots) 13 | library(foreach) 14 | library(doMC) 15 | ################################################################### 16 | ### Data sets: https://github.com/CSSEGISandData 17 | ################################################################### 18 | baseURLbr = "https://raw.githubusercontent.com/covid19br/covid19br.github.io/master/dados" 19 | 20 | covid19uf <- read.csv(file.path(baseURLbr,"EstadosCov19.csv"), check.names=FALSE, stringsAsFactors=FALSE) %>% 21 | rename(state = estado, 22 | date = data, 23 | n = casos.acumulados, 24 | d = obitos.acumulados, 25 | n_new = novos.casos, 26 | d_new = obitos.novos) %>% 27 | mutate(date = as.Date(date)) %>% 28 | select(date, n, d, -n_new, -d_new, state) %>% 29 | arrange(state,date) %>% filter(date>='2020-01-23') 30 | 31 | covid19br <- read.csv(file.path(baseURLbr,"BrasilCov19.csv"), check.names=FALSE, stringsAsFactors=FALSE) %>% 32 | mutate(state = 'BR') %>% 33 | rename(date = data, 34 | n = casos.acumulados, 35 | d = obitos.acumulados, 36 | n_new = novos.casos, 37 | d_new = obitos.novos) %>% 38 | mutate(date = as.Date(date)) %>% 39 | select(date, n, d, -n_new, -d_new, state) %>% 40 | arrange(date) %>% filter(date>='2020-01-23') 41 | 42 | covid19 <- bind_rows(covid19uf,covid19br) 43 | uf <- distinct(covid19,state) 44 | 45 | br_pop <- read.csv("../pop/pop_BR.csv") 46 | 47 | ########################################################################### 48 | ###### JAGS 49 | ########################################################################### 50 | #register cores 51 | registerDoMC(cores = detectCores()-1) # Alternativa Linux 52 | 53 | #for ( s in 1:dim(uf)[1] ) { 54 | obj <- foreach( s = 1:dim(uf)[1] ) %dopar% { 55 | #obj <- foreach( s = 1:3 ) %dopar% { 56 | source("jags_poisson.R") 57 | 58 | i = 5 # (2: confirmed, 3: deaths, 4: new confirmed, 5: new deaths) 59 | L = 300 60 | #t0 = Sys.time() 61 | estado = uf$state[s] 62 | 63 | Y <- covid19 %>% filter(state==estado) %>% 64 | mutate(n_new = n - lag(n, default=0), 65 | d_new = d - lag(d, default=0)) %>% 66 | select(date, n, d, n_new, d_new, state) %>% 67 | arrange(date) %>% filter(date>='2020-01-23') 68 | 69 | #Y = covid19 %>% filter(state==uf$state[s]) 70 | 71 | while(any(Y$d_new <0)){ 72 | pos <- which(Y$d_new <0) 73 | for(j in pos){ 74 | Y$d_new[j-1] = Y$d_new[j] + Y$d_new[j-1] 75 | Y$d_new[j] = 0 76 | Y$d[j-1] = Y$d[j] 77 | } 78 | } 79 | 80 | pop <- br_pop$pop[which(br_pop$uf == uf$state[s])] 81 | 82 | t = dim(Y)[1] 83 | 84 | #use static to provide initial values 85 | params = c("a","b","c","f","yfut","mu") 86 | nc = 1 # 3 87 | nb = 90e3 # 5e4 88 | thin = 10 89 | ni = 10e3 # 5e4 90 | data_jags = list(y=Y[[i]], t=t, L=L) 91 | mod = try(jags.model(textConnection(mod_string_new), data=data_jags, n.chains=nc, n.adapt=nb, quiet=TRUE)) 92 | try(update(mod, n.iter=ni, progress.bar="none")) 93 | mod_sim = try(coda.samples(model=mod, variable.names=params, n.iter=ni, thin=thin,progress.bar="none")) 94 | 95 | if(class(mod_sim) != "try-error" && class(mod) != "try-error"){ 96 | 97 | mod_chain = as.data.frame(do.call(rbind, mod_sim)) 98 | 99 | a_pos = "a" 100 | b_pos = "b" 101 | c_pos = "c" 102 | f_pos = "f" 103 | mu_pos = paste0("mu[",1:(t+L),"]") 104 | yfut_pos = paste0("yfut[",1:L,"]") 105 | L0 = 14 106 | 107 | mod_chain_y = as.matrix(mod_chain[yfut_pos]) 108 | mod_chain_cumy = rowCumsums(mod_chain_y) + Y[[3]][t] 109 | 110 | 111 | ### list output 112 | df_predict <- data.frame( date = as.Date((max(Y$date)+1):(max(Y$date)+L0), origin="1970-01-01"), 113 | q25 = colQuantiles(mod_chain_cumy[,1:L0], prob=.025), 114 | med = colQuantiles(mod_chain_cumy[,1:L0], prob=.5), 115 | q975 = colQuantiles(mod_chain_cumy[,1:L0], prob=.975), 116 | m = colMeans(mod_chain_cumy[,1:L0])) 117 | row.names(df_predict) <- NULL 118 | 119 | lt_predict <- lt_summary <- NULL 120 | 121 | #longterm 122 | L0 = 200 123 | 124 | #acha a curva de quantil 125 | lowquant <- colQuantiles(mod_chain_y[,1:L0], prob=.025) 126 | medquant <- colQuantiles(mod_chain_y[,1:L0], prob=.5) 127 | highquant <- colQuantiles(mod_chain_y[,1:L0], prob=.975) 128 | 129 | NTC25 =sum(lowquant)+Y[[3]][t] 130 | NTC500=sum(medquant)+Y[[3]][t] 131 | NTC975=sum(highquant)+Y[[3]][t] 132 | 133 | 134 | ##flag 135 | cm <- pop * 0.025 * 0.12 136 | ch <- pop * 0.03 * 0.15 137 | flag <- 0 #tudo bem 138 | {if(NTC500 > cm) flag <- 2 #nao plotar 139 | else{if(NTC975 > ch){flag <- 1; NTC25 <- NTC975 <- NULL}}} #plotar so mediana 140 | 141 | #vetor de data futuras e pega a posicao do maximo do percentil 25. 142 | dat.vec <- as.Date((max(Y$date)+1):(max(Y$date)+L0), origin="1970-01-01") 143 | dat.full <- c(Y[[1]],dat.vec) 144 | 145 | 146 | Dat25 <- Dat500 <- Dat975 <- NULL 147 | dat.low.end <- dat.med.end <- dat.high.end <- NULL 148 | 149 | mod_chain_mu = as.matrix(mod_chain[mu_pos]) 150 | mu50 <- apply(mod_chain_mu,2,quantile, probs=0.5) 151 | Dat500 <- dat.full[which.max(mu50[1:(t+L0)])] 152 | 153 | q <- .99 154 | med.cum <- c(medquant[1]+Y[[3]][t],medquant[2:length(medquant)]) 155 | med.cum <- colCumsums(as.matrix(med.cum)) 156 | med.cum <- med.cum/med.cum[length(med.cum)] 157 | med.end <- which(med.cum - q > 0)[1] 158 | dat.med.end <- dat.vec[med.end] 159 | 160 | if(flag == 0){ 161 | #definicao do pico usando a curva das medias 162 | mu25 <- apply(mod_chain_mu,2,quantile, probs=0.025) 163 | mu975 <- apply(mod_chain_mu,2,quantile, probs=.975) 164 | 165 | posMax.q25 <- which.max(mu25[1:(t+L0)]) 166 | aux <- mu975 - mu25[posMax.q25] 167 | aux2 <- aux[posMax.q25:(t+L0)] 168 | val <- min(aux2[aux2>0]) 169 | dat.max <- which(aux == val) 170 | 171 | aux <- mu975 - mu25[posMax.q25] 172 | aux2 <- aux[1:posMax.q25] 173 | val <- min(aux2[aux2>0]) 174 | dat.min <- which(aux == val) 175 | 176 | Dat25 <- dat.full[dat.min] 177 | Dat975 <- dat.full[dat.max] 178 | 179 | #calcula o fim da pandemia 180 | low.cum <- c(lowquant[1]+Y[[3]][t],lowquant[2:length(lowquant)]) 181 | low.cum <- colCumsums(as.matrix(low.cum)) 182 | low.cum <- low.cum/low.cum[length(low.cum)] 183 | low.end <- which(low.cum - q > 0)[1] 184 | dat.low.end <- dat.vec[low.end] 185 | 186 | high.cum <- c(highquant[1]+Y[[3]][t],highquant[2:length(highquant)]) 187 | high.cum <- colCumsums(as.matrix(high.cum)) 188 | high.cum <- high.cum/high.cum[length(high.cum)] 189 | high.end <- which(high.cum - q > 0)[1] 190 | dat.high.end <- dat.vec[high.end] 191 | } 192 | 193 | lt_predict <- data.frame( date = dat.vec, 194 | q25 = lowquant, 195 | med = medquant, 196 | q975 = highquant, 197 | m = colMeans(mod_chain_y[,1:L0])) 198 | row.names(lt_predict) <- NULL 199 | 200 | lt_summary <- list(NTC25=NTC25, 201 | NTC500=NTC500, 202 | NTC975=NTC975, 203 | high.dat.low=Dat25, 204 | high.dat.med=Dat500, 205 | high.dat.upper=Dat975, 206 | end.dat.low = dat.low.end, 207 | end.dat.med = dat.med.end, 208 | end.dat.upper = dat.high.end) 209 | 210 | 211 | muplot <- data.frame(date = dat.full, mu = mu50[1:(t+L0)]) 212 | list_out <- list( df_predict = df_predict, lt_predict=lt_predict, lt_summary=lt_summary, mu_plot = muplot, flag=flag) 213 | 214 | ### saveRDS 215 | results_directory = "/run/media/marcos/OS/UFMG/Pesquisa/Covid/app_COVID19/STpredictions/" 216 | # results_directory = 'C:/Users/ricar/Dropbox/covid19/R/predict/' 217 | file_id <- ifelse(uf$state[s]=='BR', colnames(Y)[3] , paste0(uf$state[s],'_',colnames(Y)[3],'e')) 218 | saveRDS(list_out, file=paste0(results_directory,'Brazil_',file_id,'.rds')) 219 | 220 | ### report 221 | source("mcmcplot_country.R") 222 | report_directory = "/run/media/marcos/OS/UFMG/Pesquisa/Covid/app_COVID19/STpredictions/reports" 223 | # report_directory = 'C:/Users/ricar/Dropbox/covid19/R/predict/report' 224 | #mcmcplot_country(mcmcout = mod_sim, parms = c(paste0("a[",t,"]"), paste0("b[",t,"]"), paste0("c[",t,"]")), 225 | mcmcplot_country(mcmcout = mod_sim, parms = c("a", "b", "c", "f"), 226 | dir = report_directory, 227 | filename = paste0('Brazil_',file_id,'_diagnostics'), 228 | heading = paste0('Brazil_',file_id), 229 | extension = "html", greek = TRUE, 230 | country = 'Brazil', 231 | type = file_id) 232 | 233 | ### run time 234 | #run_time = round(as.numeric(Sys.time()-t0, units="mins"),2) 235 | #print(noquote(paste(run_time, "minutes to", uf$state[s]))) 236 | 237 | } 238 | 239 | else print(paste0("ERROR:",uf$state[s])) 240 | 241 | } 242 | 243 | -------------------------------------------------------------------------------- /R/JAGS/predict_BR_par.R: -------------------------------------------------------------------------------- 1 | rm(list=ls()) 2 | 3 | setwd("/run/media/marcos/OS/UFMG/Pesquisa/Covid/R/JAGS") 4 | 5 | ################################################################### 6 | ### Packages 7 | ################################################################### 8 | library(dplyr) 9 | library(tidyr) 10 | library("rjags") 11 | library(matrixStats) 12 | library(mcmcplots) 13 | library(foreach) 14 | library(doMC) 15 | ################################################################### 16 | ### Data sets: https://github.com/CSSEGISandData 17 | ################################################################### 18 | baseURLbr = "https://raw.githubusercontent.com/covid19br/covid19br.github.io/master/dados" 19 | 20 | covid19uf <- read.csv(file.path(baseURLbr,"EstadosCov19.csv"), check.names=FALSE, stringsAsFactors=FALSE) %>% 21 | rename(state = estado, 22 | date = data, 23 | n = casos.acumulados, 24 | d = obitos.acumulados, 25 | n_new = novos.casos, 26 | d_new = obitos.novos) %>% 27 | mutate(date = as.Date(date)) %>% 28 | select(date, n, d, -n_new, -d_new, state) %>% 29 | arrange(state,date) %>% filter(date>='2020-01-23') 30 | 31 | covid19br <- read.csv(file.path(baseURLbr,"BrasilCov19.csv"), check.names=FALSE, stringsAsFactors=FALSE) %>% 32 | mutate(state = 'BR') %>% 33 | rename(date = data, 34 | n = casos.acumulados, 35 | d = obitos.acumulados, 36 | n_new = novos.casos, 37 | d_new = obitos.novos) %>% 38 | mutate(date = as.Date(date)) %>% 39 | select(date, n, d, -n_new, -d_new, state) %>% 40 | arrange(date) %>% filter(date>='2020-01-23') 41 | 42 | covid19 <- bind_rows(covid19uf,covid19br) 43 | uf <- distinct(covid19,state) 44 | 45 | br_pop <- read.csv("../pop/pop_BR.csv") 46 | 47 | ########################################################################### 48 | ###### JAGS 49 | ########################################################################### 50 | #register cores 51 | registerDoMC(cores = detectCores()-1) # Alternativa Linux 52 | 53 | #for ( s in 1:dim(uf)[1] ) { 54 | obj <- foreach( s = 1:dim(uf)[1] ) %dopar% { 55 | #obj <- foreach( s = 1:3 ) %dopar% { 56 | source("jags_poisson.R") 57 | 58 | i = 4 # (2: confirmed, 3: deaths, 4: new confirmed, 5: new deaths) 59 | L = 300 60 | #t0 = Sys.time() 61 | estado = uf$state[s] 62 | 63 | Y <- covid19 %>% filter(state==estado) %>% 64 | mutate(n_new = n - lag(n, default=0), 65 | d_new = d - lag(d, default=0)) %>% 66 | select(date, n, d, n_new, d_new, state) %>% 67 | arrange(date) %>% filter(date>='2020-01-23') 68 | #Y = covid19 %>% filter(state==uf$state[s]) 69 | 70 | while(any(Y$n_new <0)){ 71 | pos <- which(Y$n_new <0) 72 | for(j in pos){ 73 | Y$n_new[j-1] = Y$n_new[j] + Y$n_new[j-1] 74 | Y$n_new[j] = 0 75 | Y$n[j-1] = Y$n[j] 76 | } 77 | } 78 | 79 | pop <- br_pop$pop[which(br_pop$uf == uf$state[s])] 80 | 81 | t = dim(Y)[1] 82 | 83 | #use static to provide initial values 84 | params = c("a","b","c","f","yfut","mu") 85 | nc = 1 # 3 86 | nb = 90e3 # 5e4 87 | thin = 10 88 | ni = 10e3 # 5e4 89 | data_jags = list(y=Y[[i]], t=t, L=L) 90 | mod = try(jags.model(textConnection(mod_string_new), data=data_jags, n.chains=nc, n.adapt=nb, quiet=TRUE)) 91 | try(update(mod, n.iter=ni, progress.bar="none")) 92 | mod_sim = try(coda.samples(model=mod, variable.names=params, n.iter=ni, thin=thin,progress.bar="none")) 93 | 94 | if(class(mod_sim) != "try-error" && class(mod) != "try-error"){ 95 | 96 | mod_chain = as.data.frame(do.call(rbind, mod_sim)) 97 | 98 | a_pos = "a" 99 | b_pos = "b" 100 | c_pos = "c" 101 | f_pos = "f" 102 | mu_pos = paste0("mu[",1:(t+L),"]") 103 | yfut_pos = paste0("yfut[",1:L,"]") 104 | L0 = 14 105 | 106 | mod_chain_y = as.matrix(mod_chain[yfut_pos]) 107 | mod_chain_cumy = rowCumsums(mod_chain_y) + Y[[2]][t] 108 | 109 | 110 | ### list output 111 | df_predict <- data.frame( date = as.Date((max(Y$date)+1):(max(Y$date)+L0), origin="1970-01-01"), 112 | q25 = colQuantiles(mod_chain_cumy[,1:L0], prob=.025), 113 | med = colQuantiles(mod_chain_cumy[,1:L0], prob=.5), 114 | q975 = colQuantiles(mod_chain_cumy[,1:L0], prob=.975), 115 | m = colMeans(mod_chain_cumy[,1:L0])) 116 | row.names(df_predict) <- NULL 117 | 118 | lt_predict <- lt_summary <- NULL 119 | 120 | #longterm 121 | L0 = 200 122 | 123 | #acha a curva de quantil 124 | lowquant <- colQuantiles(mod_chain_y[,1:L0], prob=.025) 125 | medquant <- colQuantiles(mod_chain_y[,1:L0], prob=.5) 126 | highquant <- colQuantiles(mod_chain_y[,1:L0], prob=.975) 127 | 128 | NTC25 =sum(lowquant)+Y[[2]][t] 129 | NTC500=sum(medquant)+Y[[2]][t] 130 | NTC975=sum(highquant)+Y[[2]][t] 131 | 132 | 133 | ##flag 134 | cm <- pop * 0.025 135 | ch <- pop * 0.03 136 | flag <- 0 #tudo bem 137 | {if(NTC500 > cm) flag <- 2 #nao plotar 138 | else{if(NTC975 > ch){flag <- 1; NTC25 <- NTC975 <- NULL}}} #plotar so mediana 139 | 140 | #vetor de data futuras e pega a posicao do maximo do percentil 25. 