├── .Rbuildignore ├── .gitignore ├── DESCRIPTION ├── LICENSE.md ├── NAMESPACE ├── R ├── eSAIR.R ├── eSIR.R ├── qh.eSIR.R ├── tvt.eSIR.R ├── tvt.eSIR2.R └── utils.R ├── README.Rmd ├── README.md ├── README_cn.md ├── data ├── USA_state_N.rda ├── confirmed.rda ├── death.rda └── recovered.rda ├── eSIR.Rproj ├── eSIR.pdf ├── install_pkg ├── eSIR_0.2.5.tgz ├── eSIR_0.2.6.tgz ├── eSIR_0.2.7.tgz ├── eSIR_0.2.8.tgz ├── eSIR_0.3.0.tar.gz ├── eSIR_0.3.0.tgz ├── eSIR_0.3.1.tar.gz ├── eSIR_0.3.1.tgz ├── eSIR_0.3.2.tar.gz ├── eSIR_0.3.2.tgz ├── eSIR_0.3.3.tar.gz └── eSIR_0.3.3.tgz ├── man ├── eSAIR.Rd ├── figures │ ├── BDSSM.png │ ├── Hubei_qthetaQ_plot.png │ ├── README-model 3-1.png │ ├── README-model1-1.png │ ├── README-model1-10.png │ ├── README-model1-11.png │ ├── README-model1-12.png │ ├── README-model1-2.png │ ├── README-model1-3.png │ ├── README-model1-4.png │ ├── README-model1-5.png │ ├── README-model1-6.png │ ├── README-model1-7.png │ ├── README-model1-8.png │ ├── README-model1-9.png │ ├── README-model2-1.png │ ├── README-model2-2.png │ ├── RK4.png │ ├── SAIR_ODE.png │ ├── algorithm.png │ ├── eSAIR_compartment.png │ ├── model0.png │ ├── model1.png │ ├── model2.png │ ├── phi.png │ ├── phi_functions.png │ ├── pi.png │ ├── pi_exp.png │ ├── pi_functions.png │ └── priors.png ├── qh.eSIR.Rd ├── tvt.eSIR.Rd └── tvt.eSIR2.Rd └── meta ├── Hubei_exp2_plot_data.RData ├── Hubei_exp_plot_data.RData ├── Hubei_qR0_p.png ├── Hubei_q_Gelman_diag.txt ├── Hubei_q_forecast.png ├── Hubei_q_forecast2.png ├── Hubei_q_spaghetti.png ├── Hubei_q_summary.csv ├── Hubei_qbeta_p.png ├── Hubei_qderiv.png ├── Hubei_qgamma_p.png ├── Hubei_qk_p.png ├── Hubei_qlambdaR_p.png ├── Hubei_qlambdaY_p.png ├── Hubei_qthetaQ_p.png ├── Hubei_qthetaQ_plot.png ├── Hubei_qtheta_p.png ├── Hubei_step2_plot_data.RData └── Hubei_step_plot_data.RData /.Rbuildignore: -------------------------------------------------------------------------------- 1 | ^.*\.Rproj$ 2 | ^\.Rproj\.user$ 3 | ^LICENSE.md$ 4 | ^README.Rmd$ 5 | ^README_cn.md$ 6 | ^eSIR.pdf$ 7 | ^install_binary$ 8 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | .Rproj.user 2 | .Rhistory 3 | .RData 4 | .Ruserdata 5 | -------------------------------------------------------------------------------- /DESCRIPTION: -------------------------------------------------------------------------------- 1 | Package: eSIR 2 | Type: Package 3 | Title: Extended State-Space SIR Models 4 | Version: 0.4.1 5 | Authors@R: c( 6 | person("Lili", "Wang", email = "lilywang@umich.edu", role = c("aut")), 7 | person("Song Lab", role = "aut", comment = ""), 8 | person("Paul", "Egeler", email = "paul.egeler@spectrumhealth.org", role = "ctb", comment = "Spectrum Health Office of Research and Education"), 9 | person("Michael", "Kleinsasser", email = "biostat-cran-manager@umich.edu", role = c("cre")) 10 | ) 11 | Description: An implementation of extended state-space SIR models developed by 12 | Song Lab at UM school of Public Health. There are several functions available 13 | by 1) including a time-varying transmission modifier, 2) adding a time-dependent 14 | quarantine compartment, 3) adding a time-dependent antibody-immunization compartment. 15 | License: CC BY 4.0 16 | Encoding: UTF-8 17 | Imports: 18 | coda (>= 0.19.3), 19 | chron (>= 2.3.54), 20 | data.table (>= 1.12.0), 21 | ggplot2 (>= 3.2.1), 22 | grDevices (>= 3.5.2), 23 | graphics (>= 3.5.2), 24 | gtools (>= 3.8.1), 25 | scales (>= 1.1.0), 26 | stats (>= 3.5.2), 27 | reshape2 (>= 1.4.3), 28 | rjags (>= 4.10), 29 | utils (>= 3.5.2) 30 | Depends: R (>= 3.5.2) 31 | RoxygenNote: 7.1.1 32 | LazyData: true 33 | Suggests: 34 | testthat (>= 3.0.0) 35 | Config/testthat/edition: 3 36 | -------------------------------------------------------------------------------- /LICENSE.md: -------------------------------------------------------------------------------- 1 | Attribution 4.0 International 2 | 3 | ======================================================================= 4 | 5 | Creative Commons Corporation ("Creative Commons") is not a law firm and 6 | does not provide legal services or legal advice. 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For 392 | the avoidance of doubt, this paragraph does not form part of the 393 | public licenses. 394 | 395 | Creative Commons may be contacted at creativecommons.org. 396 | -------------------------------------------------------------------------------- /NAMESPACE: -------------------------------------------------------------------------------- 1 | # Generated by roxygen2: do not edit by hand 2 | 3 | export(eSAIR) 4 | export(qh.eSIR) 5 | export(tvt.eSIR) 6 | export(tvt.eSIR2) 7 | import(chron) 8 | import(coda) 9 | import(data.table) 10 | import(ggplot2) 11 | import(grDevices) 12 | import(graphics) 13 | import(gtools) 14 | import(rjags) 15 | import(scales) 16 | import(stats) 17 | import(utils) 18 | importFrom(coda,as.mcmc.list) 19 | -------------------------------------------------------------------------------- /R/eSAIR.R: -------------------------------------------------------------------------------- 1 | # This is the source code for R package eSIR: extended-SIR 2 | # Added on May 10, 2020, and last edited on Oct 27, 2021 3 | # Correspondence : Peter X.K. Song, Ph.D. (pxsong@umich.edu) 4 | # Creator: Lili Wang, Ph.D. (lilywang@umich.edu) 5 | # An extend SIR with time-varying immunization among a subset of the population, which follows a Dirac Delta function 6 | #' Extended state-space SIR with a subset of the population showing antibody positivity 7 | #' 8 | #' 9 | #' In this function we allow it to characterize time-varying immunization among a subset of the population that have been tested positive in an antibody assessment. We expanded the SIR model by adding a time-varying antibody-positive proportion \eqn{\alpha_t}. 10 | #' 11 | #' @param Y the time series of daily observed infected compartment proportions. 12 | #' @param R the time series of daily observed removed compartment proportions, including death and recovered. 13 | #' @param alpha0 a vector of values of the dirac delta function \eqn{\alpha_t}. Each entry denotes the proportion that will be immunized at each change time point. Note that all the entries lie between 0 and 1, its default is \code{NULL}. 14 | #' @param change_time the change points over time corresponding to \code{alpha0}, to formulate the dirac delta function \eqn{\alpha_t}; its defalt value is \code{NULL}. 15 | #' @param begin_str the character of starting time, the default is "01/13/2020". 16 | #' @param T_fin the end of follow-up time after the beginning date \code{begin_str}, the default is 200. 17 | #' @param nchain the number of MCMC chains generated by \code{\link[rjags]{rjags}}, the default is 4. 18 | #' @param nadapt the iteration number of adaptation in the MCMC. We recommend using at least the default value 1e4 to obtained fully adapted chains. 19 | #' @param M the number of draws in each chain, with no thinning. The default is M=5e2 but suggest using 5e5. 20 | #' @param thn the thinning interval between mixing. The total number of draws thus would become \code{round(M/thn)*nchain}. The default is 10. 21 | #' @param nburnin the burn-in period. The default is 2e2 but suggest 2e5. 22 | #' @param dic logical, whether compute the DIC (deviance information criterion) for model selection. 23 | #' @param death_in_R the numeric value of average of cumulative deaths in the removed compartments. The default is 0.4 within Hubei and 0.02 outside Hubei. 24 | #' @param casename the string of the job's name. The default is "eSAIR". 25 | #' @param beta0 the hyperparameter of average transmission rate, the default is the one estimated from the SARS first-month outbreak (0.2586). 26 | #' @param gamma0 the hyperparameter of average removed rate, the default is the one estimated from the SARS first-month outbreak (0.0821). 27 | #' @param R0 the hyperparameter of the mean reproduction number R0. The default is thus the ratio of \code{beta0/gamma0}, which can be specified directly. 28 | #' @param gamma0_sd the standard deviation for the prior distrbution of the removed rate \eqn{\gamma}, the default is 0.1. 29 | #' @param R0_sd the standard deviation for the prior disbution of R0, the default is 1. 30 | #' @param file_add the string to denote the location of saving output files and tables. 31 | #' 32 | #' @param save_mcmc logical, whether save (\code{TRUE}) all the MCMC outputs or not (\code{FALSE}).The output file will be an \code{.RData} file named by the \eqn{casename}. We include arrays of prevalence values of the three compartments with their matrices of posterior draws up to the last date of the collected data as \code{theta_p[,,1]} and afterwards as \code{theta_pp[,,1]} for \eqn{\theta_t^S}, \code{theta_p[,,2]} and \code{theta_pp[,,2]} for \eqn{\theta_t^I}, and \code{theta_p[,,3]} and \code{theta_pp[,,3]} for \eqn{\theta_t^R}. The posterior draws of the prevalence process of the antibody-immunized compartment can be obtained via \code{thetaA_p} and \code{thetaA_pp}. Moreover, the input and predicted proportions \code{Y}, \code{Y_pp}, \code{R} and \code{R_pp} can also be retrieved. The prevalence and prediceted proportion matrices have rows for MCMC replicates, and columns for days. The MCMC posterior draws of other parameters including \code{beta}, \code{gamma}, \code{R0}, and variance controllers \code{k_p}, \code{lambdaY_p}, \code{lambdaR_p} are also available. 33 | #' @param save_plot_data logical, whether save the plotting data or not. 34 | #' @param save_files logical, whether to save plots to file. 35 | #' @param add_death logical, whether add the approximate death curve to the plot, default is false. 36 | #' @param eps a non-zero controller so that all the input \code{Y} and \code{R} values would be bounded above 0 (at least \code{eps}). Its default value is 1e-10 37 | #' 38 | #' @return 39 | #' \item{casename}{the predefined \code{casename}.} 40 | #' \item{incidence_mean}{mean cumulative incidence, the mean prevalence of cumulative confirmed cases at the end of the study.} 41 | #' \item{incidence_ci}{2.5\%, 50\%, and 97.5\% quantiles of the incidences.} 42 | #' \item{out_table}{summary tables including the posterior mean of the prevalance processes of the 3 states compartments (\eqn{\theta_t^S,\theta_t^I,\theta_t^R,\theta_t^H}) at last date of data collected ((\eqn{t^\prime}) decided by the lengths of your input data \code{Y} and \code{R}), and their respective credible inctervals (ci); the respective means and ci's of the reporduction number (R0), removed rate (\eqn{\gamma}), transmission rate (\eqn{\beta}).} 43 | #' \item{plot_infection}{plot of summarizing and forecasting for the infection compartment, in which the vertial blue line denotes the last date of data collected (\eqn{t^\prime}), the vertial darkgray line denotes the deacceleration point (first turning point) that the posterior mean first-derivative of infection prevalence \eqn{\dot{\theta}_t^I} achieves the maximum, the vertical purple line denotes the second turning point that the posterior mean first-derivative infection proportion \eqn{\dot{\theta}_t^I} equals zero, the darkgray line denotes the posterior mean of the infection prevalence \eqn{\theta_t^I} and the red line denotes its posterior median. } 44 | #' \item{plot_removed}{plot of summarizing and forecasting for the removed compartment with lines similar to those in the \code{plot_infection}. The vertical lines are identical, but the horizontal mean and median correspond to the posterior mean and median of the removed process \eqn{\theta_t^R}. An additional line indicates the estimated death prevalence from the input \code{death_in_R}.} 45 | #' \item{spaghetti_plot}{20 randomly selected MCMC draws of the first-order derivative of the posterior prevalence of infection, namely \eqn{\dot{\theta}_t^I}. The black curve is the posterior mean of the derivative, and the vertical lines mark times of turning points corresponding respectively to those shown in \code{plot_infection} and \code{plot_removed}. Moreover, the 95\% credible intervals of these turning points are also highlighted by semi-transparent rectangles. } 46 | #' \item{first_tp_mean}{the date t at which \eqn{\ddot{\theta}_t^I=0}, calculated as the average of the time points with maximum posterior first-order derivatives \eqn{\dot{\theta}_t^I}; this value may be slightly different from the one labeled by the "darkgreen" lines in the two plots \code{plot_infection} and \code{plot_removed}, which indicate the stationary point such that the first-order derivative of the averaged posterior of \eqn{\theta_t^I} reaches its maximum.