141 | dat.vec <- as.Date((max(Y$date)+1):(max(Y$date)+L0), origin="1970-01-01") 142 | dat.full <- c(Y[[1]],dat.vec) 143 | 144 | 145 | Dat25 <- Dat500 <- Dat975 <- NULL 146 | dat.low.end <- dat.med.end <- dat.high.end <- NULL 147 | 148 | mod_chain_mu = as.matrix(mod_chain[mu_pos]) 149 | mu50 <- apply(mod_chain_mu,2,quantile, probs=0.5) 150 | Dat500 <- dat.full[which.max(mu50[1:(t+L0)])] 151 | 152 | q <- .99 153 | med.cum <- c(medquant[1]+Y[[2]][t],medquant[2:length(medquant)]) 154 | med.cum <- colCumsums(as.matrix(med.cum)) 155 | med.cum <- med.cum/med.cum[length(med.cum)] 156 | med.end <- which(med.cum - q > 0)[1] 157 | dat.med.end <- dat.vec[med.end] 158 | 159 | if(flag == 0){ 160 | #definicao do pico usando a curva das medias 161 | mu25 <- apply(mod_chain_mu,2,quantile, probs=0.025) 162 | mu975 <- apply(mod_chain_mu,2,quantile, probs=.975) 163 | 164 | posMax.q25 <- which.max(mu25[1:(t+L0)]) 165 | aux <- mu975 - mu25[posMax.q25] 166 | aux2 <- aux[posMax.q25:(t+L0)] 167 | val <- min(aux2[aux2>0]) 168 | dat.max <- which(aux == val) 169 | 170 | aux <- mu975 - mu25[posMax.q25] 171 | aux2 <- aux[1:posMax.q25] 172 | val <- min(aux2[aux2>0]) 173 | dat.min <- which(aux == val) 174 | 175 | Dat25 <- dat.full[dat.min] 176 | Dat975 <- dat.full[dat.max] 177 | 178 | #calcula o fim da pandemia 179 | low.cum <- c(lowquant[1]+Y[[2]][t],lowquant[2:length(lowquant)]) 180 | low.cum <- colCumsums(as.matrix(low.cum)) 181 | low.cum <- low.cum/low.cum[length(low.cum)] 182 | low.end <- which(low.cum - q > 0)[1] 183 | dat.low.end <- dat.vec[low.end] 184 | 185 | high.cum <- c(highquant[1]+Y[[2]][t],highquant[2:length(highquant)]) 186 | high.cum <- colCumsums(as.matrix(high.cum)) 187 | high.cum <- high.cum/high.cum[length(high.cum)] 188 | high.end <- which(high.cum - q > 0)[1] 189 | dat.high.end <- dat.vec[high.end] 190 | } 191 | 192 | lt_predict <- data.frame( date = dat.vec, 193 | q25 = lowquant, 194 | med = medquant, 195 | q975 = highquant, 196 | m = colMeans(mod_chain_y[,1:L0])) 197 | row.names(lt_predict) <- NULL 198 | 199 | lt_summary <- list(NTC25=NTC25, 200 | NTC500=NTC500, 201 | NTC975=NTC975, 202 | high.dat.low=Dat25, 203 | high.dat.med=Dat500, 204 | high.dat.upper=Dat975, 205 | end.dat.low = dat.low.end, 206 | end.dat.med = dat.med.end, 207 | end.dat.upper = dat.high.end) 208 | 209 | muplot <- data.frame(date = dat.full, mu = mu50[1:(t+L0)]) 210 | list_out <- list( df_predict = df_predict, lt_predict=lt_predict, lt_summary=lt_summary, mu_plot = muplot, flag=flag) 211 | 212 | ### saveRDS 213 | results_directory = "/run/media/marcos/OS/UFMG/Pesquisa/Covid/app_COVID19/STpredictions/" 214 | # results_directory = 'C:/Users/ricar/Dropbox/covid19/R/predict/' 215 | file_id <- ifelse(uf$state[s]=='BR', colnames(Y)[2] , paste0(uf$state[s],'_',colnames(Y)[2],'e')) 216 | saveRDS(list_out, file=paste0(results_directory,'Brazil_',file_id,'.rds')) 217 | 218 | ### report 219 | source("mcmcplot_country.R") 220 | report_directory = "/run/media/marcos/OS/UFMG/Pesquisa/Covid/app_COVID19/STpredictions/reports" 221 | # report_directory = 'C:/Users/ricar/Dropbox/covid19/R/predict/report' 222 | #mcmcplot_country(mcmcout = mod_sim, parms = c(paste0("a[",t,"]"), paste0("b[",t,"]"), paste0("c[",t,"]")), 223 | mcmcplot_country(mcmcout = mod_sim, parms = c("a", "b", "c", "f"), 224 | dir = report_directory, 225 | filename = paste0('Brazil_',file_id,'_diagnostics'), 226 | heading = paste0('Brazil_',file_id), 227 | extension = "html", greek = TRUE, 228 | country = 'Brazil', 229 | type = file_id) 230 | 231 | ### run time 232 | #run_time = round(as.numeric(Sys.time()-t0, units="mins"),2) 233 | #print(noquote(paste(run_time, "minutes to", uf$state[s]))) 234 | 235 | } 236 | 237 | else print(paste0("ERROR:",uf$state[s])) 238 | 239 | } 240 | 241 | -------------------------------------------------------------------------------- /R/Video/Video_BR.R: -------------------------------------------------------------------------------- 1 | ############################################ 2 | ###### GERACAO DE DADOS PARA O VIDEO ####### 3 | ############################################ 4 | 5 | ############################################ 6 | ###### Packages ###### 7 | ############################################ 8 | library(dplyr) 9 | library(tidyr) 10 | library(matrixStats) 11 | library(mcmcplots) 12 | library(MCMCvis) 13 | library(foreach) 14 | library(doMC) 15 | library(rstan) 16 | library(lubridate) 17 | 18 | #setwd("~/Desktop/app_COVID19/R/STAN") 19 | setwd("/run/media/marcos/OS/UFMG/Pesquisa/Covid/R/STAN") 20 | 21 | ################################################################### 22 | ### Data sets: https://github.com/CSSEGISandData 23 | ################################################################### 24 | baseURLbr = "https://raw.githubusercontent.com/covid19br/covid19br.github.io/master/dados" 25 | 26 | covid19br <- read.csv(file.path(baseURLbr,"BrasilCov19.csv"), check.names=FALSE, stringsAsFactors=FALSE) %>% 27 | mutate(state = 'BR') %>% 28 | rename(date = data, 29 | n = casos.acumulados, 30 | d = obitos.acumulados, 31 | n_new = novos.casos, 32 | d_new = obitos.novos) %>% 33 | mutate(date = as.Date(date)) %>% 34 | select(date, n, d, -n_new, -d_new, state) %>% 35 | arrange(date) %>% filter(date>='2020-01-23') 36 | 37 | br_pop <- read.csv("../pop/pop_BR.csv") 38 | 39 | ########################################################################### 40 | ###### JAGS/STAN 41 | ########################################################################### 42 | 43 | results.video <- list() 44 | 45 | data_final_prev <- ymd('2021-07-01') 46 | data_max <- max(covid19br$date) 47 | 48 | ## Verifica se tem o RDS - Se tiver, ele só atualiza, se não, ele roda de novo 49 | setwd("/run/media/marcos/OS/UFMG/Pesquisa/Covid/app_COVID19/STvideos") 50 | arquivos <- list.files(pattern = '*.rds', full.names = F) 51 | arquivo <- "Brazil_n.rds" %in% arquivos 52 | 53 | {if(arquivo == TRUE){ 54 | arquivo_rds <- readRDS("Brazil_n.rds") 55 | data_final <- arquivo_rds[[length(arquivo_rds)]]$last_date 56 | data_usada <- data_final + ddays(1) 57 | a <- length(arquivo_rds) + 1 58 | results.video <- arquivo_rds 59 | } 60 | else{ 61 | data_usada <- min(covid19br$date) + ddays(30) 62 | a <- 1 63 | }} 64 | 65 | 66 | setwd("/run/media/marcos/OS/UFMG/Pesquisa/Covid/R/STAN") 67 | #complie stan model 68 | model="stan_model_poisson_gen.stan" #modelo STAN 69 | mod<- try(stan_model(file = model,verbose=FALSE)) 70 | 71 | if(class(mod) == "try-error") stop("STAN DID NOT COMPILE") 72 | 73 | pop <- br_pop$pop[which(br_pop$uf == 'BR')] 74 | key <- FALSE 75 | while(data_usada <= data_max) { 76 | 77 | ## SELECIONAR OS DADOS QUE VAO SER USADOS -> VAI ACRESCENTANDO UM DIA NA DATA ATE O FINAL 78 | dados <- subset(covid19br,covid19br$date <= data_usada) 79 | 80 | i = 4 # (2: confirmed, 3: deaths, 4: new confirmed, 5: new deaths) 81 | L = as.numeric(difftime(data_final_prev, data_usada, units = "days")) 82 | ## Todas as previsões precisam ir até o mesmo dia -> dia final definido no parâmetro data_final_prev 83 | 84 | # Preparação dos dados para rodar o modelo no Stan 85 | Y <- dados %>% 86 | mutate(n_new = n - lag(n, default=0), 87 | d_new = d - lag(d, default=0)) %>% 88 | select(date, n, d, n_new, d_new, state) %>% 89 | arrange(date) %>% filter(date>='2020-01-23') 90 | 91 | while(any(Y$n_new <0)){ 92 | pos <- which(Y$n_new <0) 93 | for(j in pos){ 94 | Y$n_new[j-1] = Y$n_new[j] + Y$n_new[j-1] 95 | Y$n_new[j] = 0 96 | Y$n[j-1] = Y$n[j] 97 | } 98 | } 99 | 100 | t = dim(Y)[1] 101 | 102 | params = c("a","b","c","f","mu") 103 | 104 | burn_in= 2e3 105 | lag= 3 106 | sample_size= 1e3 107 | number_iterations= burn_in + lag*sample_size 108 | number_chains= 1 109 | 110 | data_stan = list(y=Y[[i]], n=t, L=L, pop=pop, perPop=0.1) 111 | 112 | init <- list( 113 | list(a = 1, b1 = log(1), c = .5, f = 1) 114 | ) 115 | 116 | mod_sim<- try(sampling(object = mod, data = data_stan, 117 | pars = params, 118 | chains = number_chains, 119 | init = init, 120 | iter = number_iterations, warmup = burn_in, thin = lag, 121 | control = list(max_treedepth = 50, adapt_delta=0.999), 122 | verbose = FALSE, open_progress=FALSE, show_messages=FALSE)) 123 | 124 | mod_chain = as.data.frame(mod_sim) 125 | 126 | a_pos = "a" 127 | b_pos = "b" 128 | c_pos = "c" 129 | f_pos = "f" 130 | #mu_pos = c(paste0("mu[",1:t,"]"),paste0("mufut[",1:L,"]")) 131 | mu_pos = paste0("mu[",1:t,"]") 132 | yfut_pos = paste0("yfut[",1:L,"]") 133 | 134 | source("posterior_sample.R") 135 | fut <- predL(L=L,t,pop,Y[[2]][t],c(mod_chain[[a_pos]]),c(mod_chain[[b_pos]]),c(mod_chain[[c_pos]]),c(mod_chain[[f_pos]])) 136 | 137 | 138 | mod_chain_y = fut$y.fut 139 | #mod_chain_y = as.matrix(mod_chain[yfut_pos]) 140 | mod_chain_cumy = rowCumsums(mod_chain_y) + Y[[2]][t] 141 | 142 | lt_predict <- lt_summary <- NULL 143 | L0 = as.numeric(difftime(data_final_prev, data_usada, units = "days")) 144 | ## Todas as previsões precisam ir até o mesmo dia -> dia final definido no parâmetro data_final_prev 145 | 146 | #acha a curva de quantil 147 | if(Y[[2]][t] > 1000){ 148 | #acha a curva de quantil 149 | lowquant <- colQuantiles(mod_chain_y[,1:L0], prob=.025) 150 | medquant <- colQuantiles(mod_chain_y[,1:L0], prob=.5) 151 | highquant <- colQuantiles(mod_chain_y[,1:L0], prob=.975) 152 | } 153 | else{ 154 | lowquant <- c(Y[[2]][t],colQuantiles(mod_chain_cumy[,1:L0], prob=.025)) 155 | lowquant <- (lowquant-lag(lowquant,default=0))[-1] 156 | medquant <- c(Y[[2]][t],colQuantiles(mod_chain_cumy[,1:L0], prob=.5)) 157 | medquant <- (medquant-lag(medquant,default=0))[-1] 158 | highquant <- c(Y[[2]][t],colQuantiles(mod_chain_cumy[,1:L0], prob=.975)) 159 | highquant <- (highquant-lag(highquant,default=0))[-1] 160 | } 161 | 162 | NTC25 =sum(lowquant)+Y[[2]][t] 163 | NTC500=sum(medquant)+Y[[2]][t] 164 | NTC975=sum(highquant)+Y[[2]][t] 165 | 166 | ##flag 167 | cm <- pop * 0.2 168 | ch <- pop * 0.2 169 | flag <- 0 #tudo bem 170 | {if(NTC500 > cm) flag <- 2 #nao plotar 171 | else{if(NTC975 > ch){flag <- 1; NTC25 <- NTC975 <- NULL}}} #plotar so mediana 172 | 173 | #vetor de data futuras e pega a posicao do maximo do percentil 25. 174 | dat.vec <- as.Date((max(Y$date)+1):(max(Y$date)+L0), origin="1970-01-01") 175 | dat.full <- c(Y[[1]],dat.vec) 176 | 177 | 178 | Dat25 <- Dat500 <- Dat975 <- NULL 179 | dat.low.end <- dat.med.end <- dat.high.end <- NULL 180 | 181 | #mod_chain_mu = as.matrix(mod_chain[mu_pos]) 182 | ifelse(length(fut$pos) > 0, 183 | mod_chain_mu <- cbind(as.matrix(mod_chain[mu_pos])[-fut$pos,],fut$mu.fut), 184 | mod_chain_mu <- cbind(as.matrix(mod_chain[mu_pos]),fut$mu.fut)) 185 | mu50 <- apply(mod_chain_mu,2,quantile, probs=0.5) 186 | Dat500 <- dat.full[which.max(mu50[1:(t+L0)])] 187 | 188 | q <- .99 189 | med.cum <- c(medquant[1]+Y[[2]][t],medquant[2:length(medquant)]) 190 | med.cum <- colCumsums(as.matrix(med.cum)) 191 | med.cum <- med.cum/med.cum[length(med.cum)] 192 | med.end <- which(med.cum - q > 0)[1] 193 | dat.med.end <- dat.vec[med.end] 194 | 195 | if(flag == 0){ 196 | #definicao do pico usando a curva das medias 197 | mu25 <- apply(mod_chain_mu,2,quantile, probs=0.025) 198 | mu975 <- apply(mod_chain_mu,2,quantile, probs=.975) 199 | 200 | posMax.q25 <- which.max(mu25[1:(t+L0)]) 201 | aux <- mu975 - mu25[posMax.q25] 202 | aux2 <- aux[posMax.q25:(t+L0)] 203 | val <- min(aux2[aux2>0]) 204 | dat.max <- which(aux == val) 205 | 206 | aux <- mu975 - mu25[posMax.q25] 207 | aux2 <- aux[1:posMax.q25] 208 | val <- min(aux2[aux2>0]) 209 | dat.min <- which(aux == val) 210 | 211 | Dat25 <- dat.full[dat.min] 212 | Dat975 <- dat.full[dat.max] 213 | 214 | #calcula o fim da pandemia 215 | low.cum <- c(lowquant[1]+Y[[2]][t],lowquant[2:length(lowquant)]) 216 | low.cum <- colCumsums(as.matrix(low.cum)) 217 | low.cum <- low.cum/low.cum[length(low.cum)] 218 | low.end <- which(low.cum - q > 0)[1] 219 | dat.low.end <- dat.vec[low.end] 220 | 221 | high.cum <- c(highquant[1]+Y[[2]][t],highquant[2:length(highquant)]) 222 | high.cum <- colCumsums(as.matrix(high.cum)) 223 | high.cum <- high.cum/high.cum[length(high.cum)] 224 | high.end <- which(high.cum - q > 0)[1] 225 | dat.high.end <- dat.vec[high.end] 226 | } 227 | 228 | lt_predict <- data.frame( date = dat.vec, 229 | q25 = lowquant, 230 | med = medquant, 231 | q975 = highquant, 232 | m = colMeans(mod_chain_y[,1:L0])) 233 | row.names(lt_predict) <- NULL 234 | 235 | lt_summary <- list(NTC25=NTC25, 236 | NTC500=NTC500, 237 | NTC975=NTC975, 238 | high.dat.low=Dat25, 239 | high.dat.med=Dat500, 240 | high.dat.upper=Dat975, 241 | end.dat.low = dat.low.end, 242 | end.dat.med = dat.med.end, 243 | end.dat.upper = dat.high.end) 244 | 245 | muplot <- data.frame(date = dat.full, mu = mu50[1:(t+L0)]) 246 | list_out <- list(lt_predict=lt_predict, lt_summary=lt_summary, mu_plot = muplot, flag=flag, last_date = data_usada) 247 | 248 | results.video[[a]] <- list_out 249 | a = a + 1 250 | data_usada <- data_usada + ddays(1) 251 | key <- TRUE 252 | } 253 | 254 | {if(key){ 255 | ### saveRDS 256 | results_directory = "/run/media/marcos/OS/UFMG/Pesquisa/Covid/app_COVID19/STvideos/" 257 | # results_directory = 'C:/Users/ricar/Dropbox/covid19/R/predict/' 258 | file_id <- colnames(Y)[2] 259 | saveRDS(results.video, file=paste0(results_directory,'Brazil_',file_id,'.rds')) 260 | } 261 | else print("No update necessary")} 262 | -------------------------------------------------------------------------------- /app_v1/www/markdown/CoronaUFMG_MD.md: -------------------------------------------------------------------------------- 1 | --- 2 | title: "Modelando a pandemia de Covid19" 3 | author: "Dani Gamerman" 4 | # output: slidy_presentation 5 | output: 6 | html_document: 7 | toc: true 8 | # toc_depth: 5 9 | # toc_float: true 10 | --- 11 | 12 | 13 | ### Modelando a pandemia de Covid19 14 | 15 | Dani Gamerman - Programa de PG em Estatística - UFMG 16 | 17 | *1º semestre de 2020* 18 | 19 | (motivado a partir de notas de José Marcos Andrade Figueiredo - UFMG) 20 | 21 | #### Modelo de crescimento logı́stico básico 22 | 23 | $$ 24 | Y(t) \sim N ( \mu (t) , \sigma^2 ), \qquad t = 1, 2, ... 25 | $$ 26 | 27 | onde $Y(t)$ é o número de casos acumulados até o dia $t$ em uma dada região, com 28 | 29 | $$ 30 | \mu ( t ) = \frac{ a \exp{ \{ c t \} } } {1 + b \exp { \{ c t \} }}. 31 | $$ 32 | **Caso especial:** $b = 0$ (crescimento exponencial) $ \rightarrow \mu(t) = a \exp \{ ct \} $. 33 | 34 | - Adequado para os estágios iniciais da pandemia 35 | 36 | ##### Problemas do modelo básico: 37 | 38 | a) os dados são contagens e a distribuição normal pressupõe dados contı́nuo; 39 | 40 | b) a variância deveria aumentar com a magnitude dos dados. 41 | 42 | 43 | ##### Características de interesse: 44 | 45 | As características mais importantes são: 46 | 47 | 48 | **1) Taxa de infecção** 49 | 50 | - $c$ mede a velocidade da aceleração e reflete a taxa de infecção da doença. 51 | 52 | 53 | **2) Assíntota** 54 | $$\lim_{t \to \infty} \mu( t) = \lim_{t \to \infty} \frac{ a \exp{ \{ c t \} } } {1 + b \exp { \{ ct \} }} = \frac ab$$ 55 | - Reflete o total de casos acululados ao longo de toda a pandemia. 56 | 57 | - Crescimento exponencial ($b=0$): assíntota $= \infty$ ! 58 | 59 | 60 | **3) Ponto de inflexão** 61 | 62 | - É o tempo $t*$ onde o número de novos casos para de crescer e começa a diminuir. 63 | 64 | - Crescimento exponencial ($b=0$): número de novos casos nunca para de crescer! 65 | 66 | 67 | **4) Previsão:** 68 | 69 | - O que podemos dizer sobre $Y (t+k ), \forall k$, para $t$ fixo (hoje)? 70 | Depende da distribuição de $Y( t)$ mas será sempre dada pela distribuição preditiva de $Y(t+k)$ dado $Y(1:t) = \{ Y( 1) , ... , Y( t ) \}$, o que foi observado. 71 | 72 | Funciona como se fosse a distribuição a posteriori de $Y(t + k )$. 73 | 74 | **Resultado útil:** Se $Z$ e $W$ são 2 v. a.'s quaisquer então: 75 | 76 | $E[Z] = E[ E(Z \mid W ) ]$ 77 | 78 | $Var[Z] = Var[ E(Z \mid W ) ] + E[ Var( Z \mid W ) ]$ 79 | 80 | Em particular, 81 | $E[Y ( t + k ) \mid Y( 1:t)] = E\{ E[ Y ( t + k ) \mid \mu( 1:t)] \mid Y( 1:t) \}$ 82 | $= E[ \mu( t+k )] \mid Y( 1:t) ]$, a média a posteriori de $\mu ( t + k )$. 83 | 84 | A inferência para tudo que foi dito acima deve ser reportada através de estimadores pontuais (ex: médias a posteriori), junto com os respectivos intervalos de credibilidade. 85 | 86 | 87 | **5) Número de reprodutibilidade $R_0$** 88 | 89 | $R_0$ é o número esperado de casos secundários de uma doença produzidos por um indivíduo infectado. 90 | 91 | No tempo $t$, ele é definido como 92 | $$R_0 = \frac {\mu ( t ) - \mu ( t-1)}{\mu ( t-1)} = \frac {\mu ( t )}{\mu ( t-1)} - 1$$ 93 | 94 | **Início da epidemia:** 95 | $1 \gg b \exp { \{ ct \} } \to \mu (t) \approx a \exp { \{ ct \} } \to R_0 \approx e^c - 1$ 96 | 97 | **Final da epidemia:** 98 | $1 \ll b \exp { \{ ct \} } \to \mu (t) \approx a / b \to R_0 \approx 0$ 99 | 100 | **Meio da epidemia:** 101 | $R_0$ é função dos parâmetros $(a,b,c)$ e do tempo $t$, e é dado por 102 | $$R_0 (t) = e^c \ \frac{1 + b e^c e^{ct} } {1 + b e^{ct} } \ - \ 1$$ 103 | 104 | Para cada $t$ fixado, podemos obter sua distribuição a posteriori (via amostra MCMC) e calcular média, quantis e intervalos de credibilidade. 105 | 106 | 107 | **6) Número médio de novos casos (NMNC)** 108 | 109 | NMNC no tempo $t+k$: 110 | $n_t ( k ) = E [Y ( t + k ) - Y ( t + k -1 ) ] = \mu ( t + k ) - \mu ( t + k -1 )$ 111 | 112 | Logo, NMNC também é função dos parâmetros $(a,b,c)$ e pode ser facilmente calculado. 113 | 114 | Para cada $t$ e $k$ fixados, podemos obter sua distribuição a posteriori (via amostra MCMC) e calcular média, quantis e intervalos de credibilidade. 115 | 116 | ![Long Term Graph](FigApp.png "Estimativas e Intervalo de Credibilidade para o pico da pandemia e para o total de casos") 117 | 118 | 119 | #### Alternativas 120 | 121 | 1.1) $Y( t ) \sim Poisson ( \mu ( t ) )$ com $E[ Y(t)] = \mu (t )$ e $Var(Y(t)) = \mu ( t )$ 122 | 123 | 1.2) $Y ( t ) \sim N ( \mu ( t ) , \sigma^2 \ \mu ( t ) )$ com $E[ Y(t)] = \mu (t )$ e $Var(Y(t)) = \sigma^2 \ \mu ( t )$ 124 | 125 | Obs: 126 | 127 | - Modelo (1.2) admite sobredispersão se $\sigma^2 > 1$ 128 | 129 | - Alternativa (1.2) só cuida do comentário (b) 130 | 131 | - Alternativa (1.1) cuida dos 2 comentários mas não permite sobredispersão 132 | 133 | ##### Poisson com sobredispersão 134 | 135 | 1.3) $Y( t ) \mid \epsilon ( t ) \sim Poisson ( \mu ( t ) + \epsilon ( t ) )$ com $E[ \epsilon (t)] = 0$ e $Var( \epsilon (t)) = \sigma^2$ 136 | 137 | 1.4) $Y( t ) \mid \epsilon ( t ) \sim Poisson ( \mu ( t ) \times \epsilon ( t ) )$ com $E[ \epsilon (t)] = 1$ e $Var( \epsilon (t)) = \sigma^2$ 138 | 139 | 140 | Usando os resultados úteis anteriores: 141 | 142 | **Mod(1.3):** 143 | $E [ Y ( t ) ] = E[ E( Y(t) \mid \epsilon (t ) ) ] = E[ \mu ( t ) + \epsilon ( t ) ] = \mu ( t ) + E[ \epsilon ( t ) ] = \mu ( t )$ 144 | 145 | $Var[ Y ( t ) ] = Var[ E( Y(t) \mid \epsilon (t) ) ] + E[ Var ( Y(t) \mid \epsilon (t) ) ] = Var[ \mu ( t ) + \epsilon ( t ) ] + E [ \mu ( t ) + \epsilon ( t ) ] = \sigma^2 + \mu_t > \mu ( t )$ 146 | 147 | **Mod(1.4):** 148 | $E [ Y ( t ) ] = E[ E( Y(t) \mid \epsilon (t) ) ] = E[ \mu ( t ) \times \epsilon ( t ) ] = \mu ( t ) \times E[ \epsilon ( t ) ] = \mu ( t )$ 149 | 150 | $Var[ Y ( t ) ] = Var[ E( Y(t) \mid \epsilon (t) ) ] + E[ Var ( Y(t) \mid \epsilon (t) ) ] = Var[ \mu ( t ) \times \epsilon ( t ) ] + E [ \mu ( t ) \times \epsilon ( t ) ] = 151 | \mu_t ^2 \sigma^2 + \mu_t > \mu ( t )$ 152 | 153 | Ambos preservam média da Poisson e aumentam dispersão da Poisson. 154 | 155 | ##### Extensões dinâmicas 156 | 157 | Modelos anteriores assumem comportamento estático $\Rightarrow$ a forma 158 | da doença não se modifica ao longo do tempo $\Rightarrow$ taxa de 159 | infecção será sempre a mesma, assintota será sempre a mesma, \... 160 | 161 | **Modelos dinâmicos** flexibilizam isso. 162 | 163 | $$\mu ( t ) = \frac{ a( {\color{red} t )} \ \exp{ \{ c( {\color{red}t) } \ t \} } } {1 + b( {\color{red}t) } \ \exp { \{ c({\color{red}t) } \ t \} }}$$ 164 | 165 | com: 166 | $a ( t ) = a ( t-1) + w_a ( t )$, onde $w_a ( t ) \sim N ( 0 , W_a ), \forall t $. 167 | 168 | $b ( t ) = b ( t-1) + w_b ( t )$, onde $w_b ( t ) \sim N ( 0 , W_b ), \forall t $. 169 | 170 | $c ( t ) = c ( t-1) + w_c ( t )$, onde $w_c ( t ) \sim N ( 0 , W_c ), \forall t $. 171 | 172 | 173 | **Vantagens:** 174 | 175 | a) $E[ a(t) \mid a(t-1 )]= a (t-1)$, e o mesmo vale para $b(t)$ e $c(t) \Rightarrow$ constância local. 176 | 177 | b) $Var[ a(t) \mid a(t-1 )]= W_a$, e o mesmo vale para $b(t)$ e $c(t) \Rightarrow$ aumento da incerteza. 178 | 179 | **Problemas:** 180 | 181 | a) variâncias $W_a, W_b, W_c$ conhecidas $\Rightarrow$ difíceis de especificar. 182 | 183 | b) variâncias $W_a, W_b, W_c$ deconhecidas $\Rightarrow$ difíceis de estimar. 184 | 185 | c) não dá para simplificar $W_a = W_b = W_c = W$ (magnitudes diferentes de $(a,b,c)$). 186 | 187 | - Outra forma de introduzir dinamismo, agora multiplicativo: 188 | 189 | $a ( t ) = a ( t-1) \times w_a ( t )$, onde $w_a ( t ) \sim Gamma ( d_a ,d_a ), \forall t $. 190 | 191 | $b ( t ) = b ( t-1) \times w_b ( t )$, onde $w_b ( t ) \sim Gamma ( d_b ,d_b ), \forall t $. 192 | 193 | $c ( t ) = c ( t-1) \times w_c ( t )$, onde $w_c ( t ) \sim Gamma ( d_c ,d_c ), \forall t $. 194 | 195 | 196 | **Vantagens:** 197 | 198 | a) $E[ a(t) \mid a(t-1 )]= a (t-1)$ e o mesmo vale para $b(t)$ e $c(t) \Rightarrow$ constância local. 199 | 200 | b) $Var[ a(t) \mid a(t-1 )]= d_c^{-1}$ e o mesmo vale para $b(t)$ e $c(t) \Rightarrow$ aumento da incerteza. 201 | 202 | c) Hiperparâmetros $d_a, d_b, d_c$ fáceis de especificar. 203 | 204 | Exemplos: 205 | $$d=1000 \ \to \ 0,90= P ( 0,95 < w(t) < 1,05 ) = P \left( 0,95 < \frac {a(t)}{a(t-1) } < 1,05 \right)$$ 206 | $$d=1500 \ \to \ 0,95= P ( 0,95 < w(t) < 1,05 ) = P \left( 0,95 < \frac {a(t)}{a(t-1) } < 1,05 \right)$$ 207 | 208 | 209 | **Problemas:** 210 | 211 | a) As magnitures de $a, b, c$ ainda interferem no aumento da incerteza. 212 | 213 | b) não sei se software lida bem com Gammas tendo parâmetros tão altos. 214 | 215 | 216 | **Evolução multiplicativa com erros normais** 217 | 218 | Considere a evolução multiplicativa abaixo para o parâmetro $a$: 219 | 220 | $$a ( t ) = a ( t-1) \times \exp \{ w_a ( t ) \}, \mbox{ onde } w_a ( t ) \sim N( 0 , W_a )$$ 221 | Tomando o logartimo nos dois lados, obtem-se: 222 | $$\log \ a ( t ) = \log \ a ( t-1) + w_a ( t ), \mbox{ onde } w_a ( t ) \sim N( 0 , W_a )$$ 223 | Passando $\log \ a ( t-1)$ para a esquerda, vem que: 224 | $$\log \ a ( t ) - \log \ a ( t-1) = \log \left[ \frac{ a ( t )}{ a ( t-1)} \right] = w_a ( t ), \mbox{ onde } w_a ( t ) \sim N( 0 , W_a )$$ 225 | 226 | Especificação de $W_a$: pode-se pensar em percentual de incremento, como antes. 227 | 228 | $$0,95 = P \left( 0,95 < \frac {a(t)}{a(t-1) } < 1,05 \right) = P ( - 0,05 < w_a(t) < 0,05 )$$ 229 | Isso implica $2 \sqrt{W_a} = 0,05$, que implica $\sqrt{W_a} = 0,025 \ \Rightarrow W_a = (0,025)^2$. 230 | 231 | Mesma especificação vale para $W_b$ e $W_c$, pois dimensões de $b$ e $c$ não importam. 232 | 233 | 234 | **Caso particular** 235 | 236 | Baseado em Gamerman, Santos e Franco (J. Time Series Analysis, 2013): 237 | 238 | $$\mu ( t ) = \frac{ a( {\color{red}t)} \ \exp{ \{ c \ t \} } } {1 + b \ \exp { \{ c \ t \} }}$$ 239 | $a ( t ) = a ( t-1) \times w_a ( t )$, onde $ w_a ( t ) \sim Beta, \forall t$. 240 | 241 | Pode ser usado também para crescimento exponencial ($b=0$). 242 | 243 | 244 | **Vantagem:** 245 | 246 | a) Permite contas exatas, dispensando aproximações MCMC. 247 | 248 | 249 | **Desvantagem:** 250 | 251 | a) Não permite $b$ e $c$ dinâmicos. 252 | 253 | #### Generalizações da logística 254 | 255 | Até agora, usamos a logística para especificar a média $\mu ( t )$ como 256 | $$\mu ( t ) = \frac{ a \exp{ \{ c t \} } } {1 + b \exp { \{ ct \} }} = \frac{ a} { b + \exp { \{ - ct \} }}.$$ 257 | Essa expressão é a forma mais simples da logística. 258 | 259 | Ela pode ser generalizada de várias formas. Uma possível forma da **logística generalizada** é 260 | $$\mu ( t ) = d + \frac{ a - d} {( b + \exp { \{ - ct \} } )^f}$$ 261 | 262 | A logística é obtida fazendo $d=0$ e $f=1$. 