} 47 | #' \item{first_tp_mean}{the date t at which \eqn{\ddot{\theta}_t^I=0}, calculated as the average of the time points with maximum posterior first-order derivatives \eqn{\dot{\theta}_t^I}; this value may be slightly different from the one labeled by the "darkgreen" lines in the two plots \code{plot_infection} and \code{plot_removed}, which indicate the stationary point such that the first-order derivative of the averaged posterior of \eqn{\theta_t^I} reaches its maximum.} 48 | #' 49 | #' \item{first_tp_ci}{fwith \code{first_tp_mean}, it reports the corresponding credible interval and median.} 50 | #' \item{second_tp_mean}{the date t at which \eqn{\theta_t^I=0}, calculated as the average of the stationary points of all of posterior first-order derivatives \eqn{\dot{\theta}_t^I}; this value may be slightly different from the one labeled by the "pruple" lines in the plots of \code{plot_infection} and \code{plot_removed}. The latter indicate stationary t at which the first-order derivative of the averaged posterior of \eqn{\theta_t^I} equals zero.} 51 | #' \item{second_tp_ci}{with \code{second_tp_mean}, it reports the corresponding credible interval and median.} 52 | #' \item{dic_val}{the output of \code{dic.samples()} in \code{\link[rjags]{dic.samples}}, computing deviance information criterion for model comparison.} 53 | #' \item{gelman_diag_list}{ Since version 0.3.3, we incorporated Gelman And Rubin's Convergence Diagnostic using \code{\link[coda]{gelman.diag}}. We included both the statistics and their upper C.I. limits. Values substantially above 1 indicate lack of convergence. Error messages would be printed as they are. This would be only valid for multiple chains (e.g. nchain > 1). Note that for time dependent processes, we only compute the convergence of the last observation data (\code{T_prime}), though it shows to be \code{T_prime+1}, which is due to the day 0 for initialization.} 54 | #' 55 | #' @examples 56 | #' \dontrun{ 57 | #' NI_complete <- c( 58 | #' 41, 41, 41, 45, 62, 131, 200, 270, 375, 444, 549, 729, 59 | #' 1052, 1423, 2714, 3554, 4903, 5806, 7153, 9074, 11177, 60 | #' 13522, 16678, 19665, 22112, 24953, 27100, 29631, 31728, 33366 61 | #' ) 62 | #' RI_complete <- c( 63 | #' 1, 1, 7, 10, 14, 20, 25, 31, 34, 45, 55, 71, 94, 64 | #' 121, 152, 213, 252, 345, 417, 561, 650, 811, 1017, 65 | #' 1261, 1485, 1917, 2260, 2725, 3284, 3754 66 | #' ) 67 | #' N <- 58.5e6 68 | #' R <- RI_complete / N 69 | #' Y <- NI_complete / N - R # Jan13->Feb 11 70 | #' change_time <- c("02/08/2020") 71 | #' alpha0 <- c(0.2) # 20% of the susceptible population were found immunized 72 | #' res.antibody <- eSAIR(Y, R, 73 | #' begin_str = "01/13/2020", death_in_R = 0.4, 74 | #' alpha0 = alpha0, change_time = change_time, 75 | #' casename = "Hubei_antibody", save_files = T, save_mcmc = F, 76 | #' M = 5e2, nburnin = 2e2 77 | #' ) 78 | #' res.antibody$plot_infection 79 | #' } 80 | #' 81 | #' change_time <- c("01/16/2020") 82 | #' alpha0 <- c(0.2) 83 | #' NI_complete2 <- c(41, 45) 84 | #' RI_complete2 <- c(1, 1) 85 | #' N2 <- 1E3 86 | #' res3 <- eSAIR( 87 | #' RI_complete2 / N2, 88 | #' NI_complete2 / N2, 89 | #' begin_str = "01/13/2020", 90 | #' T_fin = 4, 91 | #' alpha0 = alpha0, 92 | #' change_time = change_time, 93 | #' dic = FALSE, 94 | #' casename = "Hubei_q", 95 | #' save_files = FALSE, 96 | #' save_mcmc = FALSE, 97 | #' save_plot_data = FALSE, 98 | #' M = 50, 99 | #' nburnin = 1 100 | #' ) 101 | #' closeAllConnections() 102 | #' 103 | #' @export 104 | eSAIR <- function(Y, R, alpha0 = NULL, change_time = NULL, begin_str = "01/13/2020", T_fin = 200, nchain = 4, nadapt = 1e4, M = 5e2, thn = 10, nburnin = 2e2, dic = FALSE, death_in_R = 0.02, casename = "eSAIR", beta0 = 0.2586, gamma0 = 0.0821, R0 = beta0 / gamma0, gamma0_sd = 0.1, R0_sd = 1, file_add = character(0), add_death = FALSE, save_files = FALSE, save_mcmc = FALSE, save_plot_data = FALSE, eps = 1e-10) { 105 | beta0 <- R0 * gamma0 106 | len <- round(M / thn) * nchain # number of MCMC draws in total 107 | 108 | T_prime <- length(Y) 109 | if (T_prime != length(R)) stop("Y and R should be matched.") 110 | if(T_prime >= T_fin) { 111 | warning("T_fin must be larger than input time series Y and R,", 112 | "we will automatically add 100 time units to it: T_fin = length(Y) + 10.") 113 | T_fin = T_prime + 10 114 | } 115 | Y <- pmax(Y, eps) 116 | R <- pmax(R, eps) 117 | if (add_death == T && death_in_R == 0.02) { 118 | message("use the default death_in_R which is equal to 0.02 to plot the death curve in the removed process forecast plot") 119 | } 120 | begin <- chron(dates. = begin_str) 121 | chron_ls <- chron(begin:(begin + T_fin)) 122 | end <- chron(begin:(begin + T_fin))[T_fin] 123 | message(paste0("The follow-up is from ", begin, " to ", end, " and the last observed date is ", chron_ls[T_prime], ".")) # current data up to this date 124 | gamma_var <- gamma0_sd^2 125 | lognorm_gamma_parm <- lognorm.parm(gamma0, gamma_var) 126 | R0_var <- R0_sd^2 127 | lognorm_R0_parm <- lognorm.parm(R0, R0_var) 128 | 129 | message("Running for eSAIR") 130 | 131 | if (length(change_time) != length(alpha0)) { 132 | stop("We need the length of vector change_time to be the length of alpha0. ") 133 | } 134 | change_time_chorn <- chron(dates. = change_time) 135 | alpha_vec <- rep(0, T_fin) 136 | alpha_vec[as.numeric(change_time_chorn - begin)] <- alpha0 137 | 138 | 139 | ################ MCMC ########## 140 | gamma_H_vec <- rep(0, T_fin) # remove the Hospitalization for now 141 | ## gamma_H_vec[as.numeric(change_hospitalization-begin)] <- gamma_H 142 | 143 | ################ MCMC ########## 144 | model2.string <- paste0(" 145 | model{ 146 | for(t in 2:(T_prime+1)){ 147 | Km[t-1,1] <- -beta*theta[t-1,1]*theta[t-1,2] 148 | Km[t-1,9] <- gamma*theta[t-1,2] 149 | Km[t-1,5] <- -Km[t-1,1]-Km[t-1,9] 150 | Km[t-1,2] <- -beta*(theta[t-1,1]+0.5*Km[t-1,1])*(theta[t-1,2]+0.5*Km[t-1,5]) 151 | Km[t-1,10] <- gamma*(theta[t-1,2]+0.5*Km[t-1,5]) 152 | Km[t-1,6] <- -Km[t-1,2]-Km[t-1,10] 153 | Km[t-1,3] <- -beta*(theta[t-1,1]+0.5*Km[t-1,2])*(theta[t-1,2]+0.5*Km[t-1,6]) 154 | Km[t-1,11] <- gamma*(theta[t-1,2]+0.5*Km[t-1,6]) 155 | Km[t-1,7] <- -Km[t-1,3]-Km[t-1,11] 156 | Km[t-1,4] <- -beta*(theta[t-1,1]+Km[t-1,3])*(theta[t-1,2]+Km[t-1,7]) 157 | Km[t-1,12] <- gamma*(theta[t-1,2]+Km[t-1,7]) 158 | Km[t-1,8] <- -Km[t-1,4]-Km[t-1,12] 159 | alpha_temp[t-1,1] <- max(theta[t-1,1]+(Km[t-1,1]+2*Km[t-1,2]+2*Km[t-1,3]+Km[t-1,4])/6-alpha_vec[t-1]*theta[t-1,1],0) 160 | alpha_temp[t-1,2] <- max(theta[t-1,2]+(Km[t-1,5]+2*Km[t-1,6]+2*Km[t-1,7]+Km[t-1,8])/6-gamma_H_vec[t-1]*theta[t-1,2],0) 161 | alpha_temp[t-1,3] <- theta[t-1,3]+(Km[t-1,9]+2*Km[t-1,10]+2*Km[t-1,11]+Km[t-1,12])/6 162 | theta_A[t] <- theta_A[t-1]+min(alpha_vec[t-1]*theta[t-1,1],theta[t-1,1]+(Km[t-1,1]+2*Km[t-1,2]+2*Km[t-1,3]+Km[t-1,4])/6) 163 | theta_H[t] <- theta_H[t-1]+min(gamma_H_vec[t-1]*theta[t-1,2],theta[t-1,2]+(Km[t-1,5]+2*Km[t-1,6]+2*Km[t-1,7]+Km[t-1,8])/6) 164 | v[t-1] <- (1-theta_A[t]-theta_H[t]) 165 | alpha[t-1,1] <- (1-step(-v[t-1]))*alpha_temp[t-1,1]/v[t-1] 166 | alpha[t-1,2] <- (1-step(-v[t-1]))*alpha_temp[t-1,2]/v[t-1] 167 | alpha[t-1,3] <- (1-step(-v[t-1]))*alpha_temp[t-1,3]/v[t-1] 168 | theta_temp[t,1:3] ~ ddirch(k*alpha[t-1,1:3]) 169 | theta[t,1:3] <- v[t-1]*theta_temp[t,1:3] 170 | Y[t-1] ~ dbeta(lambdaY*theta[t,2],lambdaY*(1-theta[t,2])) 171 | R[t-1] ~ dbeta(lambdaR*theta[t,3],lambdaR*(1-theta[t,3])) 172 | } 173 | theta_A[1] <- 0 174 | theta_H[1] <- 0 175 | theta0[1:3]<-c(", 1 - Y[1] - R[1], ",", Y[1], ",", R[1], ") 176 | theta[1,1:3] ~ ddirch(theta0[1:3]) 177 | gamma ~ dlnorm(", lognorm_gamma_parm$mu, ",", 1 / lognorm_gamma_parm$var, ") 178 | R0 ~ dlnorm(", lognorm_R0_parm$mu, ",", 1 / lognorm_R0_parm$var, ") 179 | beta <- R0*gamma 180 | k ~ dgamma(2,0.0001) 181 | lambdaY ~ dgamma(2,0.0001) 182 | lambdaR ~ dgamma(2,0.0001) 183 | } 184 | ") 185 | model.spec <- textConnection(model2.string) 186 | 187 | posterior <- suppressWarnings( 188 | jags.model( 189 | model.spec, 190 | data = list( 191 | "Y" = Y, 192 | "R" = R, 193 | "T_prime" = T_prime, 194 | "alpha_vec" = alpha_vec, 195 | "gamma_H_vec" = gamma_H_vec 196 | ), 197 | n.chains = nchain, 198 | n.adapt = nadapt 199 | ) 200 | ) 201 | 202 | suppressWarnings(update(posterior, nburnin)) # burn-in 203 | 204 | jags_sample <- suppressWarnings( 205 | jags.samples( 206 | posterior, 207 | c("theta", 208 | "theta_H", 209 | "theta_A", 210 | "gamma", 211 | "R0", 212 | "beta", 213 | "Y", 214 | "lambdaY", 215 | "lambdaR", 216 | "k", 217 | "v" 218 | ), 219 | n.iter = M, 220 | thin = thn 221 | ) 222 | ) 223 | 224 | if (dic) { 225 | dic_val <- dic.samples(posterior, n.iter = M, thin = thn) 226 | # message(paste0("DIC is: ", dic_val)) 227 | } else { 228 | dic_val <- NULL 229 | } 230 | 231 | 232 | if (save_files) { 233 | png(paste0(file_add, casename, "theta_p.png"), width = 700, height = 900) 234 | plot(as.mcmc.list(jags_sample$theta)[, (1:3) * (T_prime + 1)]) # posterior true porbabilities 235 | dev.off() 236 | 237 | png(paste0(file_add, casename, "thetaA_p.png"), width = 700, height = 900) 238 | plot(as.mcmc.list(jags_sample$theta_A)[, T_prime], main = "thetaA[T_prime]") # posterior true porbabilities 239 | dev.off() 240 | 241 | 242 | png(paste0(file_add, casename, "R0_p.png"), width = 700, height = 350) 243 | R0_p <- unlist(as.mcmc.list(jags_sample$R0)) 244 | plot(as.mcmc.list(jags_sample$R0)) 245 | dev.off() 246 | png(paste0(file_add, casename, "gamma_p.png"), width = 700, height = 350) 247 | gamma_p <- unlist(as.mcmc.list(jags_sample$gamma)) 248 | plot(as.mcmc.list(jags_sample$gamma)) 249 | dev.off() 250 | 251 | png(paste0(file_add, casename, "beta_p.png"), width = 700, height = 350) 252 | beta_p <- unlist(as.mcmc.list(jags_sample$beta)) 253 | plot(as.mcmc.list(jags_sample$beta)) 254 | dev.off() 255 | 256 | 257 | png(paste0(file_add, casename, "lambdaY_p.png"), width = 700, height = 350) 258 | lambdaY_p <- unlist(as.mcmc.list(jags_sample$lambdaY)) 259 | plot(as.mcmc.list(jags_sample$lambdaY)) 260 | dev.off() 261 | 262 | png(paste0(file_add, casename, "lambdaR_p.png"), width = 700, height = 350) 263 | lambdaR_p <- unlist(as.mcmc.list(jags_sample$lambdaR)) 264 | plot(as.mcmc.list(jags_sample$lambdaR)) 265 | dev.off() 266 | 267 | png(paste0(file_add, casename, "k_p.png"), width = 700, height = 350) 268 | k_p <- unlist(as.mcmc.list(jags_sample$k)) 269 | plot(as.mcmc.list(jags_sample$k)) 270 | dev.off() 271 | } else { 272 | R0_p <- unlist(as.mcmc.list(jags_sample$R0)) 273 | gamma_p <- unlist(as.mcmc.list(jags_sample$gamma)) 274 | beta_p <- unlist(as.mcmc.list(jags_sample$beta)) 275 | lambdaY_p <- unlist(as.mcmc.list(jags_sample$lambdaY)) 276 | lambdaR_p <- unlist(as.mcmc.list(jags_sample$lambdaR)) 277 | k_p <- unlist(as.mcmc.list(jags_sample$k)) 278 | } 279 | 280 | 281 | theta_p <- array(Reduce(rbind, as.mcmc.list(jags_sample$theta)), dim = c(len, T_prime + 1, 3)) 282 | theta_p_mean <- apply(theta_p[, T_prime + 1, ], 2, mean) 283 | theta_p_ci <- as.vector(apply(theta_p[, T_prime + 1, ], 2, quantile, c(0.025, 0.5, 0.975))) 284 | 285 | thetaA_p <- matrix(Reduce(rbind, as.mcmc.list(jags_sample$theta_A)), nrow = len, ncol = T_prime + 1) 286 | thetaH_p <- matrix(Reduce(rbind, as.mcmc.list(jags_sample$theta_H)), nrow = len, ncol = T_prime + 1) 287 | 288 | thetaA_p_mean <- mean(thetaA_p[, T_prime + 1]) 289 | thetaA_p_ci <- quantile(thetaA_p[, T_prime + 1], c(0.025, 0.5, 0.975)) 290 | 291 | R0_p_mean <- mean(R0_p) 292 | R0_p_ci <- quantile(R0_p, c(0.025, 0.5, 0.975)) 293 | 294 | gamma_p_mean <- mean(gamma_p) 295 | gamma_p_ci <- quantile(gamma_p, c(0.025, 0.5, 0.975)) 296 | 297 | beta_p_mean <- mean(beta_p) 298 | beta_p_ci <- quantile(beta_p, c(0.025, 0.5, 0.975)) 299 | 300 | lambdaY_p_mean <- mean(lambdaY_p) 301 | lambdaY_p_ci <- quantile(lambdaY_p, c(0.025, 0.5, 0.975)) 302 | 303 | lambdaR_p_mean <- mean(lambdaR_p) 304 | lambdaR_p_ci <- quantile(lambdaR_p, c(0.025, 0.5, 0.975)) 305 | 306 | k_p_mean <- mean(k_p) 307 | k_p_ci <- quantile(k_p, c(0.025, 0.5, 0.975)) 308 | 309 | #### Forecast #### 310 | theta_pp <- array(0, dim = c(len, T_fin - T_prime, 3)) 311 | thetaA_pp <- thetaH_pp <- matrix(0, nrow = len, ncol = T_fin - T_prime) 312 | 313 | Y_pp <- matrix(NA, nrow = len, ncol = T_fin - T_prime) 314 | R_pp <- matrix(NA, nrow = len, ncol = T_fin - T_prime) 315 | v_pp <- matrix(NA, nrow = len, ncol = T_fin - T_prime) 316 | 317 | for (l in 1:len) { 318 | thetalt1 <- theta_p[l, T_prime + 1, 1] 319 | thetalt2 <- theta_p[l, T_prime + 1, 2] 320 | thetalt3 <- theta_p[l, T_prime + 1, 3] 321 | thetaltH <- thetaH_p[l, T_prime + 1] 322 | thetaltA <- thetaA_p[l, T_prime + 1] 323 | 324 | betal <- c(beta_p)[l] 325 | gammal <- c(gamma_p)[l] 326 | kl <- c(k_p)[l] 327 | lambdaYl <- c(lambdaY_p)[l] 328 | lambdaRl <- c(lambdaR_p)[l] 329 | if (betal < 0 | gammal < 0 | thetalt1 < 0 | thetalt2 < 0 | thetalt3 < 0 | thetaltH < 0 | thetaltA < 0) next 330 | for (t in 1:(T_fin - T_prime)) { 331 | Km <- NULL 332 | theta_temp <- alpha_temp <- alpha <- NULL 333 | Km[1] <- -betal * thetalt1 * thetalt2 334 | Km[9] <- gammal * thetalt2 335 | Km[5] <- -Km[1] - Km[9] 336 | 337 | Km[2] <- -betal * (thetalt1 + 0.5 * Km[1]) * (thetalt2 + 0.5 * Km[5]) 338 | Km[10] <- gammal * (thetalt2 + 0.5 * Km[5]) 339 | Km[6] <- -Km[2] - Km[10] 340 | 341 | Km[3] <- -betal * (thetalt1 + 0.5 * Km[2]) * (thetalt2 + 0.5 * Km[6]) 342 | Km[11] <- gammal * (thetalt2 + 0.5 * Km[6]) 343 | Km[7] <- -Km[3] - Km[11] 344 | 345 | Km[4] <- -betal * (thetalt1 + Km[3]) * (thetalt2 + Km[7]) 346 | Km[12] <- gammal * (thetalt2 + Km[7]) 347 | Km[8] <- -Km[4] - Km[12] 348 | # if(is.na(thetat1)|is.na(thetat2)) stop("NA1") 349 | alpha_temp[1] <- max(thetalt1 + (Km[1] + 2 * Km[2] + 2 * Km[3] + Km[4]) / 6 - alpha_vec[t + T_prime] * thetalt1, 0) 350 | alpha_temp[2] <- max(thetalt2 + (Km[5] + 2 * Km[6] + 2 * Km[7] + Km[8]) / 6 - gamma_H_vec[t + T_prime] * thetalt2, 0) 351 | alpha_temp[3] <- max(thetalt3 + (Km[9] + 2 * Km[10] + 2 * Km[11] + Km[12]) / 6, 0) 352 | 353 | thetaA_pp[l, t] <- thetaltA <- thetaltA + min(alpha_vec[t + T_prime] * thetalt1, thetalt1 + (Km[1] + 2 * Km[2] + 2 * Km[3] + Km[4]) / 6) 354 | thetaH_pp[l, t] <- thetaltH <- thetaltH + min(gamma_H_vec[t + T_prime] * thetalt2, thetalt2 + (Km[5] + 2 * Km[6] + 2 * Km[7] + Km[8]) / 6) 355 | 356 | 357 | 358 | v_pp[l, t] <- 1 - thetaA_pp[l, t] - thetaH_pp[l, t] 359 | 360 | alpha[1] <- ifelse(v_pp[l, t] > 0, alpha_temp[1] / v_pp[l, t], 0) 361 | alpha[2] <- ifelse(v_pp[l, t] > 0, alpha_temp[2] / v_pp[l, t], 0) 362 | alpha[3] <- ifelse(v_pp[l, t] > 0, alpha_temp[3] / v_pp[l, t], 0) 363 | 364 | theta_temp <- rdirichlet(1, kl * alpha) 365 | 366 | thetalt1 <- theta_pp[l, t, 1] <- theta_temp[1] * v_pp[l, t] 367 | thetalt2 <- theta_pp[l, t, 2] <- theta_temp[2] * v_pp[l, t] 368 | thetalt3 <- theta_pp[l, t, 3] <- theta_temp[3] * v_pp[l, t] 369 | # if(is.na(thetat1)|is.na(thetat2)) stop("NA2") 370 | Y_pp[l, t] <- rbeta(1, lambdaYl * thetalt2, lambdaYl * (1 - thetalt2)) 371 | if (is.na(Y_pp[l, t])) stop("NA") 372 | R_pp[l, t] <- rbeta(1, lambdaRl * thetalt3, lambdaRl * (1 - thetalt3)) 373 | } 374 | } 375 | par(mfrow = c(1, 1)) 376 | col2 <- gg_color_hue(2) 377 | Y_band <- data.frame(t(apply(Y_pp, 2, quantile, probs = c(0.025, 0.975), na.rm = T))) 378 | thetaI_band <- data.frame(t(apply(theta_p[, -1, 2], 2, quantile, probs = c(0.025, 0.975), na.rm = T))) 379 | Y_mean <- c(colMeans(Y_pp, na.rm = T)) 380 | thetaI_mean <- c(colMeans(theta_p[, -1, 2], na.rm = T), colMeans(theta_pp[, , 2], na.rm = T)) 381 | thetaI_median <- c(apply(theta_p[, -1, 2], 2, median, na.rm = T), apply(theta_pp[, , 2], 2, median, na.rm = T)) 382 | colnames(Y_band) <- c("lower", "upper") 383 | colnames(thetaI_band) <- c("lower", "upper") 384 | data_pre <- data.frame(time = 1:T_prime, Y) 385 | data_post <- data.frame(time = 1:T_prime, thetaI_band) 386 | data_fore <- data.frame(time = (T_prime + 1):T_fin, Y_band, Y_mean) 387 | 388 | data_comp <- data.frame(time = 1:T_fin, rbind(thetaI_band, Y_band), phase = c(rep("pre", nrow(thetaI_band)), rep("post", nrow(Y_band))), mean = thetaI_mean, median = thetaI_median) 389 | 390 | data_poly <- data.frame(y = c(thetaI_band$upper, rev(thetaI_band$lower), Y_band$upper, rev(Y_band$lower)), x = c(1:T_prime, T_prime:1, (T_prime + 1):T_fin, T_fin:(T_prime + 1)), phase = c(rep("pre", T_prime * 2), rep("post", (T_fin - T_prime) * 2)), value = c(rep(col2[1], T_prime * 2), rep(col2[2], (T_fin - T_prime) * 2))) 391 | 392 | ## First-order derivative check 393 | thetaS_mat <- cbind(theta_p[, -1, 1], theta_pp[, , 1]) 394 | thetaI_mat <- cbind(theta_p[, -1, 2], theta_pp[, , 2]) 395 | thetaR_mat <- cbind(theta_p[, -1, 3], theta_pp[, , 3]) 396 | 397 | dthetaI_mat_post <- (theta_pp[, , 1] * theta_pp[, , 2]) * replicate(T_fin - T_prime, c(beta_p)) - theta_pp[, , 2] * replicate(T_fin - T_prime, c(gamma_p)) - theta_pp[, , 1] * t(replicate(len, c(alpha_vec[(T_prime + 1):T_fin]))) - theta_pp[, , 2] * t(replicate(len, c(gamma_H_vec[(T_prime + 1):T_fin]))) 398 | dthetaI_mat_pre <- t(apply(theta_p[, , 2], 1, function(v) { 399 | diff(smooth(v)) 400 | })) 401 | dthetaI_mat <- cbind(dthetaI_mat_pre, dthetaI_mat_post) 402 | 403 | dthetaI <- colMeans(dthetaI_mat, na.rm = T) 404 | dthetaI_tp1 <- (1:T_fin)[which.max(dthetaI)] # first second order derivative=0 405 | dthetaI_tp2 <- (dthetaI_tp1:T_fin)[which.min(dthetaI[dthetaI_tp1:T_fin] > 0)] # first order derivative=0 406 | 407 | dthetaI_tp1_rd <- max(round(dthetaI_tp1), 1) 408 | if (dthetaI_tp1_rd > T_prime) { 409 | thetatI_tp1_vec <- thetaI_mat[, dthetaI_tp1_rd] 410 | thetaI_tp1_mean <- mean(thetatI_tp1_vec, na.rm = T) 411 | thetaI_tp1_ci <- quantile(thetatI_tp1_vec, c(0.025, 0.5, 0.975), na.rm = T) 412 | Y_tp1_vec <- Y_pp[, dthetaI_tp1_rd - T_prime] 413 | Y_tp1_mean <- mean(Y_tp1_vec, na.rm = T) 414 | Y_tp1_ci <- quantile(Y_tp1_vec, c(0.025, 0.5, 0.975), na.rm = T) 415 | 416 | thetatR_tp1_vec <- thetaR_mat[, dthetaI_tp1_rd] 417 | thetaR_tp1_mean <- mean(thetatR_tp1_vec, na.rm = T) 418 | thetaR_tp1_ci <- quantile(thetatR_tp1_vec, c(0.025, 0.5, 0.975), na.rm = T) 419 | R_tp1_vec <- R_pp[, dthetaI_tp1_rd - T_prime] 420 | R_tp1_mean <- mean(R_tp1_vec, na.rm = T) 421 | R_tp1_ci <- quantile(R_tp1_vec, c(0.025, 0.5, 0.975), na.rm = T) 422 | } else { 423 | thetatI_tp1_vec <- thetaI_mat[, dthetaI_tp1_rd] 424 | thetaI_tp1_mean <- mean(thetatI_tp1_vec, na.rm = T) 425 | thetaI_tp1_ci <- quantile(thetatI_tp1_vec, c(0.025, 0.5, 0.975), na.rm = T) 426 | Y_tp1_vec <- NA 427 | Y_tp1_mean <- mean(Y_tp1_vec, na.rm = T) 428 | Y_tp1_ci <- quantile(Y_tp1_vec, c(0.025, 0.5, 0.975), na.rm = T) 429 | 430 | thetatR_tp1_vec <- thetaR_mat[, dthetaI_tp1_rd] 431 | thetaR_tp1_mean <- mean(thetatR_tp1_vec, na.rm = T) 432 | thetaR_tp1_ci <- quantile(thetatR_tp1_vec, c(0.025, 0.5, 0.975), na.rm = T) 433 | R_tp1_vec <- R_pp[, dthetaI_tp1_rd - T_prime] 434 | R_tp1_mean <- mean(R_tp1_vec, na.rm = T) 435 | R_tp1_ci <- quantile(R_tp1_vec, c(0.025, 0.5, 0.975), na.rm = T) 436 | } 437 | dthetaI_tp2_rd <- max(round(dthetaI_tp2), 1) 438 | if (dthetaI_tp1_rd == dthetaI_tp2_rd) { 439 | thetatI_tp2_vec <- NA 440 | thetaI_tp2_mean <- mean(thetatI_tp2_vec, na.rm = T) 441 | thetaI_tp2_ci <- quantile(thetatI_tp2_vec, c(0.025, 0.5, 0.975), na.rm = T) 442 | Y_tp2_vec <- NA 443 | Y_tp2_mean <- mean(Y_tp2_vec, na.rm = T) 444 | Y_tp2_ci <- quantile(Y_tp2_vec, c(0.025, 0.5, 0.975), na.rm = T) 445 | 446 | thetatR_tp2_vec <- NA 447 | thetaR_tp2_mean <- mean(thetatR_tp2_vec, na.rm = T) 448 | thetaR_tp2_ci <- quantile(thetatR_tp2_vec, c(0.025, 0.5, 0.975), na.rm = T) 449 | R_tp2_vec <- NA 450 | R_tp2_mean <- mean(R_tp2_vec, na.rm = T) 451 | R_tp2_ci <- quantile(R_tp2_vec, c(0.025, 0.5, 0.975), na.rm = T) 452 | } else if (dthetaI_tp2_rd > T_prime) { 453 | thetatI_tp2_vec <- thetaI_mat[, dthetaI_tp2_rd] 454 | thetaI_tp2_mean <- mean(thetatI_tp2_vec, na.rm = T) 455 | thetaI_tp2_ci <- quantile(thetatI_tp2_vec, c(0.025, 0.5, 0.975), na.rm = T) 456 | Y_tp2_vec <- Y_pp[, dthetaI_tp2_rd - T_prime] 457 | Y_tp2_mean <- mean(Y_tp2_vec, na.rm = T) 458 | Y_tp2_ci <- quantile(Y_tp2_vec, c(0.025, 0.5, 0.975), na.rm = T) 459 | 460 | thetatR_tp2_vec <- thetaR_mat[, dthetaI_tp2_rd] 461 | thetaR_tp2_mean <- mean(thetatR_tp2_vec, na.rm = T) 462 | thetaR_tp2_ci <- quantile(thetatR_tp2_vec, c(0.025, 0.5, 0.975), na.rm = T) 463 | R_tp2_vec <- R_pp[, dthetaI_tp2_rd - T_prime] 464 | R_tp2_mean <- mean(R_tp2_vec, na.rm = T) 465 | R_tp2_ci <- quantile(R_tp2_vec, c(0.025, 0.5, 0.975), na.rm = T) 466 | } else { 467 | thetatI_tp2_vec <- thetaI_mat[, dthetaI_tp2_rd] 468 | thetaI_tp2_mean <- mean(thetatI_tp2_vec, na.rm = T) 469 | thetaI_tp2_ci <- quantile(thetatI_tp2_vec, c(0.025, 0.5, 0.975), na.rm = T) 470 | Y_tp2_vec <- NA 471 | Y_tp2_mean <- mean(Y_tp2_vec, na.rm = T) 472 | Y_tp2_ci <- quantile(Y_tp2_vec, c(0.025, 0.5, 0.975), na.rm = T) 473 | 474 | thetatR_tp2_vec <- thetaR_mat[, dthetaI_tp2_rd] 475 | thetaR_tp2_mean <- mean(thetatR_tp2_vec, na.rm = T) 476 | thetaR_tp2_ci <- quantile(thetatR_tp2_vec, c(0.025, 0.5, 0.975), na.rm = T) 477 | R_tp2_vec <- NA 478 | R_tp2_mean <- mean(R_tp2_vec, na.rm = T) 479 | R_tp2_ci <- quantile(R_tp2_vec, c(0.025, 0.5, 0.975), na.rm = T) 480 | } 481 | thetaR_max_vec <- thetaR_mat[, T_fin] 482 | thetaR_max_mean <- mean(thetaR_max_vec) 483 | thetaR_max_ci <- quantile(thetaR_max_vec, c(0.025, 0.5, 0.975), na.rm = T) 484 | 485 | cumInf_vec <- thetaR_mat[, T_fin] + thetaI_mat[, T_fin] 486 | cumInf_mean <- mean(cumInf_vec) 487 | cumInf_ci <- quantile(cumInf_vec, c(0.025, 0.5, 0.975), na.rm = T) 488 | 489 | 490 | 491 | dthetaI_tp1_date <- chron_ls[dthetaI_tp1] 492 | dthetaI_tp2_date <- chron_ls[dthetaI_tp2] 493 | 494 | incidence_vec <- thetaI_mat[, T_fin] + thetaR_mat[, T_fin] 495 | incidence_mean <- mean(incidence_vec, na.rm = T) 496 | 497 | incidence_ci <- quantile(incidence_vec, c(0.025, 0.5, 0.975), na.rm = T) 498 | 499 | first_tp_vec <- (1:T_fin)[apply(dthetaI_mat, 1, which.max)] # first second order derivative=0 500 | 501 | second_tp_vec <- sapply(1:len, function(l) { 502 | (first_tp_vec[l]:T_fin)[which.min(dthetaI_mat[l, first_tp_vec[l]:T_fin] > 0)] 503 | }) 504 | 505 | end_p_vec <- sapply(1:len, function(l) { 506 | if (any(thetaI_mat[l, first_tp_vec[l]:T_fin] <= eps, na.rm = TRUE)) { 507 | (first_tp_vec[l]:T_fin)[which.max(thetaI_mat[l, first_tp_vec[l]:T_fin] <= eps)] 508 | } else { 509 | T_fin 510 | } 511 | }) 512 | 513 | 514 | # first order derivative=0 515 | first_tp_mean <- mean(first_tp_vec, na.rm = T) 516 | second_tp_mean <- mean(second_tp_vec, na.rm = T) 517 | end_p_mean <- mean(end_p_vec, na.rm = T) 518 | 519 | first_tp_ci <- quantile(first_tp_vec, c(0.025, 0.5, 0.975), na.rm = T) 520 | second_tp_ci <- quantile(second_tp_vec, c(0.025, 0.5, 0.975), na.rm = T) 521 | end_p_ci <- quantile(end_p_vec, c(0.025, 0.5, 0.975), na.rm = T) 522 | 523 | first_tp_date_mean <- chron_ls[first_tp_mean] 524 | second_tp_date_mean <- chron_ls[second_tp_mean] 525 | end_p_date_mean <- chron_ls[end_p_mean] 526 | 527 | first_tp_date_ci <- chron_ls[first_tp_ci] 528 | second_tp_date_ci <- chron_ls[second_tp_ci] 529 | end_p_date_ci <- chron_ls[end_p_ci] 530 | 531 | names(first_tp_date_ci) <- c("2.5%", "50%", "97.5%") 532 | names(second_tp_date_ci) <- c("2.5%", "50%", "97.5%") 533 | names(end_p_date_ci) <- c("2.5%", "50%", "97.5%") 534 | 535 | if (save_files) { 536 | png(paste0(file_add, casename, "deriv.png"), width = 700, height = 350) 537 | plot(y = dthetaI, x = chron_ls, type = "l", ylab = "1st order derivative", main = "Infection prevalence process") 538 | abline(h = 0, col = 2) 539 | if (!is.null(change_time_chorn)) abline(v = change_time_chorn, col = "gray") 540 | abline(v = chron_ls[T_prime], col = "blue") 541 | legend("topright", legend = c("Last observation", "change point"), col = c("blue", "gray"), lty = 1, title = "", bty = "n") 542 | dev.off() 543 | 544 | png(paste0(file_add, casename, "thetaA_plot.png"), width = 700, height = 350) 545 | plot(y = colMeans(cbind(thetaA_p, thetaA_pp)), x = chron_ls, type = "l", xlab = "date", main = "Prevalence process for those immunized with antibody") 546 | if (!is.null(change_time_chorn)) abline(v = change_time_chorn, col = "gray") 547 | abline(v = chron_ls[T_prime], col = "blue") 548 | legend("topright", legend = c("Last observation", "change point"), col = c("blue", "gray"), lty = 1, title = "", bty = "n") 549 | dev.off() 550 | } 551 | 552 | ## Prepare the Spaghetti plot 553 | sample_dthetaI_mat <- cbind(dthetaI_mat[sample.int(len, 20, replace = F), ]) 554 | colnames(sample_dthetaI_mat) <- c(as.character(chron_ls)[-1]) 555 | sample_dthetaI_mat_long <- reshape2::melt(sample_dthetaI_mat) 556 | colnames(sample_dthetaI_mat_long) <- c("id", "date", "dthetaI") 557 | sample_dthetaI_mat_long$date <- (chron(as.character(sample_dthetaI_mat_long$date))) 558 | 559 | dthetaI_mean_data <- data.frame(dthetaI, date = chron_ls[-1]) 560 | spaghetti_ht <- mean(range(sample_dthetaI_mat)) / 2 561 | spaghetti_plot <- ggplot() + 562 | theme_bw() + 563 | theme( 564 | plot.title = element_text(hjust = 0.5, size = 16, face = "bold"), 565 | plot.subtitle = element_text(hjust = 0.5, size = 12), 566 | axis.text.x = element_text(angle = 45, hjust = 1), 567 | axis.text = element_text(size = 15), 568 | axis.title = element_text(size = 14) 569 | ) + 570 | geom_line(data = sample_dthetaI_mat_long, aes(x = date, y = dthetaI, group = id, color = id)) + 571 | scale_color_gradientn(colours = rainbow(5, alpha = 0.5)) + 572 | labs(title = "spaghetti plot of infection prevalence process", x = "time", y = "1st order derivative") + 573 | geom_line(data = dthetaI_mean_data, aes(x = date, y = dthetaI), color = 1) + 574 | scale_x_continuous( 575 | labels = as.character(chron_ls)[seq(1, T_fin, 30)], 576 | breaks = as.numeric(chron_ls[-1][seq(1, T_fin, 30)]) 577 | ) + 578 | annotate(geom = "text", label = as.character(chron(chron_ls[T_prime]), format = "mon day"), x = as.numeric(chron_ls[T_prime]) + 12, y = spaghetti_ht, color = "blue") + 579 | annotate(geom = "text", label = as.character(chron(dthetaI_tp1_date, format = "mon day")), x = as.numeric(dthetaI_tp1_date) + 12, y = spaghetti_ht * 1.25, color = "darkgreen") + 580 | geom_vline(xintercept = as.numeric(chron_ls[T_prime]), color = "blue", show.legend = TRUE) + 581 | geom_vline(xintercept = as.numeric(dthetaI_tp1_date), color = "darkgreen", show.legend = TRUE) 582 | # if(dthetaI_tp1>T_prime) 583 | spaghetti_plot <- spaghetti_plot + 584 | geom_rect(data = data.frame(xmin = as.numeric(first_tp_date_ci[1]), xmax = as.numeric(first_tp_date_ci[3]), ymin = -Inf, ymax = Inf, ci = "first tp"), aes(xmin = xmin, xmax = xmax, ymin = ymin, ymax = ymax), fill = "darkgreen", alpha = 0.15) 585 | # if(dthetaI_tp2>T_prime) 586 | spaghetti_plot <- spaghetti_plot + 587 | geom_rect(data = data.frame(xmin = as.numeric(second_tp_date_ci[1]), xmax = as.numeric(second_tp_date_ci[3], ci = "second tp"), ymin = -Inf, ymax = Inf), aes(xmin = xmin, xmax = xmax, ymin = ymin, ymax = ymax), fill = "purple", alpha = 0.15) 588 | if (dthetaI_tp2_date > dthetaI_tp1_date) { 589 | spaghetti_plot <- spaghetti_plot + 590 | geom_vline(xintercept = as.numeric(dthetaI_tp2_date), color = "purple", show.legend = TRUE) + 591 | annotate(geom = "text", label = as.character(chron(dthetaI_tp2_date, format = "mon day")), x = as.numeric(dthetaI_tp2_date) + 12, y = spaghetti_ht * 1.5, color = "purple") 592 | } 593 | 594 | if (save_files) ggsave(paste0(file_add, casename, "_spaghetti.png"), width = 12, height = 10) 595 | ############## 596 | y_text_ht <- max(rbind(thetaI_band, Y_band), na.rm = T) / 2 597 | plot1 <- ggplot(data = data_poly, aes(x = x, y = y)) + 598 | geom_polygon(alpha = 0.5, aes(fill = value, group = phase)) + 599 | labs(title = substitute(paste(casename, ": infection forecast with prior ", beta[0], "=", v1, ",", gamma[0], "=", v2, " and ", R[0], "=", v3), list(casename = casename, v1 = format(beta0, digits = 3), v2 = format(gamma0, digits = 3), v3 = format(R0, digits = 3))), subtitle = substitute(paste("Posterior ", beta[p], "=", v1, ",", gamma[p], "=", v2, " and ", R[0], "=", v3), list(v1 = format(beta_p_mean, digits = 3), v2 = format(gamma_p_mean, digits = 3), v3 = format(R0_p_mean, digits = 3))), x = "time", y = "P(Infected)") + 600 | geom_line(data = data_comp, aes(x = time, y = median), color = "red") + 601 | geom_vline(xintercept = T_prime, color = "blue", show.legend = TRUE) + 602 | geom_vline(xintercept = dthetaI_tp1, color = "darkgreen", show.legend = TRUE) + 603 | geom_line(data = data_comp, aes(x = time, y = mean), color = "darkgray") + 604 | geom_point(data = data_pre, aes(x = time, y = Y)) + 605 | theme_bw() + 606 | theme( 607 | plot.title = element_text(hjust = 0.5, size = 16, face = "bold"), 608 | plot.subtitle = element_text(hjust = 0.5, size = 12), 609 | axis.text.x = element_text(angle = 45, hjust = 1), 610 | axis.text = element_text(size = 15), 611 | axis.title = element_text(size = 14), 612 | legend.title = element_text(size = 15), 613 | legend.text = element_text(size = 12) 614 | ) + 615 | scale_x_continuous( 616 | labels = as.character(chron_ls)[seq(1, T_fin, 30)], 617 | breaks = seq(1, T_fin, 30) 618 | ) + 619 | scale_fill_discrete( 620 | name = "Posterior", 621 | labels = c( 622 | expression(paste(y[t[0] + 1:T]^I, " | ", y[1:t[0]]^I, ", ", y[1:t[0]]^R)), 623 | expression(paste(theta[1:t[0]]^I, " | ", y[1:t[0]]^I, ", ", y[1:t[0]]^R)) 624 | ) 625 | ) + 626 | annotate(geom = "text", label = as.character(chron(chron_ls[T_prime]), format = "mon day"), x = T_prime + 12, y = y_text_ht, color = "blue") + 627 | annotate(geom = "text", label = as.character(chron(dthetaI_tp1_date, format = "mon day")), x = dthetaI_tp1 + 12, y = y_text_ht * 1.25, color = "darkgreen") 628 | if (dthetaI_tp2 > dthetaI_tp1) { 629 | plot1 <- plot1 + geom_vline(xintercept = dthetaI_tp2, color = "purple", show.legend = TRUE) + annotate(geom = "text", label = as.character(chron(dthetaI_tp2_date, format = "mon day")), x = dthetaI_tp2 + 12, y = y_text_ht * 1.5, color = "purple") 630 | } 631 | # plot_list <- list(data_poly=data_poly,data_comp=data_comp,T_prime=T_prime,dthetaI_stationary2=dthetaI_stationary2,dthetaI_stationary1=dthetaI_stationary1,data_pre=data_pre,dthetaI_stationary2_date,dthetaI_stationary1_date,y_text_ht) 632 | 633 | if (save_files) ggsave(paste0(file_add, casename, "_forecast.png"), width = 12, height = 10) 634 | 635 | ### Removed 636 | R_band <- data.frame(t(apply(R_pp, 2, quantile, probs = c(0.025, 0.975), na.rm = T))) 637 | thetaR_band <- data.frame(t(apply(theta_p[, -1, 3], 2, quantile, probs = c(0.025, 0.975), na.rm = T))) 638 | R_mean <- c(colMeans(R_pp, na.rm = T)) 639 | thetaR_mean <- c(colMeans(theta_p[, -1, 3], na.rm = T), colMeans(theta_pp[, , 3], na.rm = T)) 640 | thetaR_med <- c(apply(theta_p[, -1, 3], 2, median, na.rm = T), apply(theta_pp[, , 3], 2, median, na.rm = T)) 641 | colnames(R_band) <- c("lower", "upper") 642 | colnames(thetaR_band) <- c("lower", "upper") 643 | data_pre_R <- data.frame(time = 1:T_prime, R) # previous data 644 | data_post_R <- data.frame(time = 1:T_prime, thetaR_band) # posterior of theta^R 645 | data_fore_R <- data.frame(time = (T_prime + 1):T_fin, R_band, R_mean) # The forecast of R after T_prime 646 | 647 | data_comp_R <- data.frame(time = 1:T_fin, rbind(thetaR_band, R_band), phase = c(rep("pre", nrow(thetaR_band)), rep("post", nrow(R_band))), mean = thetaR_mean, median = thetaR_med, dead = thetaR_mean * death_in_R, dead_med = thetaR_med * death_in_R) # the filled area--polygon 648 | 649 | data_poly_R <- data.frame(y = c(thetaR_band$upper, rev(thetaR_band$lower), R_band$upper, rev(R_band$lower)), x = c(1:T_prime, T_prime:1, (T_prime + 1):T_fin, T_fin:(T_prime + 1)), phase = c(rep("pre", T_prime * 2), rep("post", (T_fin - T_prime) * 2)), value = c(rep(col2[1], T_prime * 2), rep(col2[2], (T_fin - T_prime) * 2))) 650 | 651 | r_text_ht <- max(rbind(thetaR_band, R_band), na.rm = T) / 2 652 | plot2 <- ggplot(data = data_poly_R, aes(x = x, y = y)) + 653 | geom_polygon(alpha = 0.5, aes(fill = value, group = phase)) + 654 | labs( 655 | title = substitute( 656 | paste( 657 | casename, 658 | ": removed forecast with prior ", beta[0], "=", v1, ",", 659 | gamma[0], "=", v2, " and ", R[0], "=", v3 660 | ), 661 | list( 662 | casename = casename, v1 = format(beta0, digits = 3), 663 | v2 = format(gamma0, digits = 3), v3 = format(R0, digits = 3) 664 | ) 665 | ), 666 | subtitle = substitute( 667 | paste( 668 | "posterior: ", beta[p], "=", v1, ",", 669 | gamma[p], "=", v2, " and ", R[0], "=", v3 670 | ), 671 | list( 672 | v1 = format(beta_p_mean, digits = 3), v2 = format(gamma_p_mean, digits = 3), 673 | v3 = format(R0_p_mean, digits = 3) 674 | ) 675 | ), x = "time", y = "P(Removed)" 676 | ) + 677 | geom_line(data = data_comp_R, aes(x = time, y = median), color = "red", linetype = 1) + 678 | geom_vline(xintercept = T_prime, color = "blue") + 679 | geom_vline(xintercept = dthetaI_tp1, color = "darkgreen") + 680 | geom_line(data = data_comp_R, aes(x = time, y = mean), color = "darkgray") + 681 | geom_point(data = data_pre_R, aes(x = time, y = R)) + 682 | theme_bw() + 683 | theme( 684 | plot.title = element_text(hjust = 0.5, size = 16, face = "bold"), 685 | plot.subtitle = element_text(hjust = 0.5, size = 12), 686 | axis.text.x = element_text(angle = 45, hjust = 1), 687 | axis.text = element_text(size = 15), 688 | axis.title = element_text(size = 14), 689 | legend.title = element_text(size = 15), 690 | legend.text = element_text(size = 12) 691 | ) + 692 | scale_x_continuous(labels = as.character(chron_ls)[seq(1, T_fin, 30)], breaks = seq(1, T_fin, 30)) + 693 | scale_fill_discrete( 694 | name = "Posterior", 695 | labels = c( 696 | expression(paste(y[t[0] + 1:T]^R, " | ", y[1:t[0]]^I, ", ", y[1:t[0]]^R)), 697 | expression(paste(theta[1:t[0]]^R, " | ", y[1:t[0]]^I, ", ", y[1:t[0]]^R)) 698 | ) 699 | ) + 700 | annotate(geom = "text", label = as.character(chron(chron_ls[T_prime]), format = "mon day"), x = T_prime + 12, y = r_text_ht, color = "blue") + 701 | annotate(geom = "text", label = as.character(chron(dthetaI_tp1_date, format = "mon day")), x = dthetaI_tp1 + 12, y = r_text_ht * 1.25, color = "darkgreen") 702 | 703 | if (dthetaI_tp2 > dthetaI_tp1) { 704 | plot2 <- plot2 + geom_vline(xintercept = dthetaI_tp2, color = "purple", show.legend = TRUE) + annotate(geom = "text", label = as.character(chron(dthetaI_tp2_date, format = "mon day")), x = dthetaI_tp2 + 12, y = r_text_ht * 1.5, color = "purple") 705 | } 706 | if (add_death) plot2 <- plot2 + geom_line(data = data_comp_R, aes(x = time, y = dead), color = "black", linetype = 1) + geom_line(data = data_comp_R, aes(x = time, y = dead_med), color = "black", linetype = 2) 707 | # plot2_list <- list(data_poly_R=data_poly_R,data_comp_R=data_comp_R,T_prime=T_prime,dthetaI_stationary2=dthetaI_stationary2,dthetaI_stationary1=dthetaI_stationary1,data_pre_R=data_pre_R,dthetaI_stationary2_date,dthetaI_stationary1_date) 708 | 709 | 710 | 711 | if (save_files) ggsave(paste0(file_add, casename, "_forecast2.png"), width = 12, height = 10) 712 | 713 | out_table <- matrix(c(theta_p_mean, theta_p_ci, thetaA_p_mean, thetaA_p_ci, R0_p_mean, R0_p_ci, gamma_p_mean, gamma_p_ci, beta_p_mean, beta_p_ci), nrow = 1) 714 | 715 | out_table1 <- data.frame(matrix(c(theta_p_mean, theta_p_ci, thetaA_p_mean, thetaA_p_ci, R0_p_mean, R0_p_ci, gamma_p_mean, gamma_p_ci, beta_p_mean, beta_p_ci, incidence_mean = incidence_mean, incidence_ci = incidence_ci, thetaI_tp1_mean = thetaI_tp1_mean, thetaI_tp1_ci = thetaI_tp1_ci, thetaR_tp1_mean = thetaR_tp1_mean, thetaR_tp1_ci = thetaR_tp1_ci, Y_tp1_mean = Y_tp1_mean, Y_tp1_ci = Y_tp1_ci, R_tp1_mean = R_tp1_mean, R_tp1_ci = R_tp1_ci, thetaI_tp2_mean = thetaI_tp2_mean, thetaI_tp2_ci = thetaI_tp2_ci, thetaR_tp2_mean = thetaR_tp2_mean, thetaR_tp2_ci = thetaR_tp2_ci, Y_tp2_mean = Y_tp2_mean, Y_tp2_ci = Y_tp2_ci, R_tp2_mean = R_tp2_mean, R_tp2_ci = R_tp2_ci, thetaR_max_mean, thetaR_max_ci, cumInf_mean = cumInf_mean, cumInf_ci = cumInf_ci), nrow = 1)) 716 | 717 | out_table2 <- data.frame(matrix(c(dthetaI_tp1_date = as.character(dthetaI_tp1_date), first_tp_mean = as.character(first_tp_date_mean), first_tp_ci = as.character(first_tp_date_ci), dthetaI_tp2_date = as.character(dthetaI_tp2_date), second_tp_mean = as.character(second_tp_date_mean), second_tp_ci = as.character(second_tp_date_ci), end_p_date_mean = as.character(end_p_date_mean), end_p_date_ci = as.character(end_p_date_ci), begin_str = begin_str), nrow = 1)) 718 | 719 | out_table <- cbind(out_table1, out_table2) 720 | # out_table<-matrix(c(theta_p_mean,theta_p_ci,R0_p_mean,R0_p_ci,gamma_p_mean,gamma_p_ci,beta_p_mean,beta_p_ci,k_p_mean,k_p_ci,lambdaY_p_mean,lambdaY_p_ci,lambdaR_p_mean,lambdaR_p_ci,as.character(first_order_change_date),as.character(second_order_change_date)),nrow=1) 721 | 722 | 723 | 724 | colnames(out_table) <- c("thetaS_last_obs_p_mean", "thetaI_last_obs_p_mean", "thetaR_last_obs_p_mean", "thetaS_last_obs_p_ci_low", "thetaS_last_obs_p_ci_med", "thetaS_last_obs_p_ci_up", "thetaI_last_obs_p_ci_low", "thetaI_last_obs_p_ci_med", "thetaI_last_obs_p_ci_up", "thetaR_last_obs_p_ci_low", "thetaR_last_obs_p_ci_med", "thetaR_last_obs_p_ci_up", "thetaA_last_obs_p_mean", "thetaA_last_obs_p_ci_low", "thetaA_last_obs_p_ci_med", "thetaA_last_obs_p_ci_up", "R0_p_mean", "R0_p_ci_low", "R0_p_ci_med", "R0_p_ci_up", "gamma_p_mean", "gamma_p_ci_low", "gamma_p_ci_med", "gamma_p_ci_up", "beta_p_mean", "beta_p_ci_low", "beta_p_ci_med", "beta_p_ci_up", "incidence_mean", "incidence_ci_low", "incidence_ci_median", "incidence_ci_up", "thetaI_tp1_mean", "thetaI_tp1_ci_low", "thetaI_tp1_ci_med", "thetaI_tp1_ci_up", "thetaR_tp1_mean", "thetaR_tp1_ci_low", "thetaR_tp1_ci_med", "thetaR_tp1_ci_up", "Y_tp1_mean", "Y_tp1_ci_low", "Y_tp1_ci_med", "Y_tp1_ci_up", "R_tp1_mean", "R_tp1_ci_low", "R_tp1_ci_med", "R_tp1_ci_up", "thetaI_tp2_mean", "thetaI_tp2_ci_low", "thetaI_tp2_ci_med", "thetaI_tp2_ci_up", "thetaR_tp2_mean", "thetaR_tp2_ci_low", "thetaR_tp2_ci_med", "thetaR_tp2_ci_up", "Y_tp2_mean", "Y_tp2_ci_low", "Y_tp2_ci_med", "Y_tp2_ci_up", "R_tp2_mean", "R_tp2_ci_low", "R_tp2_ci_med", "R_tp2_ci_up", "thetaR_max_mean", "thetaR_max_ci_low", "thetaR_max_ci_med", "thetaR_max_ci_up", "cumInf_mean", "cumInf_ci_low", "cumInf_ci_med", "cumInf_ci_up", "dthetaI_tp1_date", "first_tp_mean", "first_tp_ci_low", "first_tp_ci_med", "first_tp_ci_up", "dthetaI_tp2_date", "second_tp_mean", "second_tp_ci_low", "second_tp_ci_med", "second_tp_ci_up", "end_p_mean", "end_p_ci_low", "end_p_ci_med", "end_p_ci_up", "begin_str") 725 | # colnames(out_table)<-c("thetaS_p_mean","thetaI_p_mean","thetaR_p_mean","thetaS_p_ci_low","thetaS_p_ci_med","thetaS_p_ci_up","thetaI_p_ci_low","thetaI_p_ci_med","thetaI_p_ci_up","thetaR_p_ci_low","thetaR_p_ci_med","thetaR_p_ci_up","R0_p_mean","R0_p_ci_low","R0_p_ci_med","R0_p_ci_up","gamma_p_mean","gamma_p_ci_low","gamma_p_ci_med","gamma_p_ci_up","beta_p_mean","beta_p_ci_low","beta_p_ci_med","beta_p_ci_up","k_p_mean","k_p_ci_low","k_p_ci_med","k_p_ci_up","lambdaY_p_mean","lambdaY_p_ci_low","lambdaY_p_ci_med","lambdaY_p_ci_up","lambdaR_p_mean","lambdaR_p_ci_low","lambdaR_p_ci_med","lambdaR_p_ci_up","first_order_change_date","second_order_change_date") 