263 | -------------------------------------------------------------------------------- /app_v1/CoronaUFMG_MD.md: -------------------------------------------------------------------------------- 1 | --- 2 | title: "Modelando a pandemia de Covid19" 3 | author: "Dani Gamerman" 4 | # output: slidy_presentation 5 | output: 6 | html_document: 7 | toc: true 8 | # toc_depth: 5 9 | # toc_float: true 10 | --- 11 | 12 | 13 | ### Modelando a pandemia de Covid19 14 | 15 | Dani Gamerman - Programa de PG em Estatística - UFMG 16 | 17 | 18 | 19 | *1º semestre de 2020* 20 | 21 | (motivado a partir de notas de José Marcos Andrade Figueiredo - UFMG) 22 | 23 | #### Modelo de crescimento logı́stico básico 24 | 25 | $$ 26 | Y(t) \sim N ( \mu (t) , \sigma^2 ), \qquad t = 1, 2, ... 27 | $$ 28 | 29 | onde $Y(t)$ é o número de casos acumulados até o dia $t$ em uma dada região, com 30 | 31 | $$ 32 | \mu ( t ) = \frac{ a \exp{ \{ c t \} } } {1 + b \exp { \{ c t \} }}. 33 | $$ 34 | **Caso especial:** $b = 0$ (crescimento exponencial) $ \rightarrow \mu(t) = a \exp \{ ct \} $. 35 | 36 | - Adequado para os estágios iniciais da pandemia 37 | 38 | ##### Problemas do modelo básico: 39 | 40 | a) os dados são contagens e a distribuição normal pressupõe dados contı́nuo; 41 | 42 | b) a variância deveria aumentar com a magnitude dos dados. 43 | 44 | 45 | ##### Características de interesse: 46 | 47 | As características mais importantes são: 48 | 49 | 50 | **1) Taxa de infecção** 51 | 52 | - $c$ mede a velocidade da aceleração e reflete a taxa de infecção da doença. 53 | 54 | 55 | **2) Assíntota** 56 | $$\lim_{t \to \infty} \mu( t) = \lim_{t \to \infty} \frac{ a \exp{ \{ c t \} } } {1 + b \exp { \{ ct \} }} = \frac ab$$ 57 | - Reflete o total de casos acululados ao longo de toda a pandemia. 58 | 59 | - Crescimento exponencial ($b=0$): assíntota $= \infty$ ! 60 | 61 | 62 | **3) Ponto de inflexão** 63 | 64 | - É o tempo $t*$ onde o número de novos casos para de crescer e começa a diminuir. 65 | 66 | - Crescimento exponencial ($b=0$): número de novos casos nunca para de crescer! 67 | 68 | 69 | **4) Previsão:** 70 | 71 | - O que podemos dizer sobre $Y (t+k ), \forall k$, para $t$ fixo (hoje)? 72 | Depende da distribuição de $Y( t)$ mas será sempre dada pela distribuição preditiva de $Y(t+k)$ dado $Y(1:t) = \{ Y( 1) , ... , Y( t ) \}$, o que foi observado. 73 | 74 | Funciona como se fosse a distribuição a posteriori de $Y(t + k )$. 75 | 76 | **Resultado útil:** Se $Z$ e $W$ são 2 v. a.'s quaisquer então: 77 | 78 | $E[Z] = E[ E(Z \mid W ) ]$ 79 | 80 | $Var[Z] = Var[ E(Z \mid W ) ] + E[ Var( Z \mid W ) ]$ 81 | 82 | Em particular, 83 | $E[Y ( t + k ) \mid Y( 1:t)] = E\{ E[ Y ( t + k ) \mid \mu( 1:t)] \mid Y( 1:t) \}$ 84 | $= E[ \mu( t+k )] \mid Y( 1:t) ]$, a média a posteriori de $\mu ( t + k )$. 85 | 86 | A inferência para tudo que foi dito acima deve ser reportada através de estimadores pontuais (ex: médias a posteriori), junto com os respectivos intervalos de credibilidade. 87 | 88 | 89 | **5) Número de reprodutibilidade $R_0$** 90 | 91 | $R_0$ é o número esperado de casos secundários de uma doença produzidos por um indivíduo infectado. 92 | 93 | No tempo $t$, ele é definido como 94 | $$R_0 = \frac {\mu ( t ) - \mu ( t-1)}{\mu ( t-1)} = \frac {\mu ( t )}{\mu ( t-1)} - 1$$ 95 | 96 | **Início da epidemia:** 97 | $1 \gg b \exp { \{ ct \} } \to \mu (t) \approx a \exp { \{ ct \} } \to R_0 \approx e^c - 1$ 98 | 99 | **Final da epidemia:** 100 | $1 \ll b \exp { \{ ct \} } \to \mu (t) \approx a / b \to R_0 \approx 0$ 101 | 102 | **Meio da epidemia:** 103 | $R_0$ é função dos parâmetros $(a,b,c)$ e do tempo $t$, e é dado por 104 | $$R_0 (t) = e^c \ \frac{1 + b e^c e^{ct} } {1 + b e^{ct} } \ - \ 1$$ 105 | 106 | Para cada $t$ fixado, podemos obter sua distribuição a posteriori (via amostra MCMC) e calcular média, quantis e intervalos de credibilidade. 107 | 108 | 109 | **6) Número médio de novos casos (NMNC)** 110 | 111 | NMNC no tempo $t+k$: 112 | $n_t ( k ) = E [Y ( t + k ) - Y ( t + k -1 ) ] = \mu ( t + k ) - \mu ( t + k -1 )$ 113 | 114 | Logo, NMNC também é função dos parâmetros $(a,b,c)$ e pode ser facilmente calculado. 115 | 116 | Para cada $t$ e $k$ fixados, podemos obter sua distribuição a posteriori (via amostra MCMC) e calcular média, quantis e intervalos de credibilidade. 117 | 118 | ![Long Term Graph](FigApp.png "Estimativas e Intervalo de Credibilidade para o pico da pandemia e para o total de casos") 119 | 120 | 121 | #### Alternativas 122 | 123 | 1.1) $Y( t ) \sim Poisson ( \mu ( t ) )$ com $E[ Y(t)] = \mu (t )$ e $Var(Y(t)) = \mu ( t )$ 124 | 125 | 1.2) $Y ( t ) \sim N ( \mu ( t ) , \sigma^2 \ \mu ( t ) )$ com $E[ Y(t)] = \mu (t )$ e $Var(Y(t)) = \sigma^2 \ \mu ( t )$ 126 | 127 | Obs: 128 | 129 | - Modelo (1.2) admite sobredispersão se $\sigma^2 > 1$ 130 | 131 | - Alternativa (1.2) só cuida do comentário (b) 132 | 133 | - Alternativa (1.1) cuida dos 2 comentários mas não permite sobredispersão 134 | 135 | ##### Poisson com sobredispersão 136 | 137 | 1.3) $Y( t ) \mid \epsilon ( t ) \sim Poisson ( \mu ( t ) + \epsilon ( t ) )$ com $E[ \epsilon (t)] = 0$ e $Var( \epsilon (t)) = \sigma^2$ 138 | 139 | 1.4) $Y( t ) \mid \epsilon ( t ) \sim Poisson ( \mu ( t ) \times \epsilon ( t ) )$ com $E[ \epsilon (t)] = 1$ e $Var( \epsilon (t)) = \sigma^2$ 140 | 141 | 142 | Usando os resultados úteis anteriores: 143 | 144 | **Mod(1.3):** 145 | $E [ Y ( t ) ] = E[ E( Y(t) \mid \epsilon (t ) ) ] = E[ \mu ( t ) + \epsilon ( t ) ] = \mu ( t ) + E[ \epsilon ( t ) ] = \mu ( t )$ 146 | 147 | $Var[ Y ( t ) ] = Var[ E( Y(t) \mid \epsilon (t) ) ] + E[ Var ( Y(t) \mid \epsilon (t) ) ] = Var[ \mu ( t ) + \epsilon ( t ) ] + E [ \mu ( t ) + \epsilon ( t ) ] = \sigma^2 + \mu_t > \mu ( t )$ 148 | 149 | **Mod(1.4):** 150 | $E [ Y ( t ) ] = E[ E( Y(t) \mid \epsilon (t) ) ] = E[ \mu ( t ) \times \epsilon ( t ) ] = \mu ( t ) \times E[ \epsilon ( t ) ] = \mu ( t )$ 151 | 152 | $Var[ Y ( t ) ] = Var[ E( Y(t) \mid \epsilon (t) ) ] + E[ Var ( Y(t) \mid \epsilon (t) ) ] = Var[ \mu ( t ) \times \epsilon ( t ) ] + E [ \mu ( t ) \times \epsilon ( t ) ] = 153 | \mu_t ^2 \sigma^2 + \mu_t > \mu ( t )$ 154 | 155 | Ambos preservam média da Poisson e aumentam dispersão da Poisson. 156 | 157 | ##### Extensões dinâmicas 158 | 159 | Modelos anteriores assumem comportamento estático $\Rightarrow$ a forma 160 | da doença não se modifica ao longo do tempo $\Rightarrow$ taxa de 161 | infecção será sempre a mesma, assintota será sempre a mesma, \... 162 | 163 | **Modelos dinâmicos** flexibilizam isso. 164 | 165 | $$\mu ( t ) = \frac{ a( {\color{red} t )} \ \exp{ \{ c( {\color{red}t) } \ t \} } } {1 + b( {\color{red}t) } \ \exp { \{ c({\color{red}t) } \ t \} }}$$ 166 | 167 | com: 168 | $a ( t ) = a ( t-1) + w_a ( t )$, onde $w_a ( t ) \sim N ( 0 , W_a ), \forall t $. 169 | 170 | $b ( t ) = b ( t-1) + w_b ( t )$, onde $w_b ( t ) \sim N ( 0 , W_b ), \forall t $. 171 | 172 | $c ( t ) = c ( t-1) + w_c ( t )$, onde $w_c ( t ) \sim N ( 0 , W_c ), \forall t $. 173 | 174 | 175 | **Vantagens:** 176 | 177 | a) $E[ a(t) \mid a(t-1 )]= a (t-1)$, e o mesmo vale para $b(t)$ e $c(t) \Rightarrow$ constância local. 178 | 179 | b) $Var[ a(t) \mid a(t-1 )]= W_a$, e o mesmo vale para $b(t)$ e $c(t) \Rightarrow$ aumento da incerteza. 180 | 181 | **Problemas:** 182 | 183 | a) variâncias $W_a, W_b, W_c$ conhecidas $\Rightarrow$ difíceis de especificar. 184 | 185 | b) variâncias $W_a, W_b, W_c$ deconhecidas $\Rightarrow$ difíceis de estimar. 186 | 187 | c) não dá para simplificar $W_a = W_b = W_c = W$ (magnitudes diferentes de $(a,b,c)$). 188 | 189 | - Outra forma de introduzir dinamismo, agora multiplicativo: 190 | 191 | $a ( t ) = a ( t-1) \times w_a ( t )$, onde $w_a ( t ) \sim Gamma ( d_a ,d_a ), \forall t $. 192 | 193 | $b ( t ) = b ( t-1) \times w_b ( t )$, onde $w_b ( t ) \sim Gamma ( d_b ,d_b ), \forall t $. 194 | 195 | $c ( t ) = c ( t-1) \times w_c ( t )$, onde $w_c ( t ) \sim Gamma ( d_c ,d_c ), \forall t $. 196 | 197 | 198 | **Vantagens:** 199 | 200 | a) $E[ a(t) \mid a(t-1 )]= a (t-1)$ e o mesmo vale para $b(t)$ e $c(t) \Rightarrow$ constância local. 201 | 202 | b) $Var[ a(t) \mid a(t-1 )]= d_c^{-1}$ e o mesmo vale para $b(t)$ e $c(t) \Rightarrow$ aumento da incerteza. 203 | 204 | c) Hiperparâmetros $d_a, d_b, d_c$ fáceis de especificar. 205 | 206 | Exemplos: 207 | $$d=1000 \ \to \ 0,90= P ( 0,95 < w(t) < 1,05 ) = P \left( 0,95 < \frac {a(t)}{a(t-1) } < 1,05 \right)$$ 208 | $$d=1500 \ \to \ 0,95= P ( 0,95 < w(t) < 1,05 ) = P \left( 0,95 < \frac {a(t)}{a(t-1) } < 1,05 \right)$$ 209 | 210 | 211 | **Problemas:** 212 | 213 | a) As magnitures de $a, b, c$ ainda interferem no aumento da incerteza. 214 | 215 | b) não sei se software lida bem com Gammas tendo parâmetros tão altos. 216 | 217 | 218 | **Evolução multiplicativa com erros normais** 219 | 220 | Considere a evolução multiplicativa abaixo para o parâmetro $a$: 221 | 222 | $$a ( t ) = a ( t-1) \times \exp \{ w_a ( t ) \}, \mbox{ onde } w_a ( t ) \sim N( 0 , W_a )$$ 223 | Tomando o logartimo nos dois lados, obtem-se: 224 | $$\log \ a ( t ) = \log \ a ( t-1) + w_a ( t ), \mbox{ onde } w_a ( t ) \sim N( 0 , W_a )$$ 225 | Passando $\log \ a ( t-1)$ para a esquerda, vem que: 226 | $$\log \ a ( t ) - \log \ a ( t-1) = \log \left[ \frac{ a ( t )}{ a ( t-1)} \right] = w_a ( t ), \mbox{ onde } w_a ( t ) \sim N( 0 , W_a )$$ 227 | 228 | Especificação de $W_a$: pode-se pensar em percentual de incremento, como antes. 229 | 230 | $$0,95 = P \left( 0,95 < \frac {a(t)}{a(t-1) } < 1,05 \right) = P ( - 0,05 < w_a(t) < 0,05 )$$ 231 | Isso implica $2 \sqrt{W_a} = 0,05$, que implica $\sqrt{W_a} = 0,025 \ \Rightarrow W_a = (0,025)^2$. 232 | 233 | Mesma especificação vale para $W_b$ e $W_c$, pois dimensões de $b$ e $c$ não importam. 234 | 235 | 236 | **Caso particular** 237 | 238 | Baseado em Gamerman, Santos e Franco (J. Time Series Analysis, 2013): 239 | 240 | $$\mu ( t ) = \frac{ a( {\color{red}t)} \ \exp{ \{ c \ t \} } } {1 + b \ \exp { \{ c \ t \} }}$$ 241 | $a ( t ) = a ( t-1) \times w_a ( t )$, onde $ w_a ( t ) \sim Beta, \forall t$. 242 | 243 | Pode ser usado também para crescimento exponencial ($b=0$). 244 | 245 | 246 | **Vantagem:** 247 | 248 | a) Permite contas exatas, dispensando aproximações MCMC. 249 | 250 | 251 | **Desvantagem:** 252 | 253 | a) Não permite $b$ e $c$ dinâmicos. 254 | 255 | #### Generalizações da logística 256 | 257 | Até agora, usamos a logística para especificar a média $\mu ( t )$ como 258 | $$\mu ( t ) = \frac{ a \exp{ \{ c t \} } } {1 + b \exp { \{ ct \} }} = \frac{ a} { b + \exp { \{ - ct \} }}.$$ 259 | Essa expressão é a forma mais simples da logística. 260 | 261 | Ela pode ser generalizada de várias formas. Uma possível forma da **logística generalizada** é 262 | $$\mu ( t ) = d + \frac{ a - d} {( b + \exp { \{ - ct \} } )^f}$$ 263 | 264 | A logística é obtida fazendo $d=0$ e $f=1$. 265 | -------------------------------------------------------------------------------- /R/JAGS/predict_confirmed_par.R: -------------------------------------------------------------------------------- 1 | rm(list=ls()) 2 | 3 | setwd("/run/media/marcos/OS/UFMG/Pesquisa/Covid/R/JAGS") 4 | 5 | ################################################################### 6 | ### Packages 7 | ################################################################### 8 | library(dplyr) 9 | library(tidyr) 10 | library("rjags") 11 | library(matrixStats) 12 | library(mcmcplots) 13 | library(foreach) 14 | library(doMC) 15 | 16 | ################################################################### 17 | ### Data sets: https://github.com/CSSEGISandData 18 | ################################################################### 19 | baseURL = "https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series" 20 | source("loadData.R") 21 | 22 | covid19_confirm <- loadData("time_series_covid19_confirmed_global.csv", "confirmed") 23 | # covid19_recover <- loadData("time_series_covid19_recovered_global.csv", "recovered") 24 | covid19_deaths <- loadData("time_series_covid19_deaths_global.csv", "deaths") 25 | 26 | covid19 <- covid19_confirm %>% left_join(covid19_deaths) 27 | 28 | #countrylist = "Korea, South" 29 | countrylist <- c("Argentina","Australia","Belgium","Bolivia","Canada","Chile","China","Colombia","Ecuador","France","Germany","Greece", "India", "Iran", "Ireland", "Italy", "Japan", "Korea, South", "Mexico", "Netherlands", "New Zealand", "Norway", "Peru", "Paraguay", "Poland", "Portugal", "Russia", "South Africa", "Spain","United Kingdom", "Uruguay", "Sweden", "Switzerland", "US", "Turkey", "Venezuela") 30 | 31 | #countrylist <- c("Argentina","Bolivia","Canada","Chile","Colombia","Ecuador", "Greece", "India", "Japan", "Korea, South", "Mexico", "Peru", "Paraguay", "Poland", "Russia", "South Africa", "United Kingdom", "Uruguay", "Sweden", "US", "Venezuela") 32 | 33 | country_pop <- read.csv("../pop/pop_WR.csv") 34 | 35 | #register cores 36 | registerDoMC(cores = detectCores()-1) # Alternativa Linux 37 | 38 | #for(country_name in countrylist){ 39 | obj <- foreach(s = 1:length(countrylist) ) %dopar% { 40 | 41 | country_name <- countrylist[s] 42 | 43 | pop <- country_pop$pop[which(country_pop$country == country_name)] 44 | 45 | covid_states <- covid19 %>% filter(country==country_name) %>% 46 | mutate(confirmed_new = confirmed - lag(confirmed, default=0), 47 | # recovered_new = recovered - lag(recovered, default=0), 48 | deaths_new = deaths - lag(deaths, default=0)) %>% 49 | arrange(date,state) 50 | 51 | covid_country <- covid_states %>% group_by(date) %>% 52 | summarize(n = sum(confirmed, na.rm=T), 53 | d = sum(deaths, na.rm=T), 54 | n_new = sum(confirmed_new, na.rm=T), 55 | d_new = sum(deaths_new, na.rm=T)) %>% 56 | arrange(date) %>% filter(date>='2020-01-23') 57 | 58 | # covid_country <- covid19 %>% filter(country==country_name) %>% 59 | # mutate(n_new = confirmed - lag(confirmed, default=0), 60 | # d_new = deaths - lag(deaths, default=0)) %>% 61 | # rename(n = confirmed, 62 | # d = deaths) %>% 63 | # arrange(date) %>% filter(date>='2020-01-01') %>% 64 | # select(-c("state","country")) 65 | 66 | # covid_country %>% print(n=Inf) 67 | 68 | ########################################################################### 69 | ###### JAGS 70 | ########################################################################### 71 | Y = covid_country 72 | 73 | while(any(Y$n_new <0)){ 74 | pos <- which(Y$n_new <0) 75 | for(j in pos){ 76 | Y$n_new[j-1] = Y$n_new[j] + Y$n_new[j-1] 77 | Y$n_new[j] = 0 78 | Y$n[j-1] = Y$n[j] 79 | } 80 | } 81 | 82 | t = dim(Y)[1] 83 | 84 | source("jags_poisson.R") 85 | 86 | i = 4 # (2: confirmed, 3: deaths) 87 | L = 300 88 | #t0 = Sys.time() 89 | 90 | params = c("a","b","c","f","yfut","mu") 91 | nc = 1 # 3 92 | nb = 90e3 # 5e4 93 | thin = 10 94 | ni = 10e3 # 5e4 95 | data_jags = list(y=Y[[i]], t=t, L=L) 96 | 97 | mod = try(jags.model(textConnection(mod_string_new), data=data_jags, n.chains=nc, n.adapt=nb, quiet=TRUE)) 98 | try(update(mod, n.iter=ni, progress.bar="none")) 99 | mod_sim = try(coda.samples(model=mod, variable.names=params, n.iter=ni, thin=thin,progress.bar="none")) 100 | 101 | if(class(mod_sim) != "try-error" && class(mod) != "try-error"){ 102 | mod_chain = as.data.frame(do.call(rbind, mod_sim)) 103 | # names(mod_chain) 104 | 105 | a_pos = "a" 106 | b_pos = "b" 107 | c_pos = "c" 108 | f_pos = "f" 109 | mu_pos = paste0("mu[",1:(t+L),"]") 110 | yfut_pos = paste0("yfut[",1:L,"]") 111 | L0 = 14 112 | 113 | mod_chain_y = as.matrix(mod_chain[yfut_pos]) 114 | mod_chain_cumy = rowCumsums(mod_chain_y) + Y[[2]][t] 115 | 116 | 117 | ### list output 118 | df_predict <- data.frame( date = as.Date((max(Y$date)+1):(max(Y$date)+L0), origin="1970-01-01"), 119 | q25 = colQuantiles(mod_chain_cumy[,1:L0], prob=.025), 120 | med = colQuantiles(mod_chain_cumy[,1:L0], prob=.5), 121 | q975 = colQuantiles(mod_chain_cumy[,1:L0], prob=.975), 122 | m = colMeans(mod_chain_cumy[,1:L0])) 123 | row.names(df_predict) <- NULL 124 | 125 | lt_predict <- lt_summary <- NULL 126 | 127 | #longterm 128 | L0 = 200 129 | 130 | #acha a curva de quantil 131 | lowquant <- colQuantiles(mod_chain_y[,1:L0], prob=.025) 132 | medquant <- colQuantiles(mod_chain_y[,1:L0], prob=.5) 133 | highquant <- colQuantiles(mod_chain_y[,1:L0], prob=.975) 134 | 135 | NTC25 =sum(lowquant)+Y[[2]][t] 136 | NTC500=sum(medquant)+Y[[2]][t] 137 | NTC975=sum(highquant)+Y[[2]][t] 138 | 139 | 140 | ##flag 141 | cm <- pop * 0.025 142 | ch <- pop * 0.03 143 | flag <- 0 #tudo bem 144 | {if(NTC500 > cm) flag <- 2 #nao plotar 145 | else{if(NTC975 > ch){flag <- 1; NTC25 <- NTC975 <- NULL}}} #plotar so mediana 146 | 147 | #vetor de data futuras e pega a posicao do maximo do percentil 25. 148 | dat.vec <- as.Date((max(Y$date)+1):(max(Y$date)+L0), origin="1970-01-01") 149 | dat.full <- c(Y[[1]],dat.vec) 150 | 151 | 152 | Dat25 <- Dat500 <- Dat975 <- NULL 153 | dat.low.end <- dat.med.end <- dat.high.end <- NULL 154 | 155 | mod_chain_mu = as.matrix(mod_chain[mu_pos]) 156 | mu50 <- apply(mod_chain_mu,2,quantile, probs=0.5) 157 | Dat500 <- dat.full[which.max(mu50[1:(t+L0)])] 158 | 159 | q <- .99 160 | med.cum <- c(medquant[1]+Y[[2]][t],medquant[2:length(medquant)]) 161 | med.cum <- colCumsums(as.matrix(med.cum)) 162 | med.cum <- med.cum/med.cum[length(med.cum)] 163 | med.end <- which(med.cum - q > 0)[1] 164 | dat.med.end <- dat.vec[med.end] 165 | 166 | if(flag == 0){ 167 | #definicao do pico usando a curva das medias 168 | mu25 <- apply(mod_chain_mu,2,quantile, probs=0.025) 169 | mu975 <- apply(mod_chain_mu,2,quantile, probs=.975) 170 | 171 | posMax.q25 <- which.max(mu25[1:(t+L0)]) 172 | aux <- mu975 - mu25[posMax.q25] 173 | aux2 <- aux[posMax.q25:(t+L0)] 174 | val <- min(aux2[aux2>0]) 175 | dat.max <- which(aux == val) 176 | 177 | aux <- mu975 - mu25[posMax.q25] 178 | aux2 <- aux[1:posMax.q25] 179 | val <- min(aux2[aux2>0]) 180 | dat.min <- which(aux == val) 181 | 182 | Dat25 <- dat.full[dat.min] 183 | Dat975 <- dat.full[dat.max] 184 | 185 | #calcula o fim da pandemia 186 | low.cum <- c(lowquant[1]+Y[[2]][t],lowquant[2:length(lowquant)]) 187 | low.cum <- colCumsums(as.matrix(low.cum)) 188 | low.cum <- low.cum/low.cum[length(low.cum)] 189 | low.end <- which(low.cum - q > 0)[1] 190 | dat.low.end <- dat.vec[low.end] 191 | 192 | high.cum <- c(highquant[1]+Y[[2]][t],highquant[2:length(highquant)]) 193 | high.cum <- colCumsums(as.matrix(high.cum)) 194 | high.cum <- high.cum/high.cum[length(high.cum)] 195 | high.end <- which(high.cum - q > 0)[1] 196 | dat.high.end <- dat.vec[high.end] 197 | } 198 | 199 | lt_predict <- data.frame( date = dat.vec, 200 | q25 = lowquant, 201 | med = medquant, 202 | q975 = highquant, 203 | m = colMeans(mod_chain_y[,1:L0])) 204 | row.names(lt_predict) <- NULL 205 | 206 | lt_summary <- list(NTC25=NTC25, 207 | NTC500=NTC500, 208 | NTC975=NTC975, 209 | high.dat.low=Dat25, 210 | high.dat.med=Dat500, 211 | high.dat.upper=Dat975, 212 | end.dat.low = dat.low.end, 213 | end.dat.med = dat.med.end, 214 | end.dat.upper = dat.high.end) 215 | 216 | muplot <- data.frame(date = dat.full, mu = mu50[1:(t+L0)]) 217 | list_out <- list( df_predict = df_predict, lt_predict=lt_predict, lt_summary=lt_summary, mu_plot = muplot, flag=flag) 218 | name.to.save <- gsub(" ", "-", country_name) 219 | 220 | ### saveRDS 221 | results_directory = "/run/media/marcos/OS/UFMG/Pesquisa/Covid/app_COVID19/STpredictions/" 222 | #results_directory = getwd()#'C:/Users/ricar/Dropbox/covid19/R/predict/' 223 | name.file <- paste0(results_directory,name.to.save,'_',colnames(Y)[2],'.rds') 224 | saveRDS(list_out, file=name.file) 225 | 226 | source("mcmcplot_country.R") 227 | report_directory = "/run/media/marcos/OS/UFMG/Pesquisa/Covid/app_COVID19/STpredictions/reports" 228 | #mcmcplot_country(mcmcout = mod_sim, parms = c(paste0("a[",t,"]"), paste0("b[",t,"]"), paste0("c[",t,"]")), 229 | mcmcplot_country(mcmcout = mod_sim, parms = c("a", "b", "c", "f"), 230 | dir = report_directory, 231 | filename = paste0(country_name,'_',colnames(Y)[i],'_diagnostics'), 232 | heading = paste0(country_name,'_',colnames(Y)[i]), 233 | extension = "html", greek = TRUE, 234 | country = country_name, 235 | type = colnames(Y)[i]) 236 | } 237 | else print(paste0("ERROR:",country_name)) 238 | } 239 | -------------------------------------------------------------------------------- /R/JAGS/death_confirmed_par.R: -------------------------------------------------------------------------------- 1 | rm(list=ls()) 2 | 3 | setwd("/run/media/marcos/OS/UFMG/Pesquisa/Covid/R/JAGS") 4 | 5 | ################################################################### 6 | ### Packages 7 | ################################################################### 8 | library(dplyr) 9 | library(tidyr) 10 | library("rjags") 11 | library(matrixStats) 12 | library(mcmcplots) 13 | library(foreach) 14 | library(doMC) 15 | 16 | ################################################################### 17 | ### Data sets: https://github.com/CSSEGISandData 18 | ################################################################### 19 | baseURL = "https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series" 20 | source("loadData.R") 21 | 22 | covid19_confirm <- loadData("time_series_covid19_confirmed_global.csv", "confirmed") 23 | # covid19_recover <- loadData("time_series_covid19_recovered_global.csv", "recovered") 24 | covid19_deaths <- loadData("time_series_covid19_deaths_global.csv", "deaths") 25 | 26 | covid19 <- covid19_confirm %>% left_join(covid19_deaths) 27 | 28 | #countrylist = "Korea, South" 29 | countrylist <- c("Argentina","Australia","Belgium","Bolivia","Canada","Chile","China","Colombia","Ecuador","France","Germany","Greece", "India", "Iran", "Ireland", "Italy", "Japan", "Korea, South", "Mexico", "Netherlands", "New Zealand", "Norway", "Peru", "Paraguay", "Poland", "Portugal", "Russia", "South Africa", "Spain","United Kingdom", "Uruguay", "Sweden", "Switzerland", "US", "Turkey", "Venezuela") 30 | 31 | #countrylist <- c("Argentina","Bolivia","Canada","Chile","Colombia","Ecuador", "Greece", "India", "Japan", "Korea, South", "Mexico", "Peru", "Paraguay", "Poland", "Russia", "South Africa", "United Kingdom", "Uruguay", "Sweden", "US", "Venezuela") 32 | 33 | country_pop <- read.csv("../pop/pop_WR.csv") 34 | 35 | #register cores 36 | registerDoMC(cores = detectCores()-1) # Alternativa Linux 37 | 38 | #for(country_name in countrylist){ 39 | obj <- foreach(s = 1:length(countrylist) ) %dopar% { 40 | 41 | country_name <- countrylist[s] 42 | 43 | pop <- country_pop$pop[which(country_pop$country == country_name)] 44 | 45 | covid_states <- covid19 %>% filter(country==country_name) %>% 46 | mutate(confirmed_new = confirmed - lag(confirmed, default=0), 47 | # recovered_new = recovered - lag(recovered, default=0), 48 | deaths_new = deaths - lag(deaths, default=0)) %>% 49 | arrange(date,state) 50 | 51 | covid_country <- covid_states %>% group_by(date) %>% 52 | summarize(n = sum(confirmed, na.rm=T), 53 | d = sum(deaths, na.rm=T), 54 | n_new = sum(confirmed_new, na.rm=T), 55 | d_new = sum(deaths_new, na.rm=T)) %>% 56 | arrange(date) %>% filter(date>='2020-01-23') 57 | 58 | # covid_country <- covid19 %>% filter(country==country_name) %>% 59 | # mutate(n_new = confirmed - lag(confirmed, default=0), 60 | # d_new = deaths - lag(deaths, default=0)) %>% 61 | # rename(n = confirmed, 62 | # d = deaths) %>% 63 | # arrange(date) %>% filter(date>='2020-01-23') %>% 64 | # select(-c("state","country")) 65 | 66 | # covid_country %>% print(n=Inf) 67 | 68 | ########################################################################### 69 | ###### JAGS 70 | ########################################################################### 71 | Y = covid_country 72 | 73 | while(any(Y$d_new <0)){ 74 | pos <- which(Y$d_new <0) 75 | for(j in pos){ 76 | Y$d_new[j-1] = Y$d_new[j] + Y$d_new[j-1] 77 | Y$d_new[j] = 0 78 | Y$d[j-1] = Y$d[j] 79 | } 80 | } 81 | 82 | t = dim(Y)[1] 83 | 84 | source("jags_poisson.R") 85 | 86 | i = 5 # (2: confirmed, 3: deaths) 87 | L = 300 88 | #t0 = Sys.time() 89 | 90 | #use static to provide initial values 91 | params = c("a","b","c","f","yfut","mu") 92 | nc = 1 # 3 93 | nb = 90e3 # 5e4 94 | thin = 10 95 | ni = 10e3 # 5e4 96 | data_jags = list(y=Y[[i]], t=t, L=L) 97 | mod = try(jags.model(textConnection(mod_string_new), data=data_jags, n.chains=nc, n.adapt=nb, quiet=TRUE)) 98 | try(update(mod, n.iter=ni, progress.bar="none")) 99 | mod_sim = try(coda.samples(model=mod, variable.names=params, n.iter=ni, thin=thin,progress.bar="none")) 100 | 101 | if(class(mod_sim) != "try-error" && class(mod) != "try-error"){ 102 | mod_chain = as.data.frame(do.call(rbind, mod_sim)) 103 | # names(mod_chain) 104 | 105 | a_pos = "a" 106 | b_pos = "b" 107 | c_pos = "c" 108 | f_pos = "f" 109 | mu_pos = paste0("mu[",1:(t+L),"]") 110 | yfut_pos = paste0("yfut[",1:L,"]") 111 | L0 = 14 112 | 113 | mod_chain_y = as.matrix(mod_chain[yfut_pos]) 114 | mod_chain_cumy = rowCumsums(mod_chain_y) + Y[[3]][t] 115 | 116 | 117 | ### list output 118 | df_predict <- data.frame( date = as.Date((max(Y$date)+1):(max(Y$date)+L0), origin="1970-01-01"), 119 | q25 = colQuantiles(mod_chain_cumy[,1:L0], prob=.025), 120 | med = colQuantiles(mod_chain_cumy[,1:L0], prob=.5), 121 | q975 = colQuantiles(mod_chain_cumy[,1:L0], prob=.975), 122 | m = colMeans(mod_chain_cumy[,1:L0])) 123 | row.names(df_predict) <- NULL 124 | 125 | lt_predict <- lt_summary <- NULL 126 | 127 | #longterm 128 | L0 = 200 129 | 130 | #acha a curva de quantil 131 | lowquant <- colQuantiles(mod_chain_y[,1:L0], prob=.025) 132 | medquant <- colQuantiles(mod_chain_y[,1:L0], prob=.5) 133 | highquant <- colQuantiles(mod_chain_y[,1:L0], prob=.975) 134 | 135 | NTC25 =sum(lowquant)+Y[[3]][t] 136 | NTC500=sum(medquant)+Y[[3]][t] 137 | NTC975=sum(highquant)+Y[[3]][t] 138 | 139 | 140 | ##flag 141 | cm <- pop * 0.025 * 0.12 142 | ch <- pop * 0.03 * 0.15 143 | flag <- 0 #tudo bem 144 | {if(NTC500 > cm) flag <- 2 #nao plotar 145 | else{if(NTC975 > ch){flag <- 1; NTC25 <- NTC975 <- NULL}}} #plotar so mediana 146 | 147 | #vetor de data futuras e pega a posicao do maximo do percentil 25. 