726 | 727 | if (save_files) write.csv(out_table, file = paste0(file_add, casename, "_summary.csv")) 728 | if (save_mcmc) { 729 | save(theta_pp, thetaA_pp, Y_pp, R_pp, file = paste0(file_add, casename, "_forecast_MCMC.RData")) # @ 730 | save(jags_sample, file = paste0(file_add, casename, "_rjags_MCMC.RData")) 731 | } 732 | if (save_plot_data) { 733 | other_plot <- list(T_prime = T_prime, T_fin = T_fin, chron_ls = chron_ls, dthetaI_tp1 = dthetaI_tp1, dthetaI_tp2 = dthetaI_tp2, dthetaI_tp1_date = dthetaI_tp1_date, dthetaI_tp2_date = dthetaI_tp2_date, beta_p_mean = beta_p_mean, gamma_p_mean = gamma_p_mean, R0_p_mean = R0_p_mean) 734 | spaghetti_plot_ls <- list(spaghetti_ht = spaghetti_ht, dthetaI_mean_data = dthetaI_mean_data, sample_dthetaI_mat_long = sample_dthetaI_mat_long, first_tp_date_ci = first_tp_date_ci, second_tp_date_ci = second_tp_date_ci) 735 | infection_plot_ls <- list(y_text_ht = y_text_ht, data_poly = data_poly, data_comp = data_comp, data_pre = data_pre) 736 | removed_plot_ls <- list(r_text_ht = r_text_ht, data_poly_R = data_poly_R, data_comp_R = data_comp_R, data_pre_R = data_pre_R) 737 | plot_data_ls <- list(casename = casename, other_plot = other_plot, spaghetti_plot_ls = spaghetti_plot_ls, infection_plot_ls = infection_plot_ls, removed_plot_ls = removed_plot_ls) 738 | save(plot_data_ls, file = paste0(file_add, casename, "_plot_data.RData")) 739 | } 740 | 741 | # Gelman-Rubin convergence diagnostics 742 | gelman_out_name <- c("R0", "gamma", "beta", "theta", "theta_A", "lambdaY", "lambdaR", "k") 743 | gelman_diag_list <- lapply(gelman_out_name, function(name) { 744 | if (name == "theta") { 745 | tryCatch( 746 | gelman.diag(as.mcmc.list(jags_sample[[name]])[, (1:3) * (T_prime + 1)], 747 | autoburnin = FALSE 748 | ), 749 | error = function(e) e 750 | ) 751 | } else if (name == "theta_A") { 752 | list("theta_A: ", tryCatch( 753 | gelman.diag(as.mcmc.list(jags_sample[[name]])[, (T_prime + 1)], 754 | autoburnin = FALSE 755 | ), 756 | error = function(e) e 757 | )) 758 | } else { 759 | tryCatch( 760 | gelman.diag(as.mcmc.list(jags_sample[[name]]), 761 | autoburnin = FALSE 762 | ), 763 | error = function(e) e 764 | ) 765 | } 766 | }) 767 | if (save_files) { 768 | sink(paste0(file_add, casename, "_Gelman_diag.txt")) 769 | print(gelman_diag_list) 770 | sink() 771 | } 772 | res <- list( 773 | casename = casename, 774 | incidence_mean = incidence_mean, 775 | incidence_ci = incidence_ci, 776 | out_table = out_table, 777 | plot_infection = plot1, 778 | plot_removed = plot2, 779 | spaghetti_plot = spaghetti_plot, 780 | first_tp_mean = as.character(first_tp_date_mean), 781 | first_tp_ci = as.character(first_tp_date_ci), 782 | second_tp_mean = as.character(second_tp_date_mean), 783 | second_tp_ci = as.character(second_tp_date_ci), 784 | dic_val = dic_val, 785 | gelman_diag_list = gelman_diag_list 786 | ) 787 | return(res) 788 | } 789 | 790 | 791 | if (FALSE) { 792 | NI_complete <- c( 793 | 41, 41, 41, 45, 62, 131, 200, 270, 375, 444, 549, 729, 794 | 1052, 1423, 2714, 3554, 4903, 5806, 7153, 9074, 11177, 795 | 13522, 16678, 19665, 22112, 24953, 27100, 29631, 31728, 33366 796 | ) 797 | RI_complete <- c( 798 | 1, 1, 7, 10, 14, 20, 25, 31, 34, 45, 55, 71, 94, 121, 152, 213, 799 | 252, 345, 417, 561, 650, 811, 1017, 1261, 1485, 1917, 2260, 800 | 2725, 3284, 3754 801 | ) 802 | N <- 58.5e6 803 | R <- RI_complete / N 804 | Y <- NI_complete / N - R # Jan13->Feb 11 805 | 806 | change_time <- c("02/08/2020") 807 | alpha0 <- c(0.2) # 20% of the susceptible population were found immunized 808 | res.antibody <- eSAIR(Y, R, 809 | begin_str = "01/13/2020", death_in_R = 0.4, 810 | alpha0 = alpha0, change_time = change_time, 811 | casename = "Hubei_antibody", save_files = F, save_mcmc = F, 812 | M = 5e2, nburnin = 2e2 813 | ) 814 | res.antibody$plot_infection 815 | res.antibody$gelman_diag_list 816 | } 817 | -------------------------------------------------------------------------------- /R/eSIR.R: -------------------------------------------------------------------------------- 1 | #' @import rjags 2 | #' @import scales 3 | #' @import ggplot2 4 | #' @import chron 5 | #' @import gtools 6 | #' @import data.table 7 | #' @import stats 8 | #' @import grDevices 9 | #' @import graphics 10 | #' @import utils 11 | #' @import coda 12 | #' @importFrom coda as.mcmc.list 13 | NULL 14 | -------------------------------------------------------------------------------- /R/utils.R: -------------------------------------------------------------------------------- 1 | gg_color_hue <- function(n) { 2 | hues = seq(15, 375, length = n + 1) 3 | hcl(h = hues, l = 65, c = 100)[1:n] 4 | } 5 | 6 | lognorm.parm <- function(mu0,var0){ 7 | var <- log(var0 / mu0^2 + 1) 8 | mu <- log(mu0) - var / 2 9 | list(mu = mu, var = var) 10 | } 11 | 12 | -------------------------------------------------------------------------------- /README.Rmd: -------------------------------------------------------------------------------- 1 | --- 2 | title: "R package eSIR: extended state-space SIR epidemiological models" 3 | author: "[Song Lab](http://www.umich.edu/~songlab/)" 4 | date: "`r Sys.Date()`" 5 | output: github_document 6 | --- 7 | 8 | ```{r setup, include=FALSE, echo=FALSE} 9 | knitr::opts_chunk$set(collapse = TRUE, 10 | comment = "#>", 11 | fig.width=12, fig.height=8, 12 | fig.path = "man/figures/README-", 13 | file.path = "man/files/README-") 14 | 15 | ``` 16 | 17 | **Notice**: 18 | 19 | 1. We add new features in `tvt.eSIR()`. Now the new function `tvt.eSIR2()` adds `time_unit` which will allow users to change their time unit from 1 day to any arbitrary numbers of days. 20 | 21 | 22 | 2. Since version 0.3.1, we added the US data. The most recent update was on June 25th, 2021. We used data summarized from [JHU CSSE GitHub](https://github.com/CSSEGISandData/COVID-19) and [1Point3Acres](https://coronavirus.1point3acres.com). Only 41 states have complete recovery data. We will update the data every Thursday or Friday evening. Using following codes for the data: 23 | ```{r load data, eval = FALSE} 24 | data("confirmed") # From JHU CSSE 25 | data("death") # From JHU CSSE 26 | data("recovered") # partly from 1Point3Acres 27 | data("USA_state_N") #population in each state 28 | 29 | ``` 30 | 31 | 3. Since version 0.3.3, we added Gelman-Rubin statistic for convergence check using [gelman.diag](https://www.rdocumentation.org/packages/coda/versions/0.19-3/topics/gelman.diag) from [`rjags`](https://cran.r-project.org/web/packages/rjags/index.html). Their values substantially larger than 1 imply a failure of convergence of the MCMC chains. Save it in a `.txt` file by setting `save_files = TRUE` or retrieve it via following R code (assuming that `res` is object returned from `tvt.eSIR` or `qh.eSIR`): 32 | 33 | ```r 34 | res$gelman_diag_list 35 | ``` 36 | 37 | 38 | Chinese version:[中文](https://github.com/lilywang1988/eSIR/blob/master/README_cn.md) 39 | 40 | ## Purpose 41 | 42 | The outbreak of novel Corona Virus disease (a.k.a. COVID-19), originated in Wuhan, the capital of Hubei Province spreads quickly and affects many cities in China as well as many countries in the world. The Chinese government has enforced very stringent quarantine and inspection to prevent the worsening spread of COVID-19. Although various forms of forecast on the turning points of this epidemic within and outside Hubei Province have been published in the media, none of the prediction models has explicitly accounted for the time-varying quarantine protocols. We extended the classical SIR model for infectious disease by incorporating forms of medical isolation (in-home quarantine and hospitalization) in the underlying infectious disease dynamic system. Using the state-space model for both daily infected and hospitalized incidences and MCMC algorithms, we assess the effectiveness of quarantine protocols for confining COVID-19 spread in both Hubei Province and the other regions of China. Both predicted turning points and their credible bands may be obtained from the extended SIR under a given quarantine protocol. R software packages are also made publicly available for interested users. 43 | 44 | The standard SIR model has three components: susceptible, infected, and removed (including the recovery and dead). In the following sections, we will introduce the other extended state-space SIR models and their implementation in the package. **The results provided below are based on relatively short chains.** According to our experience, this setting (`M=5e3` and `nburnin=2e3`) should provide acceptable results in terms of the trend and turning points estimation, the estimation of parameters and their credible intervals might not be accurate. Hence, if possible, we would recommend using `M=5e5` and `nburnin=2e5` to obtain stable MCMC chains via [`rjags`](https://cran.r-project.org/web/packages/rjags/index.html). 45 | 46 | ![Standard SIR](man/figures/model0.png) 47 | 48 | ![BDSSM SIR](man/figures/BDSSM.png) 49 | 50 | ![Standard SIR](man/figures/RK4.png) 51 | 52 | ![Standard SIR](man/figures/priors.png) 53 | 54 | ![Standard SIR](man/figures/algorithm.png) 55 | 56 | ## Preparation 57 | 58 | [Download packages directly](https://github.com/lilywang1988/eSIR/blob/master/install_pkg) 59 | 60 | To install and use this R package from Github, you will need to first install the R package `devtools`. Please uncomment the codes to install them. `eSIR` depends on three other packages, `rjags` (an interface to the JAGS library), `chron` and `gtools`, which could be installed with `eSIR` if not yet. 61 | 62 | An error may occur if you have not yet installed JAGS-4.x.y.exe (for any x >= 0, y >=0). **Windows** users may download and install JAGS from [here](http://www.sourceforge.net/projects/mcmc-jags/files). **Mac** users may follow steps at [casallas/8411082](https://gist.github.com/casallas/8411082). 63 | 64 | 65 | ``` r 66 | # install.packages("devtools") 67 | # library(devtools) 68 | # install_github("lilywang1988/eSIR") 69 | library(eSIR) 70 | ``` 71 | 72 | Our data are collected daily from [dxy.com](https://mama.dxy.com/outbreak/daily-of-nationwide-new?index=20200206&locationIds=999&from=todh5). Alternatively, we notice some convenient access to COVID-19 data from [GuangchuangYu/nCov2019](https://github.com/GuangchuangYu/nCov2019). 73 | 74 | For data outside China, we use [JHU CSSE GitHub](https://github.com/CSSEGISandData/COVID-19) data. Another package [coronavirus](https://github.com/RamiKrispin/coronavirus) has its GitHub version udpated daily, which is also quite useful. 75 | 76 | ``` r 77 | # Data of COVID-19 can be found in the following R packages: 78 | # install_github("GuangchuangYu/nCov2019") 79 | #library(nCov2019) 80 | # install_github("qingyuanzhao/2019-nCov-Data") 81 | #library(2019-nCov-Data) 82 | ``` 83 | 84 | In Ubuntu (18.04) Linux, please first update R to a version >= 3.6. You may need to install jags package as well by `sudo apt-get install jags` before install devtools by `install.packages("devtools")`. [This](https://stackoverflow.com/questions/31114991/installation-of-package-devtools-had-non-zero-exit-status-on-ubuntu) stackoverflow question perfectly solved the issue I encountered when 85 | installing `devtools` on ubuntu. You may follow this [gist](https://gist.github.com/lilywang1988/170fbf1bbea1a6c23bc43a0dc871a0ca) to resolve other possible issues when installing `eSIR` on the recent version of Ubuntu. 86 | 87 | 88 | ## Model 1 using `tvt.eSIR()`: a SIR model with a time-varying transmission rate 89 | 90 | By introducing a time-dependent $$\pi(t)\in [0,1]$$ function that modifies the transmission rate $$\beta$$, we can depict a series of time-varying changes caused by either external variations like government policies, protective measures and environment changes, or internal variations like mutations and evolutions of the pathogen. 