148 | dat.vec <- as.Date((max(Y$date)+1):(max(Y$date)+L0), origin="1970-01-01") 149 | dat.full <- c(Y[[1]],dat.vec) 150 | 151 | 152 | Dat25 <- Dat500 <- Dat975 <- NULL 153 | dat.low.end <- dat.med.end <- dat.high.end <- NULL 154 | 155 | mod_chain_mu = as.matrix(mod_chain[mu_pos]) 156 | mu50 <- apply(mod_chain_mu,2,quantile, probs=0.5) 157 | Dat500 <- dat.full[which.max(mu50[1:(t+L0)])] 158 | 159 | q <- .99 160 | med.cum <- c(medquant[1]+Y[[3]][t],medquant[2:length(medquant)]) 161 | med.cum <- colCumsums(as.matrix(med.cum)) 162 | med.cum <- med.cum/med.cum[length(med.cum)] 163 | med.end <- which(med.cum - q > 0)[1] 164 | dat.med.end <- dat.vec[med.end] 165 | 166 | if(flag == 0){ 167 | #definicao do pico usando a curva das medias 168 | mu25 <- apply(mod_chain_mu,2,quantile, probs=0.025) 169 | mu975 <- apply(mod_chain_mu,2,quantile, probs=.975) 170 | 171 | posMax.q25 <- which.max(mu25[1:(t+L0)]) 172 | aux <- mu975 - mu25[posMax.q25] 173 | aux2 <- aux[posMax.q25:(t+L0)] 174 | val <- min(aux2[aux2>0]) 175 | dat.max <- which(aux == val) 176 | 177 | aux <- mu975 - mu25[posMax.q25] 178 | aux2 <- aux[1:posMax.q25] 179 | val <- min(aux2[aux2>0]) 180 | dat.min <- which(aux == val) 181 | 182 | Dat25 <- dat.full[dat.min] 183 | Dat975 <- dat.full[dat.max] 184 | 185 | #calcula o fim da pandemia 186 | low.cum <- c(lowquant[1]+Y[[3]][t],lowquant[2:length(lowquant)]) 187 | low.cum <- colCumsums(as.matrix(low.cum)) 188 | low.cum <- low.cum/low.cum[length(low.cum)] 189 | low.end <- which(low.cum - q > 0)[1] 190 | dat.low.end <- dat.vec[low.end] 191 | 192 | high.cum <- c(highquant[1]+Y[[3]][t],highquant[2:length(highquant)]) 193 | high.cum <- colCumsums(as.matrix(high.cum)) 194 | high.cum <- high.cum/high.cum[length(high.cum)] 195 | high.end <- which(high.cum - q > 0)[1] 196 | dat.high.end <- dat.vec[high.end] 197 | } 198 | 199 | lt_predict <- data.frame( date = dat.vec, 200 | q25 = lowquant, 201 | med = medquant, 202 | q975 = highquant, 203 | m = colMeans(mod_chain_y[,1:L0])) 204 | row.names(lt_predict) <- NULL 205 | 206 | lt_summary <- list(NTC25=NTC25, 207 | NTC500=NTC500, 208 | NTC975=NTC975, 209 | high.dat.low=Dat25, 210 | high.dat.med=Dat500, 211 | high.dat.upper=Dat975, 212 | end.dat.low = dat.low.end, 213 | end.dat.med = dat.med.end, 214 | end.dat.upper = dat.high.end) 215 | 216 | muplot <- data.frame(date = dat.full, mu = mu50[1:(t+L0)]) 217 | list_out <- list( df_predict = df_predict, lt_predict=lt_predict, lt_summary=lt_summary, mu_plot = muplot, flag=flag) 218 | name.to.save <- gsub(" ", "-", country_name) 219 | 220 | ### saveRDS 221 | results_directory = "/run/media/marcos/OS/UFMG/Pesquisa/Covid/app_COVID19/STpredictions/" 222 | #results_directory = getwd()#'C:/Users/ricar/Dropbox/covid19/R/predict/' 223 | name.file <- paste0(results_directory,name.to.save,'_',colnames(Y)[3],'.rds') 224 | saveRDS(list_out, file=name.file) 225 | 226 | source("mcmcplot_country.R") 227 | report_directory = "/run/media/marcos/OS/UFMG/Pesquisa/Covid/app_COVID19/STpredictions/reports" 228 | #mcmcplot_country(mcmcout = mod_sim, parms = c(paste0("a[",t,"]"), paste0("b[",t,"]"), paste0("c[",t,"]")), 229 | mcmcplot_country(mcmcout = mod_sim, parms = c("a", "b", "c", "f"), 230 | dir = report_directory, 231 | filename = paste0(country_name,'_',colnames(Y)[i],'_diagnostics'), 232 | heading = paste0(country_name,'_',colnames(Y)[i]), 233 | extension = "html", greek = TRUE, 234 | country = country_name, 235 | type = colnames(Y)[i]) 236 | } 237 | else print(paste0("ERROR:",country_name)) 238 | } 239 | -------------------------------------------------------------------------------- /app_v1/www/CoronaUFMG_MD.Rmd: -------------------------------------------------------------------------------- 1 | --- 2 | title: "Modelando a pandemia de Covid19" 3 | author: "Dani Gamerman" 4 | # output: slidy_presentation 5 | output: 6 | html_document: 7 | toc: false 8 | # toc_depth: 5 9 | # toc_float: true 10 | --- 11 | 12 | 13 | ### Modelando a pandemia de Covid19 14 | 15 | Dani Gamerman - Programa de PG em Estatística - UFMG 16 | 17 | *1º semestre de 2020* 18 | 19 | (motivado a partir de notas de José Marcos Andrade Figueiredo - UFMG) 20 | 21 |
22 | #### Modelo de crescimento logı́stico básico 23 | 24 | $$ 25 | Y(t) \sim N ( \mu (t) , \sigma^2 ), \qquad t = 1, 2, ... 26 | $$ 27 | 28 | onde $Y(t)$ é o **número de casos acumulados** até o dia $t$ em uma dada região, com $\mu ( t ) = \frac{ a .\, \exp{ \{ c t \} } } {1 + b .\, \exp { \{ c t \} }}.$ 29 | 30 | 31 | **Caso especial:** 32 | 33 | - $b = 0$ (crescimento exponencial) $\rightarrow \mu(t) = a .\,\exp \{ ct \}$; 34 | 35 | - adequado para os estágios iniciais da pandemia. 36 | 37 | 38 |
39 | ##### **Problemas do modelo básico:** 40 | 41 | a) os dados são **contagens**, e a distribuição normal pressupõe dados contínuos; 42 | 43 | b) a variância deveria aumentar com a magnitude dos dados. 44 | 45 | 46 |
47 | #### Características de interesse 48 | 49 | As características mais importantes são: 50 | 51 | 52 | **1) Taxa de infecção** 53 | 54 | - $c$ mede a velocidade da aceleração e reflete a taxa de infecção da doença. 55 | 56 | 57 | **2) Assíntota** 58 | 59 | $\lim_{t \to \infty} \mu( t) = \lim_{t \to \infty} \frac{ a .\, \exp{ \{ c t \} } } {1 + b .\, \exp { \{ ct \} }} = \frac ab$ 60 | 61 | - Reflete o total de casos acumulados ao longo de toda a pandemia. 62 | 63 | - Crescimento exponencial ($b=0$): assíntota $= \infty$ ! 64 | 65 | 66 | **3) Ponto de inflexão** 67 | 68 | - É o tempo $t^*$ onde o número de novos casos para de crescer e começa a diminuir. 69 | 70 | - Crescimento exponencial ($b=0$): número de novos casos nunca para de crescer! 71 | 72 | 73 | **4) Previsão:** 74 | 75 | - O que podemos dizer sobre $Y (t+k ), \forall k$, para $t$ fixo (hoje)? 76 | 77 | Depende da distribuição de $Y( t)$ mas será sempre dada pela distribuição preditiva de $Y(t+k)$ dado $Y(1:t) = \{ Y( 1) , ... , Y( t ) \}$ - o que foi observado. 78 | 79 | Funciona como se fosse a distribuição a posteriori de $Y(t + k )$. 80 | 81 |
82 | **Resultado útil:** Se $Z$ e $W$ são 2 v. a.'s quaisquer então: 83 | 84 | * $E[Z] = E[ E(Z \mid W ) ]$ 85 | 86 | * $Var[Z] = Var[ E(Z \mid W ) ] + E[ Var( Z \mid W ) ]$ 87 | 88 | Em particular, $E[Y ( t + k ) \mid Y( 1:t)] = E\{ E[ Y ( t + k ) \mid \mu( 1:t)] \mid Y( 1:t) \} = E[ \mu( t+k )] \mid Y( 1:t) ]$, a média a posteriori de $\mu ( t + k )$. 89 | 90 | A inferência para tudo que foi dito acima deve ser reportada através de estimadores pontuais (ex: médias a posteriori), junto com os respectivos intervalos de credibilidade. 91 | 92 |
93 | **5) Número de reprodutibilidade $R_0$** 94 | 95 | $R_0$ é o número esperado de casos secundários de uma doença produzidos por um indivíduo infectado. 96 | 97 | No tempo $t$, ele é definido como $R_0 = \frac {\mu ( t ) - \mu ( t-1)}{\mu ( t-1)} = \frac {\mu ( t )}{\mu ( t-1)} - 1$. 98 | 99 | - **Início da epidemia:** $1 \gg b \exp { \{ ct \} } \to \mu (t) \approx a \exp { \{ ct \} } \to R_0 \approx e^c - 1$ 100 | 101 | - **Final da epidemia:** $1 \ll b \exp { \{ ct \} } \to \mu (t) \approx a / b \to R_0 \approx 0$ 102 | 103 | - **Meio da epidemia:** $R_0$ é função dos parâmetros $(a,b,c)$ e do tempo $t$, e é dado por $R_0 (t) = e^c \ \frac{1 + b e^c e^{ct} } {1 + b e^{ct} } \ - \ 1$. 104 | 105 | Para cada $t$ fixado, podemos obter sua distribuição a posteriori (via amostra MCMC) e calcular média, quantis e intervalos de credibilidade. 106 | 107 | 108 | **6) Número médio de novos casos (NMNC)** 109 | 110 | Número médio de novos casos no tempo $t+k$: 111 | 112 | $n_t ( k ) = E [Y ( t + k ) - Y ( t + k -1 ) ] = \mu ( t + k ) - \mu ( t + k -1 )$ 113 | 114 | Logo, NMNC também é função dos parâmetros $(a,b,c)$ e pode ser facilmente calculado. 115 | 116 | Para cada $t$ e $k$ fixados, podemos obter sua distribuição a posteriori (via amostra MCMC) e calcular média, quantis e intervalos de credibilidade. 117 | 118 | 119 | 120 | 121 | 122 | Estimativas e Intervalo de Credibilidade para o pico da pandemia e para o total de casos 123 | 124 |
125 | #### Alternativas: 126 | 127 | 1.1) $Y( t ) \sim Poisson ( \mu ( t ) )$ com $E[ Y(t)] = \mu (t )$ e $Var(Y(t)) = \mu ( t )$ 128 | 129 | 1.2) $Y ( t ) \sim N ( \mu ( t ) , \sigma^2 \ \mu ( t ) )$ com $E[ Y(t)] = \mu (t )$ e $Var(Y(t)) = \sigma^2 \ \mu ( t )$ 130 | 131 | Observações: 132 | 133 | - Modelo (1.2) admite sobredispersão se $\sigma^2 > 1$ 134 | 135 | - Alternativa (1.2) só cuida do comentário (b) 136 | 137 | - Alternativa (1.1) cuida dos 2 comentários mas não permite sobredispersão 138 | 139 |
140 | ##### **Poisson com sobredispersão** 141 | 142 | 1.3) $Y( t ) \mid \epsilon ( t ) \sim Poisson ( \mu ( t ) + \epsilon ( t ) )$ com $E[ \epsilon (t)] = 0$ e $Var( \epsilon (t)) = \sigma^2$ 143 | 144 | 1.4) $Y( t ) \mid \epsilon ( t ) \sim Poisson ( \mu ( t ) \times \epsilon ( t ) )$ com $E[ \epsilon (t)] = 1$ e $Var( \epsilon (t)) = \sigma^2$ 145 | 146 | 147 | Usando os resultados úteis anteriores: 148 | 149 | Mod(1.3): 150 | 151 | - $E [ Y ( t ) ] = E[ E( Y(t) \mid \epsilon (t ) ) ] = E[ \mu ( t ) + \epsilon ( t ) ] = \mu ( t ) + E[ \epsilon ( t ) ] = \mu ( t )$ 152 | 153 | - $Var[ Y ( t ) ] = Var[ E( Y(t) \mid \epsilon (t) ) ] + E[ Var ( Y(t) \mid \epsilon (t) ) ] = Var[ \mu ( t ) + \epsilon ( t ) ] + E [ \mu ( t ) + \epsilon ( t ) ] = \sigma^2 + \mu_t > \mu ( t )$ 154 | 155 | 156 | Mod(1.4): 157 | 158 | - $E [ Y ( t ) ] = E[ E( Y(t) \mid \epsilon (t) ) ] = E[ \mu ( t ) \times \epsilon ( t ) ] = \mu ( t ) \times E[ \epsilon ( t ) ] = \mu ( t )$ 159 | 160 | - $Var[ Y ( t ) ] = Var[ E( Y(t) \mid \epsilon (t) ) ] + E[ Var ( Y(t) \mid \epsilon (t) ) ] = Var[ \mu ( t ) \times \epsilon ( t ) ] + E [ \mu ( t ) \times \epsilon ( t ) ] = \mu_t ^2 \sigma^2 + \mu_t > \mu ( t )$ 161 | 162 | 163 | Ambos preservam média da Poisson e aumentam dispersão da Poisson. 164 | 165 |
166 | #### Extensões dinâmicas 167 | 168 | Modelos anteriores assumem comportamento estático: 169 | 170 | - a forma da doença não se modifica ao longo do tempo; 171 | 172 | - taxa de infecção será sempre a mesma, assintota será sempre a mesma, \... 173 | 174 | **Modelos dinâmicos** flexibilizam isso. 175 | 176 |
177 | ##### 1. **Modelos dinâmicos** 178 | 179 | $\mu ( t ) = \frac{ a( {\color{red} t )} \ \exp{ \{ c( {\color{red}t) } \ t \} } } {1 + b( {\color{red}t) } \ \exp { \{ c({\color{red}t) } \ t \} }}$ 180 | 181 | com: 182 | $a ( t ) = a ( t-1) + w_a ( t )$, onde $w_a ( t ) \sim N ( 0 , W_a ), \forall t$. 183 | 184 | $b ( t ) = b ( t-1) + w_b ( t )$, onde $w_b ( t ) \sim N ( 0 , W_b ), \forall t$. 185 | 186 | $c ( t ) = c ( t-1) + w_c ( t )$, onde $w_c ( t ) \sim N ( 0 , W_c ), \forall t$. 187 | 188 | 189 | **Vantagens:** 190 | 191 | a) $E[ a(t) \mid a(t-1 )]= a (t-1)$, e o mesmo vale para $b(t)$ e $c(t) \Rightarrow$ constância local. 192 | 193 | b) $Var[ a(t) \mid a(t-1 )]= W_a$, e o mesmo vale para $b(t)$ e $c(t) \Rightarrow$ aumento da incerteza. 194 | 195 | **Problemas:** 196 | 197 | a) variâncias $W_a, W_b, W_c$ conhecidas $\Rightarrow$ difíceis de especificar. 198 | 199 | b) variâncias $W_a, W_b, W_c$ deconhecidas $\Rightarrow$ difíceis de estimar. 200 | 201 | c) não dá para simplificar $W_a = W_b = W_c = W$ (magnitudes diferentes de $(a,b,c)$). 202 | 203 |
204 | ##### 2. **Efeito multiplicativo:** 205 | 206 | Outra forma de introduzir dinamismo, agora **multiplicativo**: 207 | 208 | $a ( t ) = a ( t-1) \times w_a ( t )$, onde $w_a ( t ) \sim Gamma ( d_a ,d_a ), \forall t$. 209 | 210 | $b ( t ) = b ( t-1) \times w_b ( t )$, onde $w_b ( t ) \sim Gamma ( d_b ,d_b ), \forall t$. 211 | 212 | $c ( t ) = c ( t-1) \times w_c ( t )$, onde $w_c ( t ) \sim Gamma ( d_c ,d_c ), \forall t$. 213 | 214 | 215 | **Vantagens:** 216 | 217 | a) $E[ a(t) \mid a(t-1 )]= a (t-1)$ e o mesmo vale para $b(t)$ e $c(t) \Rightarrow$ constância local. 218 | 219 | b) $Var[ a(t) \mid a(t-1 )]= d_c^{-1}$ e o mesmo vale para $b(t)$ e $c(t) \Rightarrow$ aumento da incerteza. 220 | 221 | c) Hiperparâmetros $d_a, d_b, d_c$ fáceis de especificar. 222 | 223 | Exemplos: 224 | $d=1000 \ \to \ 0,90= P ( 0,95 < w(t) < 1,05 ) = P \left( 0,95 < \frac {a(t)}{a(t-1) } < 1,05 \right)$ 225 | $d=1500 \ \to \ 0,95= P ( 0,95 < w(t) < 1,05 ) = P \left( 0,95 < \frac {a(t)}{a(t-1) } < 1,05 \right)$ 226 | 227 | **Problemas:** 228 | 229 | a) As magnitures de $a, b, c$ ainda interferem no aumento da incerteza. 230 | 231 | b) não sei se software lida bem com Gammas tendo parâmetros tão altos. 232 | 233 |
234 | ##### 3. **Evolução multiplicativa com erros normais** 235 | 236 | Considere a evolução multiplicativa abaixo para o parâmetro $a$: 237 | 238 | $$a ( t ) = a ( t-1) \times \exp \{ w_a ( t ) \}, \mbox{ onde } w_a ( t ) \sim N( 0 , W_a )$$ 239 | Tomando o logartimo nos dois lados, obtem-se: 240 | $$\log \ a ( t ) = \log \ a ( t-1) + w_a ( t ), \mbox{ onde } w_a ( t ) \sim N( 0 , W_a )$$ 241 | Passando $\log \ a ( t-1)$ para a esquerda, vem que: 242 | $$\log \ a ( t ) - \log \ a ( t-1) = \log \left[ \frac{ a ( t )}{ a ( t-1)} \right] = w_a ( t ), \mbox{ onde } w_a ( t ) \sim N( 0 , W_a )$$ 243 | 244 | Especificação de $W_a$: pode-se pensar em percentual de incremento, como antes. 245 | 246 | $$0,95 = P \left( 0,95 < \frac {a(t)}{a(t-1) } < 1,05 \right) = P ( - 0,05 < w_a(t) < 0,05 )$$ 247 | Isso implica $2 \sqrt{W_a} = 0,05$, que implica $\sqrt{W_a} = 0,025 \ \Rightarrow W_a = (0,025)^2$. 248 | 249 | Mesma especificação vale para $W_b$ e $W_c$, pois dimensões de $b$ e $c$ não importam. 250 | 251 |
252 | - **Caso particular** 253 | 254 | Baseado em Gamerman, Santos e Franco (J. Time Series Analysis, 2013): 255 | 256 | $$\mu ( t ) = \frac{ a( {\color{red}t)} \ \exp{ \{ c \ t \} } } {1 + b \ \exp { \{ c \ t \} }}$$ 257 | $a ( t ) = a ( t-1) \times w_a ( t )$, onde $ w_a ( t ) \sim Beta, \forall t$. 258 | 259 | Pode ser usado também para crescimento exponencial ($b=0$). 260 | 261 | **Vantagem:** 262 | 263 | a) Permite contas exatas, dispensando aproximações MCMC. 264 | 265 | **Desvantagem:** 266 | 267 | a) Não permite $b$ e $c$ dinâmicos. 268 | 269 |
270 | #### Generalizações da logística 271 | 272 | Até agora, usamos a logística para especificar a média $\mu ( t )$ como $\mu ( t ) = \frac{ a \exp{ \{ c t \} } } {1 + b \exp { \{ ct \} }} = \frac{ a} { b + \exp { \{ - ct \} }}$. 273 | 274 | Essa expressão é a forma mais simples da logística. Ela pode ser generalizada de várias formas. 275 | 276 | - Uma possível forma da **logística generalizada** é 277 | $$\mu ( t ) = d + \frac{ a - d} {( b + \exp { \{ - ct \} } )^f}$$ 278 | 279 | A logística é obtida fazendo $d=0$ e $f=1$. 280 | 281 |
282 |
283 | -------------------------------------------------------------------------------- /app_v1/www/markdown/CoronaUFMG_MD.Rmd: -------------------------------------------------------------------------------- 1 | --- 2 | title: "Modelando a pandemia de Covid19" 3 | author: "Dani Gamerman" 4 | # output: slidy_presentation 5 | output: 6 | html_document: 7 | toc: false 8 | # toc_depth: 5 9 | # toc_float: true 10 | --- 11 | 12 | 13 | ### Modelando a pandemia de Covid19 14 | 15 | Dani Gamerman - Programa de PG em Estatística - UFMG 16 | 17 | *1º semestre de 2020* 18 | 19 | (motivado a partir de notas de José Marcos Andrade Figueiredo - UFMG) 20 | 21 |
22 | #### Modelo de crescimento logı́stico básico 23 | 24 | $$ 25 | Y(t) \sim N ( \mu (t) , \sigma^2 ), \qquad t = 1, 2, ... 26 | $$ 27 | 28 | onde $Y(t)$ é o **número de casos acumulados** até o dia $t$ em uma dada região, com $\mu ( t ) = \frac{ a .\, \exp{ \{ c t \} } } {1 + b .\, \exp { \{ c t \} }}.$ 29 | 30 | 31 | **Caso especial:** 32 | 33 | - $b = 0$ (crescimento exponencial) $\rightarrow \mu(t) = a .\,\exp \{ ct \}$; 34 | 35 | - adequado para os estágios iniciais da pandemia. 36 | 37 | 38 |
39 | ##### **Problemas do modelo básico:** 40 | 41 | a) os dados são **contagens**, e a distribuição normal pressupõe dados contínuos; 42 | 43 | b) a variância deveria aumentar com a magnitude dos dados. 44 | 45 | 46 |
47 | #### Características de interesse 48 | 49 | As características mais importantes são: 50 | 51 | 52 | **1) Taxa de infecção** 53 | 54 | - $c$ mede a velocidade da aceleração e reflete a taxa de infecção da doença. 55 | 56 | 57 | **2) Assíntota** 58 | 59 | $\lim_{t \to \infty} \mu( t) = \lim_{t \to \infty} \frac{ a .\, \exp{ \{ c t \} } } {1 + b .\, \exp { \{ ct \} }} = \frac ab$ 60 | 61 | - Reflete o total de casos acumulados ao longo de toda a pandemia. 62 | 63 | - Crescimento exponencial ($b=0$): assíntota $= \infty$ ! 64 | 65 | 66 | **3) Ponto de inflexão** 67 | 68 | - É o tempo $t^*$ onde o número de novos casos para de crescer e começa a diminuir. 69 | 70 | - Crescimento exponencial ($b=0$): número de novos casos nunca para de crescer! 71 | 72 | 73 | **4) Previsão:** 74 | 75 | - O que podemos dizer sobre $Y (t+k ), \forall k$, para $t$ fixo (hoje)? 76 | 77 | Depende da distribuição de $Y( t)$ mas será sempre dada pela distribuição preditiva de $Y(t+k)$ dado $Y(1:t) = \{ Y( 1) , ... , Y( t ) \}$ - o que foi observado. 78 | 79 | Funciona como se fosse a distribuição a posteriori de $Y(t + k )$. 80 | 81 |
82 | **Resultado útil:** Se $Z$ e $W$ são 2 v. a.'s quaisquer então: 83 | 84 | * $E[Z] = E[ E(Z \mid W ) ]$ 85 | 86 | * $Var[Z] = Var[ E(Z \mid W ) ] + E[ Var( Z \mid W ) ]$ 87 | 88 | Em particular, $E[Y ( t + k ) \mid Y( 1:t)] = E\{ E[ Y ( t + k ) \mid \mu( 1:t)] \mid Y( 1:t) \} = E[ \mu( t+k )] \mid Y( 1:t) ]$, a média a posteriori de $\mu ( t + k )$. 89 | 90 | A inferência para tudo que foi dito acima deve ser reportada através de estimadores pontuais (ex: médias a posteriori), junto com os respectivos intervalos de credibilidade. 91 | 92 |
93 | **5) Número de reprodutibilidade $R_0$** 94 | 95 | $R_0$ é o número esperado de casos secundários de uma doença produzidos por um indivíduo infectado. 96 | 97 | No tempo $t$, ele é definido como $R_0 = \frac {\mu ( t ) - \mu ( t-1)}{\mu ( t-1)} = \frac {\mu ( t )}{\mu ( t-1)} - 1$. 98 | 99 | - **Início da epidemia:** $1 \gg b \exp { \{ ct \} } \to \mu (t) \approx a \exp { \{ ct \} } \to R_0 \approx e^c - 1$ 100 | 101 | - **Final da epidemia:** $1 \ll b \exp { \{ ct \} } \to \mu (t) \approx a / b \to R_0 \approx 0$ 102 | 103 | - **Meio da epidemia:** $R_0$ é função dos parâmetros $(a,b,c)$ e do tempo $t$, e é dado por $R_0 (t) = e^c \ \frac{1 + b e^c e^{ct} } {1 + b e^{ct} } \ - \ 1$. 104 | 105 | Para cada $t$ fixado, podemos obter sua distribuição a posteriori (via amostra MCMC) e calcular média, quantis e intervalos de credibilidade. 106 | 107 | 108 | **6) Número médio de novos casos (NMNC)** 109 | 110 | Número médio de novos casos no tempo $t+k$: 111 | 112 | $n_t ( k ) = E [Y ( t + k ) - Y ( t + k -1 ) ] = \mu ( t + k ) - \mu ( t + k -1 )$ 113 | 114 | Logo, NMNC também é função dos parâmetros $(a,b,c)$ e pode ser facilmente calculado. 115 | 116 | Para cada $t$ e $k$ fixados, podemos obter sua distribuição a posteriori (via amostra MCMC) e calcular média, quantis e intervalos de credibilidade. 117 | 118 | 119 | 120 | 121 | 122 | Estimativas e Intervalo de Credibilidade para o pico da pandemia e para o total de casos 123 | 124 |
125 | #### Alternativas: 126 | 127 | 1.1) $Y( t ) \sim Poisson ( \mu ( t ) )$ com $E[ Y(t)] = \mu (t )$ e $Var(Y(t)) = \mu ( t )$ 128 | 129 | 1.2) $Y ( t ) \sim N ( \mu ( t ) , \sigma^2 \ \mu ( t ) )$ com $E[ Y(t)] = \mu (t )$ e $Var(Y(t)) = \sigma^2 \ \mu ( t )$ 130 | 131 | Observações: 132 | 133 | - Modelo (1.2) admite sobredispersão se $\sigma^2 > 1$ 134 | 135 | - Alternativa (1.2) só cuida do comentário (b) 136 | 137 | - Alternativa (1.1) cuida dos 2 comentários mas não permite sobredispersão 138 | 139 |
140 | ##### **Poisson com sobredispersão** 141 | 142 | 1.3) $Y( t ) \mid \epsilon ( t ) \sim Poisson ( \mu ( t ) + \epsilon ( t ) )$ com $E[ \epsilon (t)] = 0$ e $Var( \epsilon (t)) = \sigma^2$ 143 | 144 | 1.4) $Y( t ) \mid \epsilon ( t ) \sim Poisson ( \mu ( t ) \times \epsilon ( t ) )$ com $E[ \epsilon (t)] = 1$ e $Var( \epsilon (t)) = \sigma^2$ 145 | 146 | 147 | Usando os resultados úteis anteriores: 148 | 149 | Mod(1.3): 150 | 151 | - $E [ Y ( t ) ] = E[ E( Y(t) \mid \epsilon (t ) ) ] = E[ \mu ( t ) + \epsilon ( t ) ] = \mu ( t ) + E[ \epsilon ( t ) ] = \mu ( t )$ 152 | 153 | - $Var[ Y ( t ) ] = Var[ E( Y(t) \mid \epsilon (t) ) ] + E[ Var ( Y(t) \mid \epsilon (t) ) ] = Var[ \mu ( t ) + \epsilon ( t ) ] + E [ \mu ( t ) + \epsilon ( t ) ] = \sigma^2 + \mu_t > \mu ( t )$ 154 | 155 | 156 | Mod(1.4): 157 | 158 | - $E [ Y ( t ) ] = E[ E( Y(t) \mid \epsilon (t) ) ] = E[ \mu ( t ) \times \epsilon ( t ) ] = \mu ( t ) \times E[ \epsilon ( t ) ] = \mu ( t )$ 159 | 160 | - $Var[ Y ( t ) ] = Var[ E( Y(t) \mid \epsilon (t) ) ] + E[ Var ( Y(t) \mid \epsilon (t) ) ] = Var[ \mu ( t ) \times \epsilon ( t ) ] + E [ \mu ( t ) \times \epsilon ( t ) ] = \mu_t ^2 \sigma^2 + \mu_t > \mu ( t )$ 161 | 162 | 163 | Ambos preservam média da Poisson e aumentam dispersão da Poisson. 164 | 165 |
166 | #### Extensões dinâmicas 167 | 168 | Modelos anteriores assumem comportamento estático: 169 | 170 | - a forma da doença não se modifica ao longo do tempo; 171 | 172 | - taxa de infecção será sempre a mesma, assintota será sempre a mesma, \... 173 | 174 | **Modelos dinâmicos** flexibilizam isso. 175 | 176 |
177 | ##### 1. **Modelos dinâmicos** 178 | 179 | $\mu ( t ) = \frac{ a( {\color{red} t )} \ \exp{ \{ c( {\color{red}t) } \ t \} } } {1 + b( {\color{red}t) } \ \exp { \{ c({\color{red}t) } \ t \} }}$ 180 | 181 | com: 182 | $a ( t ) = a ( t-1) + w_a ( t )$, onde $w_a ( t ) \sim N ( 0 , W_a ), \forall t$. 183 | 184 | $b ( t ) = b ( t-1) + w_b ( t )$, onde $w_b ( t ) \sim N ( 0 , W_b ), \forall t$. 185 | 186 | $c ( t ) = c ( t-1) + w_c ( t )$, onde $w_c ( t ) \sim N ( 0 , W_c ), \forall t$. 187 | 188 | 189 | **Vantagens:** 190 | 191 | a) $E[ a(t) \mid a(t-1 )]= a (t-1)$, e o mesmo vale para $b(t)$ e $c(t) \Rightarrow$ constância local. 192 | 193 | b) $Var[ a(t) \mid a(t-1 )]= W_a$, e o mesmo vale para $b(t)$ e $c(t) \Rightarrow$ aumento da incerteza. 194 | 195 | **Problemas:** 196 | 197 | a) variâncias $W_a, W_b, W_c$ conhecidas $\Rightarrow$ difíceis de especificar. 198 | 199 | b) variâncias $W_a, W_b, W_c$ deconhecidas $\Rightarrow$ difíceis de estimar. 200 | 201 | c) não dá para simplificar $W_a = W_b = W_c = W$ (magnitudes diferentes de $(a,b,c)$). 202 | 203 |
204 | ##### 2. **Efeito multiplicativo:** 205 | 206 | Outra forma de introduzir dinamismo, agora **multiplicativo**: 207 | 208 | $a ( t ) = a ( t-1) \times w_a ( t )$, onde $w_a ( t ) \sim Gamma ( d_a ,d_a ), \forall t$. 209 | 210 | $b ( t ) = b ( t-1) \times w_b ( t )$, onde $w_b ( t ) \sim Gamma ( d_b ,d_b ), \forall t$. 211 | 212 | $c ( t ) = c ( t-1) \times w_c ( t )$, onde $w_c ( t ) \sim Gamma ( d_c ,d_c ), \forall t$. 213 | 214 | 215 | **Vantagens:** 216 | 217 | a) $E[ a(t) \mid a(t-1 )]= a (t-1)$ e o mesmo vale para $b(t)$ e $c(t) \Rightarrow$ constância local. 218 | 219 | b) $Var[ a(t) \mid a(t-1 )]= d_c^{-1}$ e o mesmo vale para $b(t)$ e $c(t) \Rightarrow$ aumento da incerteza. 220 | 221 | c) Hiperparâmetros $d_a, d_b, d_c$ fáceis de especificar. 222 | 223 | Exemplos: 224 | $d=1000 \ \to \ 0,90= P ( 0,95 < w(t) < 1,05 ) = P \left( 0,95 < \frac {a(t)}{a(t-1) } < 1,05 \right)$ 225 | $d=1500 \ \to \ 0,95= P ( 0,95 < w(t) < 1,05 ) = P \left( 0,95 < \frac {a(t)}{a(t-1) } < 1,05 \right)$ 226 | 227 | **Problemas:** 228 | 229 | a) As magnitures de $a, b, c$ ainda interferem no aumento da incerteza. 230 | 231 | b) não sei se software lida bem com Gammas tendo parâmetros tão altos. 232 | 233 |
234 | ##### 3. **Evolução multiplicativa com erros normais** 235 | 236 | Considere a evolução multiplicativa abaixo para o parâmetro $a$: 237 | 238 | $$a ( t ) = a ( t-1) \times \exp \{ w_a ( t ) \}, \mbox{ onde } w_a ( t ) \sim N( 0 , W_a )$$ 239 | Tomando o logartimo nos dois lados, obtem-se: 240 | $$\log \ a ( t ) = \log \ a ( t-1) + w_a ( t ), \mbox{ onde } w_a ( t ) \sim N( 0 , W_a )$$ 241 | Passando $\log \ a ( t-1)$ para a esquerda, vem que: 242 | $$\log \ a ( t ) - \log \ a ( t-1) = \log \left[ \frac{ a ( t )}{ a ( t-1)} \right] = w_a ( t ), \mbox{ onde } w_a ( t ) \sim N( 0 , W_a )$$ 243 | 244 | Especificação de $W_a$: pode-se pensar em percentual de incremento, como antes. 245 | 246 | $$0,95 = P \left( 0,95 < \frac {a(t)}{a(t-1) } < 1,05 \right) = P ( - 0,05 < w_a(t) < 0,05 )$$ 247 | Isso implica $2 \sqrt{W_a} = 0,05$, que implica $\sqrt{W_a} = 0,025 \ \Rightarrow W_a = (0,025)^2$. 248 | 249 | Mesma especificação vale para $W_b$ e $W_c$, pois dimensões de $b$ e $c$ não importam. 250 | 251 |