91 | 92 | The function can be either stepwise or exponential: 93 | 94 | ![pi functions](man/figures/pi_functions.png) 95 | 96 | ![tvt SIR](man/figures/model1.png) 97 | 98 | ```{r model1} 99 | set.seed(20192020) 100 | library(eSIR) 101 | # Hubei province data Jan13 -> Feb 11 102 | # Cumulative number of infected cases 103 | NI_complete <- c( 104 | 41, 41, 41, 45, 62, 131, 200, 270, 375, 444, 549, 729, 105 | 1052, 1423, 2714, 3554, 4903, 5806, 7153, 9074, 11177, 106 | 13522,16678,19665,22112,24953,27100,29631,31728,33366 107 | ) 108 | # Cumulative number of removed cases 109 | RI_complete <- c( 110 | 1, 1, 7, 10, 14, 20, 25, 31, 34, 45, 55, 71, 94, 111 | 121, 152, 213, 252, 345, 417, 561, 650, 811, 112 | 1017, 1261, 1485, 1917, 2260, 2725, 3284, 3754 113 | ) 114 | N <- 58.5e6 115 | R <- RI_complete / N 116 | Y <- NI_complete / N - R #Jan13->Feb 11 117 | 118 | ### Step function of pi(t) 119 | change_time <- c("01/23/2020", "02/04/2020", "02/08/2020") 120 | pi0 <- c(1.0, 0.9, 0.5, 0.1) 121 | res.step <- tvt.eSIR(Y, 122 | R, 123 | begin_str = "01/13/2020", 124 | T_fin = 200, 125 | pi0 = pi0, 126 | change_time = change_time, 127 | dic = FALSE, 128 | casename = "Hubei_step", 129 | save_files = FALSE, 130 | save_mcmc = FALSE, 131 | save_plot_data = TRUE, # can plot them 132 | M = 5e3, 133 | nburnin = 2e3 # additional to M 134 | ) 135 | 136 | res.step$plot_infection 137 | res.step$plot_removed 138 | res.step$spaghetti_plot 139 | 140 | 141 | # If we change the time unit to 5 days 142 | # Cumulative number of infected cases 143 | NI_complete2 <- NI_complete[seq(1, length(NI_complete), 5)] 144 | # Cumulative number of removed cases 145 | RI_complete2 <- RI_complete[seq(1, length(RI_complete), 5)] 146 | N2 <- 58.5e6 147 | R2 <- RI_complete2 / N2 148 | Y2 <- NI_complete2 / N2 - R2 #Jan13->Feb 11 149 | change_time2 <- c("01/23/2020", "02/04/2020", "02/08/2020") 150 | pi02 <- c(1.0, 0.9, 0.5, 0.1) 151 | res.step2 <- tvt.eSIR2(Y2, 152 | R2, 153 | begin_str = "01/13/2020", 154 | T_fin = 40, 155 | pi0 = pi02, 156 | change_time = change_time, 157 | dic = FALSE, 158 | casename = "Hubei_step2", 159 | save_files = FALSE, 160 | save_mcmc = FALSE, 161 | save_plot_data = TRUE, 162 | M = 5e3, 163 | nburnin = 2e3, 164 | time_unit = 5 #new feature! 165 | ) 166 | 167 | res.step2$plot_infection 168 | res.step2$plot_removed 169 | res.step2$spaghetti_plot 170 | res.step2$dic_val 171 | #res.step$gelman_diag_list 172 | ### continuous exponential function of pi(t) 173 | res.exp <- tvt.eSIR(Y, 174 | R, 175 | begin_str = "01/13/2020", 176 | death_in_R = 0.4, 177 | T_fin = 200, 178 | exponential = TRUE, 179 | dic = FALSE, 180 | lambda0 = 0.05, 181 | casename = "Hubei_exp", 182 | save_files = FALSE, 183 | save_mcmc = FALSE, 184 | save_plot_data = TRUE, 185 | M = 5e3, 186 | nburnin = 2e3) 187 | 188 | res.exp$plot_infection 189 | res.exp$spaghetti_plot 190 | #res.exp$plot_removed 191 | 192 | # Again, if we change our time unit to 5 days 193 | res.exp2 <- tvt.eSIR2(Y2, 194 | R2, 195 | begin_str = "01/13/2020", 196 | death_in_R = 0.4, 197 | T_fin = 200, 198 | exponential = TRUE, 199 | dic=FALSE, 200 | lambda0 = 0.05, 201 | casename = "Hubei_exp2", 202 | save_files = FALSE, 203 | save_mcmc = FALSE, 204 | save_plot_data = TRUE, 205 | M = 5e3, 206 | nburnin = 2e3, 207 | time_unit = 5) 208 | 209 | res.exp2$plot_infection 210 | res.exp2$spaghetti_plot 211 | 212 | ### without pi(t), the standard state-space SIR model without intervention 213 | res.nopi <- tvt.eSIR(Y, 214 | R, 215 | begin_str = "01/13/2020", 216 | death_in_R = 0.4, 217 | T_fin = 200, 218 | casename = "Hubei_nopi", 219 | save_files = F, 220 | save_plot_data = F, 221 | M=5e3,nburnin = 2e3) 222 | res.nopi$plot_infection 223 | res.nopi$spaghetti_plot 224 | #res.nopi$plot_removed 225 | ``` 226 | 227 | 228 | ## Model 2 using `qh.eSIR()`: SIR with time-varying quarantine, which follows a Dirac Delta function 229 | 230 | By introducing a vector of `phi` and its corresponding changing points `change_time`, we introduced a quarantine process that is dependent on a dirac delta function $\phi_t\in [0,1]$. In other words, only at time points defined by `change_time`, we have certain porportions of the at-risk (susceptible) subjects moved to the quarantine stage. The difference of this model than the previous time-varying transmission one is that we do not allow the tranmission rate to change, but only let the proportion of susceptible subjects decrease. 231 | ![Standard SIR](man/figures/model2.png) 232 | 233 | ![phi](man/figures/phi_functions.png) 234 | 235 | 236 | ```{r model2} 237 | set.seed(20192020) 238 | # Cumulative number of infected cases 239 | NI_complete <- c( 240 | 41, 41, 41, 45, 62, 131, 200, 270, 375, 444, 241 | 549, 729, 1052, 1423, 2714, 3554, 4903, 5806, 242 | 7153, 9074, 11177, 13522, 16678, 19665, 22112, 243 | 24953, 27100, 29631, 31728, 33366) 244 | # Cumulative number of removed cases 245 | RI_complete <- c( 246 | 1, 1, 7, 10, 14, 20, 25, 31, 34, 45, 55, 247 | 71, 94, 121, 152, 213, 252, 345, 417, 561, 248 | 650, 811, 1017, 1261, 1485, 1917, 2260, 249 | 2725, 3284, 3754) 250 | N <- 58.5e6 251 | R <- RI_complete / N 252 | Y <- NI_complete / N - R #Jan13->Feb 11 253 | 254 | change_time <- c("01/23/2020", "02/04/2020", "02/08/2020") 255 | phi0 <- c(0.1, 0.4, 0.4) 256 | res.q <- qh.eSIR(Y, 257 | R, 258 | begin_str = "01/13/2020", 259 | phi0 = phi0, 260 | change_time = change_time, 261 | casename = "Hubei_q", 262 | save_files = TRUE, 263 | save_mcmc = FALSE, 264 | save_plot_data = FALSE, 265 | M = 5e3, 266 | nburnin = 2e3) 267 | res.q$plot_infection 268 | ``` 269 | 270 | You will obtain the following plot in addition to the traceplots and summary table if you set `save_file=T` in `qh.eSIR`. The blue vertical line denotes the beginning date, and the other three gray lines denote the three change points. 271 | 272 | ![Standard SIR](man/figures/Hubei_qthetaQ_plot.png) 273 | 274 | 275 | ## Model 3 using `eSAIR`: SIR with time-varying subset of population immunized with antibody positivity 276 | 277 | To address the under-reporting issue associated with the available public databases and to build the self-immunization into the infection dynamics, we then further extend the previous eSIR model to an eSAIR model by adding an antibody (A) compartment. As is shown in the bottom thread of the following figure, this A compartment accounts for the probability of being self-immunized with antibodies to COVID-19, denoted by $\theta_t^A$; see equation as follows too, where $\alpha(t)$ is a function describing the proportion of people moving from the susceptible compartment to the antibody compartment over time. Compartment A helps circumvent limitations of data collection, especially embracing individuals who were infected but self-cured at home with no confirmation by viral RT-PCR diagnostic tests. This new eSAIR model characterizes the underlying population-level dynamics of the pandemic. The following system of ordinary differential equations defines collectively the continuous-time dynamics for the eSAIR model, which governs the law of movements among four compartments of Susceptible, Self-immunized, Infected and Removed. 278 | 279 | ![SAIR](man/figures/eSAIR_compartment.png) 280 | 281 | ![SAIR ODE](man/figures/SAIR_ODE.png) 282 | 283 | In the example below, we implemented this function onto New York state data assuming that by April 29, 20% of the population have been self-immunized with antibody positivity. 284 | 285 | ```{r model 3} 286 | # Cumulative number of infected cases 287 | NI_complete <- c( 288 | 1, 2, 11, 23, 31, 76, 106, 142, 150, 220, 327, 289 | 421, 613, 615, 967, 1578, 3038, 5704, 8403, 290 | 11727, 15800, 20884, 25681, 30841, 37877, 291 | 44876, 52410, 59648, 66663, 75833, 83948, 292 | 92506, 102987, 113833, 123160, 131815, 293 | 139875, 151061, 161779, 172348, 181026, 294 | 189033, 195749, 203020, 214454, 223691, 295 | 230597, 237474, 243382, 248416, 253519, 296 | 258222, 263460, 271590, 282143, 288045, 297 | 291996, 295106, 299691, 304372, 308314) 298 | # Cumulative number of removed cases 299 | RI_complete <- c( 300 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 301 | 20, 26, 38, 52, 200, 311, 468, 662, 302 | 893, 1144, 1547, 2144, 2931, 3900, 303 | 5133, 6201, 7657, 9483, 11536, 304 | 13915, 16276, 18781, 21110, 23424, 305 | 26469, 29784, 32899, 35785, 37730, 306 | 39207, 40703, 42164, 43488, 44723, 307 | 45887, 47473, 47686, 48769, 49572, 308 | 50221, 52161, 52917, 54115, 54613, 309 | 55473, 55816, 56809, 57265, 58525) 310 | N <- 8.399e6 311 | R <- RI_complete / N 312 | Y <- NI_complete / N - R 313 | 314 | change_time <- c("04/29/2020") 315 | alpha0 <- c(0.2) # 20% of the susceptible population were found immunized 316 | res.antibody <- eSAIR(Y, 317 | R, 318 | begin_str = "03/01/2020", 319 | alpha0 = alpha0, 320 | change_time = change_time, 321 | casename = "New_York_antibody", 322 | save_files = F, 323 | save_mcmc = F, 324 | M=5e2, 325 | nburnin = 2e2) 326 | res.antibody$plot_infection 327 | 328 | 329 | ``` 330 | 331 | 332 | 333 | ## Outputs and summary table 334 | 335 | To save all the plots (including trace plots) and summary tables, please set `save_files=T`, and if possible, provide a location by setting `file_add="YOUR/FAVORITE/FOLDER"`. Otherwise, the traceplots and other intermediate plots will not be saved, but you can still retrieve the forecast plots and summary table based on the return list, e.g., using `res.step$forecast_infection` and `res.step$out_table`. Moreover, if you are interested in plotting the figures on your own, you may set `save_mcmc=T` so that all the MCMC draws will be saved in a `.RData` file too. 336 | 337 | For details, please explore our package directly. We have `.rd` files established, please use `help(tvt.eSIR)` or `?qh.eSIR` to find them. 338 | 339 | ## Acknowledgements 340 | This package is created and maintained by [Lili Wang](lilywang@umich.edu), contributed by [Fei Wang](https://github.com/feiwsteven), [Lu Tang](https://github.com/ClumsyBear), and [Paul Egeler](https://github.com/pegeler). We also thank [Kangping Yang](kangpiny@umich.edu) for helping us collect the recovery data from the web page. 341 | 342 | 343 | ## References 344 | 345 | 1. Wang, L., Zhou, Y., He, J., Zhu, B., Wang, F., Tang, L., ... & Song, P. X. (2020). An epidemiological forecast model and software assessing interventions on the COVID-19 epidemic in China. Journal of Data Science, 18(3), 409-432. [link](https://www.airitilibrary.com/Publication/alDetailedMesh?DocID=16838602-202007-202008240002-202008240002-409-432&sourceBrowseType=0) 346 | 347 | 2. Osthus, D., Hickmann, K. S., Caragea, P. C., Higdon, D., & Del Valle, S. Y. (2017). Forecasting seasonal influenza with a state-space SIR model. The annals of applied statistics, 11(1), 202. 348 | 349 | 3. Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472. 350 | 351 | ----------- 352 | Shield: [![CC BY 4.0][cc-by-shield]][cc-by] 353 | 354 | This work is licensed under a [Creative Commons Attribution 4.0 International 355 | License][cc-by]. 356 | 357 | [![CC BY 4.0][cc-by-image]][cc-by] 358 | 359 | [cc-by]: http://creativecommons.org/licenses/by/4.0/ 360 | [cc-by-image]: https://i.creativecommons.org/l/by/4.0/88x31.png 361 | [cc-by-shield]: https://img.shields.io/badge/License-CC%20BY%204.0-lightgrey.svg 362 | 363 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | R package eSIR: extended state-space SIR epidemiological models 2 | ================ 3 | [Song Lab](http://www.umich.edu/~songlab/) 4 | 2021-10-31 5 | 6 | **Notice**: 7 | 8 | 1. We add new features in `tvt.eSIR()`. Now the new function 9 | `tvt.eSIR2()` adds `time_unit` which will allow users to change their 10 | time unit from 1 day to any arbitrary numbers of days. 11 | 12 | 2. Since version 0.3.1, we added the US data. The most recent update 13 | was on June 25th, 2021. We used data summarized from [JHU CSSE 14 | GitHub](https://github.com/CSSEGISandData/COVID-19) and 15 | [1Point3Acres](https://coronavirus.1point3acres.com). Only 41 states 16 | have complete recovery data. We will update the data every Thursday 17 | or Friday evening. Using following codes for the data: 18 | 19 | 20 | 21 | ``` r 22 | data("confirmed") # From JHU CSSE 23 | data("death") # From JHU CSSE 24 | data("recovered") # partly from 1Point3Acres 25 | data("USA_state_N") #population in each state 26 | ``` 27 | 28 | 3. Since version 0.3.3, we added Gelman-Rubin statistic for convergence 29 | check using 30 | [gelman.diag](https://www.rdocumentation.org/packages/coda/versions/0.19-3/topics/gelman.diag) 31 | from 32 | [`rjags`](https://cran.r-project.org/web/packages/rjags/index.html). 33 | Their values substantially larger than 1 imply a failure of 34 | convergence of the MCMC chains. Save it in a `.txt` file by setting 35 | `save_files = TRUE` or retrieve it via following R code (assuming 36 | that `res` is object returned from `tvt.eSIR` or `qh.eSIR`): 37 | 38 | 39 | 40 | ``` r 41 | res$gelman_diag_list 42 | ``` 43 | 44 | Chinese 45 | version:[中文](https://github.com/lilywang1988/eSIR/blob/master/README_cn.md) 46 | 47 | ## Purpose 48 | 49 | The outbreak of novel Corona Virus disease (a.k.a. COVID-19), originated 50 | in Wuhan, the capital of Hubei Province spreads quickly and affects many 51 | cities in China as well as many countries in the world. The Chinese 52 | government has enforced very stringent quarantine and inspection to 53 | prevent the worsening spread of COVID-19. Although various forms of 54 | forecast on the turning points of this epidemic within and outside Hubei 55 | Province have been published in the media, none of the prediction models 56 | has explicitly accounted for the time-varying quarantine protocols. We 57 | extended the classical SIR model for infectious disease by incorporating 58 | forms of medical isolation (in-home quarantine and hospitalization) in 59 | the underlying infectious disease dynamic system. Using the state-space 60 | model for both daily infected and hospitalized incidences and MCMC 61 | algorithms, we assess the effectiveness of quarantine protocols for 62 | confining COVID-19 spread in both Hubei Province and the other regions 63 | of China. Both predicted turning points and their credible bands may be 64 | obtained from the extended SIR under a given quarantine protocol. R 65 | software packages are also made publicly available for interested users. 66 | 67 | The standard SIR model has three components: susceptible, infected, and 68 | removed (including the recovery and dead). In the following sections, we 69 | will introduce the other extended state-space SIR models and their 70 | implementation in the package. **The results provided below are based on 71 | relatively short chains.** According to our experience, this setting 72 | (`M=5e3` and `nburnin=2e3`) should provide acceptable results in terms 73 | of the trend and turning points estimation, the estimation of parameters 74 | and their credible intervals might not be accurate. Hence, if possible, 75 | we would recommend using `M=5e5` and `nburnin=2e5` to obtain stable MCMC 76 | chains via 77 | [`rjags`](https://cran.r-project.org/web/packages/rjags/index.html). 78 | 79 | ![Standard SIR](man/figures/model0.png) 80 | 81 | ![BDSSM SIR](man/figures/BDSSM.png) 82 | 83 | ![Standard SIR](man/figures/RK4.png) 84 | 85 | ![Standard SIR](man/figures/priors.png) 86 | 87 | ![Standard SIR](man/figures/algorithm.png) 88 | 89 | ## Preparation 90 | 91 | [Download packages 92 | directly](https://github.com/lilywang1988/eSIR/blob/master/install_pkg) 93 | 94 | To install and use this R package from Github, you will need to first 95 | install the R package `devtools`. Please uncomment the codes to install 96 | them. `eSIR` depends on three other packages, `rjags` (an interface to 97 | the JAGS library), `chron` and `gtools`, which could be installed with 98 | `eSIR` if not yet. 99 | 100 | An error may occur if you have not yet installed JAGS-4.x.y.exe (for any 101 | x \>= 0, y \>=0). **Windows** users may download and install JAGS from 102 | [here](http://www.sourceforge.net/projects/mcmc-jags/files). **Mac** 103 | users may follow steps at 104 | [casallas/8411082](https://gist.github.com/casallas/8411082). 105 | 106 | ``` r 107 | # install.packages("devtools") 108 | # library(devtools) 109 | # install_github("lilywang1988/eSIR") 110 | library(eSIR) 111 | ``` 112 | 113 | Our data are collected daily from 114 | [dxy.com](https://mama.dxy.com/outbreak/daily-of-nationwide-new?index=20200206&locationIds=999&from=todh5). 115 | Alternatively, we notice some convenient access to COVID-19 data from 116 | [GuangchuangYu/nCov2019](https://github.com/GuangchuangYu/nCov2019). 117 | 118 | For data outside China, we use [JHU CSSE 119 | GitHub](https://github.com/CSSEGISandData/COVID-19) data. Another 120 | package [coronavirus](https://github.com/RamiKrispin/coronavirus) has 121 | its GitHub version udpated daily, which is also quite useful. 122 | 123 | ``` r 124 | # Data of COVID-19 can be found in the following R packages: 125 | # install_github("GuangchuangYu/nCov2019") 126 | #library(nCov2019) 127 | # install_github("qingyuanzhao/2019-nCov-Data") 128 | #library(2019-nCov-Data) 129 | ``` 130 | 131 | In Ubuntu (18.04) Linux, please first update R to a version \>= 3.6. You 132 | may need to install jags package as well by `sudo apt-get install jags` 133 | before install devtools by `install.packages("devtools")`. 134 | [This](https://stackoverflow.com/questions/31114991/installation-of-package-devtools-had-non-zero-exit-status-on-ubuntu) 135 | stackoverflow question perfectly solved the issue I encountered when 136 | installing `devtools` on ubuntu. You may follow this 137 | [gist](https://gist.github.com/lilywang1988/170fbf1bbea1a6c23bc43a0dc871a0ca) 138 | to resolve other possible issues when installing `eSIR` on the recent 139 | version of Ubuntu. 140 | 141 | ## Model 1 using `tvt.eSIR()`: a SIR model with a time-varying transmission rate 142 | 143 | By introducing a time-dependent \[\pi(t)\in [0,1]\] function that 144 | modifies the transmission rate \[\beta\], we can depict a series of 145 | time-varying changes caused by either external variations like 146 | government policies, protective measures and environment changes, or 147 | internal variations like mutations and evolutions of the pathogen. 148 | 149 | The function can be either stepwise or exponential: 150 | 151 | ![pi functions](man/figures/pi_functions.png) 152 | 153 | ![tvt SIR](man/figures/model1.png) 154 | 155 | ``` r 156 | set.seed(20192020) 157 | library(eSIR) 158 | # Hubei province data Jan13 -> Feb 11 159 | # Cumulative number of infected cases 160 | NI_complete <- c( 161 | 41, 41, 41, 45, 62, 131, 200, 270, 375, 444, 549, 729, 162 | 1052, 1423, 2714, 3554, 4903, 5806, 7153, 9074, 11177, 163 | 13522,16678,19665,22112,24953,27100,29631,31728,33366 164 | ) 165 | # Cumulative number of removed cases 166 | RI_complete <- c( 167 | 1, 1, 7, 10, 14, 20, 25, 31, 34, 45, 55, 71, 94, 168 | 121, 152, 213, 252, 345, 417, 561, 650, 811, 169 | 1017, 1261, 1485, 1917, 2260, 2725, 3284, 3754 170 | ) 171 | N <- 58.5e6 172 | R <- RI_complete / N 173 | Y <- NI_complete / N - R #Jan13->Feb 11 174 | 175 | ### Step function of pi(t) 176 | change_time <- c("01/23/2020", "02/04/2020", "02/08/2020") 177 | pi0 <- c(1.0, 0.9, 0.5, 0.1) 178 | res.step <- tvt.eSIR(Y, 179 | R, 180 | begin_str = "01/13/2020", 181 | T_fin = 200, 182 | pi0 = pi0, 183 | change_time = change_time, 184 | dic = FALSE, 185 | casename = "Hubei_step", 186 | save_files = FALSE, 187 | save_mcmc = FALSE, 188 | save_plot_data = TRUE, # can plot them 189 | M = 5e3, 190 | nburnin = 2e3 # additional to M 191 | ) 192 | #> The follow-up is from 01/13/20 to 07/30/20 and the last observed date is 02/11/20. 193 | #> Running for step-function pi(t) 194 | #> Compiling model graph 195 | #> Resolving undeclared variables 196 | #> Allocating nodes 197 | #> Graph information: 198 | #> Observed stochastic nodes: 60 199 | #> Unobserved stochastic nodes: 36 200 | #> Total graph size: 1875 201 | #> 202 | #> Initializing model 203 | 204 | res.step$plot_infection 205 | ``` 206 | 207 | ![](man/figures/README-model1-1.png) 208 | 209 | ``` r 210 | res.step$plot_removed 211 | ``` 212 | 213 | ![](man/figures/README-model1-2.png) 214 | 215 | ``` r 216 | res.step$spaghetti_plot 217 | ``` 218 | 219 | ![](man/figures/README-model1-3.png) 220 | 221 | ``` r 222 | 223 | 224 | # If we change the time unit to 5 days 225 | # Cumulative number of infected cases 226 | NI_complete2 <- NI_complete[seq(1, length(NI_complete), 5)] 227 | # Cumulative number of removed cases 228 | RI_complete2 <- RI_complete[seq(1, length(RI_complete), 5)] 229 | N2 <- 58.5e6 230 | R2 <- RI_complete2 / N2 231 | Y2 <- NI_complete2 / N2 - R2 #Jan13->Feb 11 232 | change_time2 <- c("01/23/2020", "02/04/2020", "02/08/2020") 233 | pi02 <- c(1.0, 0.9, 0.5, 0.1) 234 | res.step2 <- tvt.eSIR2(Y2, 235 | R2, 236 | begin_str = "01/13/2020", 237 | T_fin = 40, 238 | pi0 = pi02, 239 | change_time = change_time, 240 | dic = FALSE, 241 | casename = "Hubei_step2", 242 | save_files = FALSE, 243 | save_mcmc = FALSE, 244 | save_plot_data = TRUE, 245 | M = 5e3, 246 | nburnin = 2e3, 247 | time_unit = 5 #new feature! 248 | ) 249 | #> The follow-up is from 01/13/20 to 07/26/20 and the last observed date is 02/07/20. 250 | #> Running for step-function pi(t) 251 | #> Compiling model graph 252 | #> Resolving undeclared variables 253 | #> Allocating nodes 254 | #> Graph information: 255 | #> Observed stochastic nodes: 12 256 | #> Unobserved stochastic nodes: 12 257 | #> Total graph size: 395 258 | #> 259 | #> Initializing model 260 | 261 | res.step2$plot_infection 262 | ``` 263 | 264 | ![](man/figures/README-model1-4.png) 265 | 266 | ``` r 267 | res.step2$plot_removed 268 | ``` 269 | 270 | ![](man/figures/README-model1-5.png) 271 | 272 | ``` r 273 | res.step2$spaghetti_plot 274 | ``` 275 | 276 | ![](man/figures/README-model1-6.png) 277 | 278 | ``` r 279 | res.step2$dic_val 280 | #> NULL 281 | #res.step$gelman_diag_list 282 | ### continuous exponential function of pi(t) 283 | res.exp <- tvt.eSIR(Y, 284 | R, 285 | begin_str = "01/13/2020", 286 | death_in_R = 0.4, 287 | T_fin = 200, 288 | exponential = TRUE, 289 | dic = FALSE, 290 | lambda0 = 0.05, 291 | casename = "Hubei_exp", 292 | save_files = FALSE, 293 | save_mcmc = FALSE, 294 | save_plot_data = TRUE, 295 | M = 5e3, 296 | nburnin = 2e3) 297 | #> The follow-up is from 01/13/20 to 07/30/20 and the last observed date is 02/11/20. 298 | #> Running for exponential-function pi(t) 299 | #> Compiling model graph 300 | #> Resolving undeclared variables 301 | #> Allocating nodes 302 | #> Graph information: 303 | #> Observed stochastic nodes: 60 304 | #> Unobserved stochastic nodes: 36 305 | #> Total graph size: 1875 306 | #> 307 | #> Initializing model 308 | 309 | res.exp$plot_infection 310 | ``` 311 | 312 | ![](man/figures/README-model1-7.png) 313 | 314 | ``` r 315 | res.exp$spaghetti_plot 316 | ``` 317 | 318 | ![](man/figures/README-model1-8.png) 319 | 320 | ``` r 321 | #res.exp$plot_removed 322 | 323 | # Again, if we change our time unit to 5 days 324 | res.exp2 <- tvt.eSIR2(Y2, 325 | R2, 326 | begin_str = "01/13/2020", 327 | death_in_R = 0.4, 328 | T_fin = 200, 329 | exponential = TRUE, 330 | dic=FALSE, 331 | lambda0 = 0.05, 332 | casename = "Hubei_exp2", 333 | save_files = FALSE, 334 | save_mcmc = FALSE, 335 | save_plot_data = TRUE, 336 | M = 5e3, 337 | nburnin = 2e3, 338 | time_unit = 5) 339 | #> The follow-up is from 01/13/20 to 10/04/22 and the last observed date is 02/07/20. 340 | #> Running for exponential-function pi(t) 341 | #> Compiling model graph 342 | #> Resolving undeclared variables 343 | #> Allocating nodes 344 | #> Graph information: 345 | #> Observed stochastic nodes: 12 346 | #> Unobserved stochastic nodes: 12 347 | #> Total graph size: 555 348 | #> 349 | #> Initializing model 350 | 351 | res.exp2$plot_infection 352 | ``` 353 | 354 | ![](man/figures/README-model1-9.png) 355 | 356 | ``` r 357 | res.exp2$spaghetti_plot 358 | ``` 359 | 360 | ![](man/figures/README-model1-10.png) 361 | 362 | ``` r 363 | 364 | ### without pi(t), the standard state-space SIR model without intervention 365 | res.nopi <- tvt.eSIR(Y, 366 | R, 367 | begin_str = "01/13/2020", 368 | death_in_R = 0.4, 369 | T_fin = 200, 370 | casename = "Hubei_nopi", 371 | save_files = F, 372 | save_plot_data = F, 373 | M=5e3,nburnin = 2e3) 374 | #> The follow-up is from 01/13/20 to 07/30/20 and the last observed date is 02/11/20. 375 | #> Running without pi(t) 376 | #> Compiling model graph 377 | #> Resolving undeclared variables 378 | #> Allocating nodes 379 | #> Graph information: 380 | #> Observed stochastic nodes: 60 381 | #> Unobserved stochastic nodes: 36 382 | #> Total graph size: 1875 383 | #> 384 | #> Initializing model 385 | res.nopi$plot_infection 386 | ``` 387 | 388 | ![](man/figures/README-model1-11.png) 389 | 390 | ``` r 391 | res.nopi$spaghetti_plot 392 | ``` 393 | 394 | ![](man/figures/README-model1-12.png) 395 | 396 | ``` r 397 | #res.nopi$plot_removed 398 | ``` 399 | 400 | ## Model 2 using `qh.eSIR()`: SIR with time-varying quarantine, which follows a Dirac Delta function 401 | 402 | By introducing a vector of `phi` and its corresponding changing points 403 | `change_time`, we introduced a quarantine process that is dependent on a 404 | dirac delta function \(\phi_t\in [0,1]\). In other words, only at time 405 | points defined by `change_time`, we have certain porportions of the 406 | at-risk (susceptible) subjects moved to the quarantine stage. The 407 | difference of this model than the previous time-varying transmission one 408 | is that we do not allow the tranmission rate to change, but only let the 409 | proportion of susceptible subjects decrease. ![Standard 410 | SIR](man/figures/model2.png) 411 | 412 | ![phi](man/figures/phi_functions.png) 413 | 414 | ``` r 415 | set.seed(20192020) 416 | # Cumulative number of infected cases 417 | NI_complete <- c( 418 | 41, 41, 41, 45, 62, 131, 200, 270, 375, 444, 419 | 549, 729, 1052, 1423, 2714, 3554, 4903, 5806, 420 | 7153, 9074, 11177, 13522, 16678, 19665, 22112, 421 | 24953, 27100, 29631, 31728, 33366) 422 | # Cumulative number of removed cases 423 | RI_complete <- c( 424 | 1, 1, 7, 10, 14, 20, 25, 31, 34, 45, 55, 425 | 71, 94, 121, 152, 213, 252, 345, 417, 561, 426 | 650, 811, 1017, 1261, 1485, 1917, 2260, 427 | 2725, 3284, 3754) 428 | N <- 58.5e6 429 | R <- RI_complete / N 430 | Y <- NI_complete / N - R #Jan13->Feb 11 431 | 432 | change_time <- c("01/23/2020", "02/04/2020", "02/08/2020") 433 | phi0 <- c(0.1, 0.4, 0.4) 434 | res.q <- qh.eSIR(Y, 435 | R, 436 | begin_str = "01/13/2020", 437 | phi0 = phi0, 438 | change_time = change_time, 439 | casename = "Hubei_q", 440 | save_files = TRUE, 441 | save_mcmc = FALSE, 442 | save_plot_data = FALSE, 443 | M = 5e3, 444 | nburnin = 2e3) 445 | #> The follow-up is from 01/13/20 to 07/30/20 and the last observed date is 02/11/20. 