252 | - **Caso particular** 253 | 254 | Baseado em Gamerman, Santos e Franco (J. Time Series Analysis, 2013): 255 | 256 | $$\mu ( t ) = \frac{ a( {\color{red}t)} \ \exp{ \{ c \ t \} } } {1 + b \ \exp { \{ c \ t \} }}$$ 257 | $a ( t ) = a ( t-1) \times w_a ( t )$, onde $ w_a ( t ) \sim Beta, \forall t$. 258 | 259 | Pode ser usado também para crescimento exponencial ($b=0$). 260 | 261 | **Vantagem:** 262 | 263 | a) Permite contas exatas, dispensando aproximações MCMC. 264 | 265 | **Desvantagem:** 266 | 267 | a) Não permite $b$ e $c$ dinâmicos. 268 | 269 |
270 | #### Generalizações da logística 271 | 272 | Até agora, usamos a logística para especificar a média $\mu ( t )$ como $\mu ( t ) = \frac{ a \exp{ \{ c t \} } } {1 + b \exp { \{ ct \} }} = \frac{ a} { b + \exp { \{ - ct \} }}$. 273 | 274 | Essa expressão é a forma mais simples da logística. Ela pode ser generalizada de várias formas. 275 | 276 | - Uma possível forma da **logística generalizada** é 277 | $$\mu ( t ) = d + \frac{ a - d} {( b + \exp { \{ - ct \} } )^f}$$ 278 | 279 | A logística é obtida fazendo $d=0$ e $f=1$. 280 | 281 |
282 |
283 | -------------------------------------------------------------------------------- /app_v1/CoronaUFMG_MDen.md: -------------------------------------------------------------------------------- 1 | --- 2 | title: "Modeling the Covid-19 pandemic" 3 | author: "Dani Gamerman" 4 | # output: slidy_presentation 5 | output: 6 | html_document: 7 | toc: true 8 | # toc_depth: 5 9 | # toc_float: true 10 | --- 11 | 12 | 13 | ### Modelling the Covid19 pandemic 14 | 15 | Dani Gamerman - Graduate Program in Statistics - UFMG 16 | 17 | *1st semester 2020* 18 | 19 | (inspired on notes by José Marcos Andrade Figueiredo - UFMG) 20 | 21 |
22 | 23 | #### Basic logistic growth model 24 | 25 | $$ 26 | Y(t) \sim N ( \mu (t) , \sigma^2 ), \qquad t = 1, 2, ... 27 | $$ 28 | 29 | where $Y(t)$ is the **cumulated number of confirmed cases** by day $t$ in a given region, with $\mu ( t ) = \frac{ a \exp{ \{ c t \} } } {1 + b \exp { \{ c t \} }}.$ 30 | 31 | 32 | **Special case:** 33 | 34 | - $b = 0$ (exponential growth) $ \rightarrow \mu(t) = a \exp \{ ct \} $; 35 | 36 | - adequate for early stages of the pandemic. 37 | 38 |
39 | 40 | ##### **Problems of the basic model:** 41 | 42 | a) data are **counts**, and the normal distribution assumes continuous data; 43 | 44 | b) variance should increase with data magnitude. 45 | 46 |
47 | 48 | #### Characteristics of interest 49 | 50 | The most important characteristics are: 51 | 52 |
53 | 54 | **1) Infection rate** 55 | 56 | - $c$ measures the acceleration of growth and reflects the infection rate of the disease. 57 | 58 |
59 | 60 | **2) Assintote** 61 | 62 | $\lim_{t \to \infty} \mu( t) = \lim_{t \to \infty} \frac{ a \exp{ \{ c t \} } } {1 + b \exp { \{ ct \} }} = \frac ab$ 63 | 64 | - Reflects the total number of cases accumulated throughout the whole trajectory of the pandemic. 65 | 66 | - Exponential growth ($b=0$): assintote $= \infty$ ! 67 | 68 |
69 | 70 | **3) Peak of the pandemic** 71 | 72 | - Defined as the time $t^*$ where number of new cases stops growing and starts to decrease. 73 | 74 | - Exponential growth ($b=0$): number of new cases never stops growing! 75 | 76 |
77 | 78 | **4) Prediction** 79 | 80 | - What can be said about $Y (t+k ), \forall k$, for $t$ fixed (today)? 81 | 82 | It depends on the distribution of $Y(t)$ but will always be given by the predictive distribution of $Y(t+k)$ given $Y(1:t) = \{ Y(1) , ... , Y(t) \}$ - what was observed. 83 | 84 | It works as the posterior distribution of $Y(t + k )$. 85 | 86 |
87 | 88 | **Useful result:** If $Z$ and $W$ are any 2 r. v.'s then: 89 | 90 | - $E[Z] = E[ E(Z \mid W ) ]$ 91 | 92 | - $Var[Z] = Var[ E(Z \mid W ) ] + E[ Var( Z \mid W ) ]$ 93 | 94 | In particular, $E[Y ( t + k ) \mid Y( 1:t)] = E\{ E[ Y ( t + k ) \mid \mu( 1:t)] \mid Y( 1:t) \} = E[ \mu( t+k )] \mid Y( 1:t) ]$, the posterior mean of $\mu ( t + k )$. 95 | 96 | Inference about all that was described above should be reported through point estimators (eg: posterior means), along with respective credibility intervals. 97 | 98 |
99 | 100 | **5) Reproducibility rate $R_0$** 101 | 102 | $R_0$ is the expected number of secondary cases of a disease caused by an infected individual. 103 | 104 | At time $t$, it is defined as $R_0 = \frac {\mu ( t ) - \mu ( t-1)}{\mu ( t-1)} = \frac {\mu ( t )}{\mu ( t-1)} - 1$. 105 | 106 | - **Beginning of the pandemic:** $1 \gg b \exp { \{ ct \} } \to \mu (t) \approx a \exp { \{ ct \} } \to R_0 \approx e^c - 1$ 107 | 108 | - **End of the pandemic:** $1 \ll b \exp { \{ ct \} } \to \mu (t) \approx a / b \to R_0 \approx 0$ 109 | 110 | - **Middle of the pandemic:** $R_0$ is a function of parameters $(a,b,c)$ and time $t$, and is given by $R_0 (t) = e^c \ \frac{1 + b e^c e^{ct} } {1 + b e^{ct} } \ - \ 1$. 111 | 112 | For any fixed $t$, one can obtain its posterior distribution (via MCMC sample) and calculate mean, quantiles and credibility intervals. 113 | 114 |
115 | 116 | **6) Mean number of new cases (MNNC)** 117 | 118 | Mean number of new cases at time $t+k$: 119 | 120 | $n_t ( k ) = E [Y ( t + k ) - Y ( t + k -1 ) ] = \mu ( t + k ) - \mu ( t + k -1 )$ 121 | 122 | Thus, MNNC is also a function of parameters $(a,b,c)$ and can be easily calculated. 123 | 124 | For any fixed $t$ and $k$, one can obtain its posterior distribution (via MCMC sample) and calculate mean, quantiles and credibility intervals. 125 | 126 | ![Long Term Graph](FigApp.png Estimates and credibility intervals for the pandemic peak and for the total number of cases") 127 | 128 |
129 | 130 | #### Alternatives: 131 | 132 | 1.1) $Y( t ) \sim Poisson ( \mu ( t ) )$ with $E[ Y(t)] = \mu (t )$ and $Var(Y(t)) = \mu ( t )$ 133 | 134 | 1.2) $Y ( t ) \sim N ( \mu ( t ) , \sigma^2 \ \mu ( t ) )$ with $E[ Y(t)] = \mu (t )$ and $Var(Y(t)) = \sigma^2 \ \mu ( t )$ 135 | 136 | Observações: 137 | 138 | - Model (1.2) admits overdispersion if $\sigma^2 > 1$ 139 | 140 | - Alternative (1.2) only handles comment (b) 141 | 142 | - Alternative (1.1) handles the two comments but does not allow overdispersion 143 | 144 |
145 | 146 | ##### **Poisson with overdispersion** 147 | 148 | 1.3) $Y( t ) \mid \epsilon ( t ) \sim Poisson ( \mu ( t ) + \epsilon ( t ) )$ with $E[ \epsilon (t)] = 0$ and $Var( \epsilon (t)) = \sigma^2$ 149 | 150 | 1.4) $Y( t ) \mid \epsilon ( t ) \sim Poisson ( \mu ( t ) \times \epsilon ( t ) )$ with $E[ \epsilon (t)] = 1$ and $Var( \epsilon (t)) = \sigma^2$ 151 | 152 | 153 | Considering the usefull results presented above: 154 | 155 | Mod(1.3): 156 | 157 | - $E [ Y ( t ) ] = E[ E( Y(t) \mid \epsilon (t ) ) ] = E[ \mu ( t ) + \epsilon ( t ) ] = \mu ( t ) + E[ \epsilon ( t ) ] = \mu ( t )$ 158 | 159 | - $Var[ Y ( t ) ] = Var[ E( Y(t) \mid \epsilon (t) ) ] + E[ Var ( Y(t) \mid \epsilon (t) ) ] = Var[ \mu ( t ) + \epsilon ( t ) ] + E [ \mu ( t ) + \epsilon ( t ) ] = \sigma^2 + \mu_t > \mu ( t )$ 160 | 161 | 162 | Mod(1.4): 163 | 164 | - $E [ Y ( t ) ] = E[ E( Y(t) \mid \epsilon (t) ) ] = E[ \mu ( t ) \times \epsilon ( t ) ] = \mu ( t ) \times E[ \epsilon ( t ) ] = \mu ( t )$ 165 | 166 | - $Var[ Y ( t ) ] = Var[ E( Y(t) \mid \epsilon (t) ) ] + E[ Var ( Y(t) \mid \epsilon (t) ) ] = Var[ \mu ( t ) \times \epsilon ( t ) ] + E [ \mu ( t ) \times \epsilon ( t ) ] = \mu_t ^2 \sigma^2 + \mu_t > \mu ( t )$ 167 | 168 | 169 | Both preserve Poisson mean but increase Poisson dispersion. 170 | 171 |
172 | 173 | #### Dynamic extensions 174 | 175 | Previous models assume static behaviour: 176 | 177 | - shape of the disease does not modify along time; 178 | 179 | - infection rate will always be the same, assintote will always be the same, ... 180 | 181 | **Dynamic models** make it flexible. 182 | 183 |
184 | 185 | ##### 1. **Dynamic models** 186 | 187 | $\mu ( t ) = \frac{ a( {\color{red} t )} \ \exp{ \{ c( {\color{red}t) } \ t \} } } {1 + b( {\color{red}t) } \ \exp { \{ c({\color{red}t) } \ t \} }}$ 188 | 189 | with: 190 | $a ( t ) = a ( t-1) + w_a ( t )$, where $w_a ( t ) \sim N ( 0 , W_a ), \forall t $. 191 | 192 | $b ( t ) = b ( t-1) + w_b ( t )$, where $w_b ( t ) \sim N ( 0 , W_b ), \forall t $. 193 | 194 | $c ( t ) = c ( t-1) + w_c ( t )$, where $w_c ( t ) \sim N ( 0 , W_c ), \forall t $. 195 | 196 | 197 | **Advantages:** 198 | 199 | a) $E[ a(t) \mid a(t-1 )]= a (t-1)$, and the same goes for $b(t)$ and $c(t) \Rightarrow$ local constancy. 200 | 201 | b) $Var[ a(t) \mid a(t-1 )]= W_a$, and the same goes for $b(t)$ and $c(t) \Rightarrow$ increase in uncertainty. 202 | 203 | **Problems:** 204 | 205 | a) variances $W_a, W_b, W_c$ unknown $\Rightarrow$ difficult to specify; 206 | 207 | b) variances $W_a, W_b, W_c$ unknown $\Rightarrow$ difficult to estimate. 208 | 209 | c) it os not possible to simplify $W_a = W_b = W_c = W$ (different magnitudes of $(a,b,c)$). 210 | 211 |
212 | 213 | ##### 2. **Multiplicative effect:** 214 | 215 | Another form to introduce dynamics, now **multiplicative**: 216 | 217 | $a ( t ) = a ( t-1) \times w_a ( t )$, where $w_a ( t ) \sim Gamma ( d_a ,d_a ), \forall t $. 218 | 219 | $b ( t ) = b ( t-1) \times w_b ( t )$, where $w_b ( t ) \sim Gamma ( d_b ,d_b ), \forall t $. 220 | 221 | $c ( t ) = c ( t-1) \times w_c ( t )$, where $w_c ( t ) \sim Gamma ( d_c ,d_c ), \forall t $. 222 | 223 | **Advantages:** 224 | 225 | a) $E[ a(t) \mid a(t-1 )]= a (t-1)$ and the same goes for $b(t)$ and $c(t) \Rightarrow$ local constancy. 226 | 227 | b) $Var[ a(t) \mid a(t-1 )]= d_c^{-1}$ and the same goes for $b(t)$ and $c(t) \Rightarrow$ increase in uncertainty. 228 | 229 | c) Hiperparameters $d_a, d_b, d_c$ easier to specify. 230 | 231 | Examples: 232 | $d=1000 \ \to \ 0,90= P ( 0,95 < w(t) < 1,05 ) = P \left( 0,95 < \frac {a(t)}{a(t-1) } < 1,05 \right)$ 233 | $d=1500 \ \to \ 0,95= P ( 0,95 < w(t) < 1,05 ) = P \left( 0,95 < \frac {a(t)}{a(t-1) } < 1,05 \right)$ 234 | 235 | **Disadvantages:** 236 | 237 | a) Magnitudes of $a, b, c$ still interfere in the increase in uncertainty. 238 | 239 | b) Not sure if free software works fine with Gammas with such high parameter values. 240 | 241 |
242 | 243 | ##### 3. **Multiplicative evolution with normal errors** 244 | 245 | Consider the multiplicative evolution below for parameter $a$: 246 | 247 | $$a ( t ) = a ( t-1) \times \exp \{ w_a ( t ) \}, \mbox{ where } w_a ( t ) \sim N( 0 , W_a )$$ 248 | Taking logarithm on both sides, one obtains: 249 | $$\log \ a ( t ) = \log \ a ( t-1) + w_a ( t ), \mbox{ where } w_a ( t ) \sim N( 0 , W_a )$$ 250 | Passing $\log \ a ( t-1)$ to the left, one obtains: 251 | $$\log \ a ( t ) - \log \ a ( t-1) = \log \left[ \frac{ a ( t )}{ a ( t-1)} \right] = w_a ( t ), \mbox{ where } w_a ( t ) \sim N( 0 , W_a )$$ 252 | 253 | Specification of $W_a$: one can think of percentual increase, as before. 254 | 255 | $$0,95 = P \left( 0,95 < \frac {a(t)}{a(t-1) } < 1,05 \right) = P ( - 0,05 < w_a(t) < 0,05 )$$ 256 | This implies $2 \sqrt{W_a} = 0,05$, that implies $\sqrt{W_a} = 0,025 \ \Rightarrow W_a = (0,025)^2$. 257 | 258 | The same specification is valid for $W_b$ and $W_c$, since magnitudes of $b$ and $c$ do not matter. 259 | 260 |
261 | 262 | - **Special case** 263 | 264 | Based on Gamerman, Santos and Franco (J. Time Series Analysis, 2013): 265 | 266 | $$\mu ( t ) = \frac{ a( {\color{red}t)} \ \exp{ \{ c \ t \} } } {1 + b \ \exp { \{ c \ t \} }}$$ 267 | $a ( t ) = a ( t-1) \times w_a ( t )$, where $ w_a ( t ) \sim Beta, \forall t$. 268 | 269 | It may also be used for exponencial growth($b=0$). 270 | 271 | **Advantage:** 272 | 273 | a) Allows exact calculation, thus avoiding (MCMC) approximations. 274 | 275 | **Disadvantage:** 276 | 277 | a) Does not allow dynamic $b$ and $c$. 278 | 279 |
280 | 281 | #### Generalizations of the logistic curve 282 | 283 | So far, logistic curve was used to specify the mean $\mu ( t )$ as $\mu ( t ) = \frac{ a \exp{ \{ c t \} } } {1 + b \exp { \{ ct \} }} = \frac{ a} { b + \exp { \{ - ct \} }}$. 284 | 285 | This expression is the simplest logistic form. It can be generalized in many ways. One possible form of the **generalized logistic** is 286 | $$\mu ( t ) = d + \frac{ a - d} {( b + \exp { \{ - ct \} } )^f}$$ 287 | 288 | The logistic curve is obtained by taking $d=0$ and $f=1$. 289 | 290 | --------------------------------------------------------------------------------