446 | #> Running for qh.eSIR 447 | #> Compiling model graph 448 | #> Resolving undeclared variables 449 | #> Allocating nodes 450 | #> Graph information: 451 | #> Observed stochastic nodes: 60 452 | #> Unobserved stochastic nodes: 36 453 | #> Total graph size: 2736 454 | #> 455 | #> Initializing model 456 | res.q$plot_infection 457 | ``` 458 | 459 | ![](man/figures/README-model2-1.png) 460 | 461 | You will obtain the following plot in addition to the traceplots and 462 | summary table if you set `save_file=T` in `qh.eSIR`. The blue vertical 463 | line denotes the beginning date, and the other three gray lines denote 464 | the three change points. 465 | 466 | ![Standard SIR](man/figures/Hubei_qthetaQ_plot.png) 467 | 468 | ## Model 3 using `eSAIR`: SIR with time-varying subset of population immunized with antibody positivity 469 | 470 | To address the under-reporting issue associated with the available 471 | public databases and to build the self-immunization into the infection 472 | dynamics, we then further extend the previous eSIR model to an eSAIR 473 | model by adding an antibody (A) compartment. As is shown in the bottom 474 | thread of the following figure, this A compartment accounts for the 475 | probability of being self-immunized with antibodies to COVID-19, denoted 476 | by \(\theta_t^A\); see equation as follows too, where \(\alpha(t)\) is a 477 | function describing the proportion of people moving from the susceptible 478 | compartment to the antibody compartment over time. Compartment A helps 479 | circumvent limitations of data collection, especially embracing 480 | individuals who were infected but self-cured at home with no 481 | confirmation by viral RT-PCR diagnostic tests. This new eSAIR model 482 | characterizes the underlying population-level dynamics of the pandemic. 483 | The following system of ordinary differential equations defines 484 | collectively the continuous-time dynamics for the eSAIR model, which 485 | governs the law of movements among four compartments of Susceptible, 486 | Self-immunized, Infected and Removed. 487 | 488 | ![SAIR](man/figures/eSAIR_compartment.png) 489 | 490 | ![SAIR ODE](man/figures/SAIR_ODE.png) 491 | 492 | In the example below, we implemented this function onto New York state 493 | data assuming that by April 29, 20% of the population have been 494 | self-immunized with antibody positivity. 495 | 496 | ``` r 497 | # Cumulative number of infected cases 498 | NI_complete <- c( 499 | 1, 2, 11, 23, 31, 76, 106, 142, 150, 220, 327, 500 | 421, 613, 615, 967, 1578, 3038, 5704, 8403, 501 | 11727, 15800, 20884, 25681, 30841, 37877, 502 | 44876, 52410, 59648, 66663, 75833, 83948, 503 | 92506, 102987, 113833, 123160, 131815, 504 | 139875, 151061, 161779, 172348, 181026, 505 | 189033, 195749, 203020, 214454, 223691, 506 | 230597, 237474, 243382, 248416, 253519, 507 | 258222, 263460, 271590, 282143, 288045, 508 | 291996, 295106, 299691, 304372, 308314) 509 | # Cumulative number of removed cases 510 | RI_complete <- c( 511 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 512 | 20, 26, 38, 52, 200, 311, 468, 662, 513 | 893, 1144, 1547, 2144, 2931, 3900, 514 | 5133, 6201, 7657, 9483, 11536, 515 | 13915, 16276, 18781, 21110, 23424, 516 | 26469, 29784, 32899, 35785, 37730, 517 | 39207, 40703, 42164, 43488, 44723, 518 | 45887, 47473, 47686, 48769, 49572, 519 | 50221, 52161, 52917, 54115, 54613, 520 | 55473, 55816, 56809, 57265, 58525) 521 | N <- 8.399e6 522 | R <- RI_complete / N 523 | Y <- NI_complete / N - R 524 | 525 | change_time <- c("04/29/2020") 526 | alpha0 <- c(0.2) # 20% of the susceptible population were found immunized 527 | res.antibody <- eSAIR(Y, 528 | R, 529 | begin_str = "03/01/2020", 530 | alpha0 = alpha0, 531 | change_time = change_time, 532 | casename = "New_York_antibody", 533 | save_files = F, 534 | save_mcmc = F, 535 | M=5e2, 536 | nburnin = 2e2) 537 | #> The follow-up is from 03/01/20 to 09/16/20 and the last observed date is 04/30/20. 538 | #> Running for eSAIR 539 | #> Compiling model graph 540 | #> Resolving undeclared variables 541 | #> Allocating nodes 542 | #> Graph information: 543 | #> Observed stochastic nodes: 122 544 | #> Unobserved stochastic nodes: 67 545 | #> Total graph size: 5123 546 | #> 547 | #> Initializing model 548 | #> 549 | #> NOTE: Stopping adaptation 550 | res.antibody$plot_infection 551 | ``` 552 | 553 | ![](man/figures/README-model%203-1.png) 554 | 555 | ## Outputs and summary table 556 | 557 | To save all the plots (including trace plots) and summary tables, please 558 | set `save_files=T`, and if possible, provide a location by setting 559 | `file_add="YOUR/FAVORITE/FOLDER"`. Otherwise, the traceplots and other 560 | intermediate plots will not be saved, but you can still retrieve the 561 | forecast plots and summary table based on the return list, e.g., using 562 | `res.step$forecast_infection` and `res.step$out_table`. Moreover, if you 563 | are interested in plotting the figures on your own, you may set 564 | `save_mcmc=T` so that all the MCMC draws will be saved in a `.RData` 565 | file too. 566 | 567 | For details, please explore our package directly. We have `.rd` files 568 | established, please use `help(tvt.eSIR)` or `?qh.eSIR` to find them. 569 | 570 | ## Acknowledgements 571 | 572 | This package is created and maintained by [Lili 573 | Wang](lilywang@umich.edu), contributed by [Fei 574 | Wang](https://github.com/feiwsteven), [Lu 575 | Tang](https://github.com/ClumsyBear), and [Paul 576 | Egeler](https://github.com/pegeler). We also thank [Kangping 577 | Yang](kangpiny@umich.edu) for helping us collect the recovery data from 578 | the web page. 579 | 580 | ## References 581 | 582 | 1. Wang, L., Zhou, Y., He, J., Zhu, B., Wang, F., Tang, L., ... & Song, P. X. (2020). An epidemiological forecast model and software assessing interventions on the COVID-19 epidemic in China. Journal of Data Science, 18(3), 409-432. [link](https://www.airitilibrary.com/Publication/alDetailedMesh?DocID=16838602-202007-202008240002-202008240002-409-432&sourceBrowseType=0) 583 | 584 | 2. Osthus, D., Hickmann, K. S., Caragea, P. C., Higdon, D., & Del Valle, S. Y. (2017). Forecasting seasonal influenza with a state-space SIR model. The annals of applied statistics, 11(1), 202. 585 | 586 | 3. Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472. 587 | 588 | ----- 589 | 590 | Shield: [![CCBY 4.0](https://img.shields.io/badge/License-CC%20BY%204.0-lightgrey.svg)](http://creativecommons.org/licenses/by/4.0/) 591 | 592 | This work is licensed under a [Creative Commons Attribution 4.0 593 | International License](http://creativecommons.org/licenses/by/4.0/). 594 | 595 | [![CCBY 4.0](https://i.creativecommons.org/l/by/4.0/88x31.png)](http://creativecommons.org/licenses/by/4.0/) 596 | -------------------------------------------------------------------------------- /README_cn.md: -------------------------------------------------------------------------------- 1 | R包eSIR：扩展的状态空间SIR流行病学模型 2 | ================ 3 | [Song Lab](http://www.umich.edu/~songlab/) 4 | 2020-03-05 5 | 6 | 英文版本: [English](https://github.com/lilywang1988/eSIR/blob/master/README.md) 7 | 8 | 目的 9 | ------- 10 | 11 | 起源于湖北省省会武汉市的新型冠状病毒病（又名COVID-19）的爆发迅速蔓延，并影响了中国许多城市以及世界许多国家。中国政府已经实施了非常严格的检疫和检查，以防止COVID-19的传播恶化。尽管在媒体上已经发布了关于湖北省内外流行病拐点的各种形式的预测，但是没有一个预测模型明确说明了时变隔离协议。通过将医学隔离形式（家庭隔离和住院）纳入基本的传染病动态系统，我们扩展了传染病的经典SIR模型。使用针对每日感染和住院发病率的状态空间模型以及MCMC算法，我们评估了隔离方案对限制湖北省和中国其他地区传播的COVID-19的有效性。在给定的隔离协议下，可以从扩展的SIR获取预测的转折点及其可信带。 R软件包也向感兴趣的用户公开提供。 12 | 13 | 标准SIR模型包含三个组件：易感，受感染和已删除（包括恢复和死亡）。在以下各节中，我们将在包中介绍其他扩展状态空间SIR模型及其实现。 **以下提供的结果基于相对较短的链。** 根据我们的经验，此设置 (`M=5e3` and `nburnin=2e3`) 应在趋势和转折点估计方面提供可接受的结果， 参数及其可信区间的估计值可能不准确。 因此，如果可能，我们建议使用“ M = 5e5”和“ nburnin = 2e5”来通过[`rjags`](https://cran.r-project.org/web/packages/rjags/index.html)以获得稳定的MCMC链. 14 | 15 | ![Standard SIR](man/figures/model0.png) 16 | 17 | ![BDSSM SIR](man/figures/BDSSM.png) 18 | 19 | ![Standard SIR](man/figures/RK4.png) 20 | 21 | ![Standard SIR](man/figures/priors.png) 22 | 23 | ![Standard SIR](man/figures/algorithm.png) 24 | 25 | 安装准备 26 | ----------- 27 | [直接下载并安装](https://github.com/lilywang1988/eSIR/blob/master/install_binary) 28 | 29 | 如果要从Github安装和使用此R软件包，您需要首先安装R软件包`devtools`。 请取消注释代码以安装它们。 eSIR依赖于其他三个软件包：rjags（JAGS库的接口），chron和gtools，如果尚未安装，它们可以与eSIR一起安装。如果尚未安装JAGS-4.x.y.exe，可能会发生错误。(for any x >= 0, y >=0). **Windows** 用户可以从以下位置下载并安装JAGS [here](http://www.sourceforge.net/projects/mcmc-jags/files). **Mac** 用户可以按照以下步骤操作 [casallas/8411082](https://gist.github.com/casallas/8411082). 30 | 31 | 32 | ``` r 33 | # install.packages("devtools") 34 | # library(devtools) 35 | # install_github("lilywang1988/eSIR") 36 | library(eSIR) 37 | ``` 38 | 39 | 我们的数据来自于丁香医生 [dxy.com](https://mama.dxy.com/outbreak/daily-of-nationwide-new?index=20200206&locationIds=999&from=todh5). 其他我们知道的数据源包括 [GuangchuangYu/nCov2019](https://github.com/GuangchuangYu/nCov2019) 和 [qingyuanzhao/2019-nCov-Data](https://github.com/qingyuanzhao/2019-nCov-Data). 40 | 41 | ``` r 42 | # Data of COVID-19 can be found in the following R packages: 43 | # install_github("GuangchuangYu/nCov2019") 44 | #library(nCov2019) 45 | # install_github("qingyuanzhao/2019-nCov-Data") 46 | #library(2019-nCov-Data) 47 | ``` 48 | 在Ubuntu（18.04）Linux中，请先将R更新到一个版本 >= 3.6 的版本. 您可能还需要在通过`install.packages("devtools")`安装 devtools 之前安装jags软件包，方法是 `sudo apt-get install jags`。 49 | 50 | 模型1 `tvt.eSIR()`: 具有时变传输速率的SIR模型 51 | ----------------------------------------------------------------------------- 52 | 53 | 我们引入一个可以影响 *β* 的时间函数 *π*(*t*)∈\[0, 1\]，我们可以描述一系列时变变化，这些变化是由外部变化（例如政府政策，保护措施和环境变化）或内部变化（例如病原体的变异和进化）引起的。 54 | 55 | 该函数可以是逐步的或指数的： 56 | 57 | ![pi functions](man/figures/pi_functions.png) 58 | 59 | ![Standard SIR](man/figures/model1.png) 60 | 61 | ``` r 62 | set.seed(20192020) 63 | library(eSIR) 64 | #> Loading required package: rjags 65 | #> Loading required package: coda 66 | #> Linked to JAGS 4.3.0 67 | #> Loaded modules: basemod,bugs 68 | #> Loading required package: scales 69 | #> Loading required package: ggplot2 70 | #> Loading required package: chron 71 | #> Loading required package: gtools 72 | #> Loading required package: data.table 73 | # Hubei province data Jan13 -> Feb 11 74 | # cumulative number of infected 75 | NI_complete <- c( 41,41,41,45,62,131,200,270,375,444,549, 729, 76 | 1052,1423,2714,3554,4903,5806,7153,9074,11177, 77 | 13522,16678,19665,22112,24953,27100,29631,31728,33366) 78 | RI_complete <- c(1,1,7,10,14,20,25,31,34,45,55,71,94,121,152,213, 79 | 252,345,417,561,650,811,1017,1261,1485,1917,2260, 80 | 2725,3284,3754) 81 | N=58.5e6 82 | R <- RI_complete/N 83 | Y <- NI_complete/N- R #Jan13->Feb 11 84 | ### Step function of pi(t) 85 | change_time <- c("01/23/2020","02/04/2020","02/08/2020") 86 | pi0<- c(1.0,0.9,0.5,0.1) 87 | res.step <-tvt.eSIR(Y,R,begin_str="01/13/2020",death_in_R = 0.4,T_fin=200, 88 | pi0=pi0,change_time=change_time,dic=T,casename="Hubei_step", 89 | save_files = T, save_mcmc=F,save_plot_data = F,M=5e3,nburnin = 2e3) 90 | #> The follow-up is from 01/13/20 to 07/30/20 and the last observed date is 02/11/20. 91 | #> Running for step-function pi(t) 92 | #> Compiling model graph 93 | #> Resolving undeclared variables 94 | #> Allocating nodes 95 | #> Graph information: 96 | #> Observed stochastic nodes: 60 97 | #> Unobserved stochastic nodes: 37 98 | #> Total graph size: 1873 99 | #> 100 | #> Initializing model 101 | res.step$plot_infection 102 | ``` 103 | 104 | ![](man/figures/README-model1-1.png) 105 | 106 | ``` r 107 | res.step$plot_removed 108 | ``` 109 | 110 | ![](man/figures/README-model1-2.png) 111 | 112 | ``` r 113 | res.step$spaghetti_plot 114 | ``` 115 | 116 | ![](man/figures/README-model1-3.png) 117 | 118 | ``` r 119 | res.step$dic_val 120 | #> Mean deviance: -1262 121 | #> penalty 37.98 122 | #> Penalized deviance: -1224 123 | 124 | ### continuous exponential function of pi(t) 125 | res.exp <- tvt.eSIR(Y,R,begin_str="01/13/2020",death_in_R = 0.4, 126 | T_fin=200,exponential=TRUE,dic=F,lambda0=0.05, 127 | casename="Hubei_exp",save_files = F,save_mcmc=F, 128 | save_plot_data = F,M=5e3,nburnin = 2e3) 129 | #> The follow-up is from 01/13/20 to 07/30/20 and the last observed date is 02/11/20. 130 | #> Running for exponential-function pi(t) 131 | #> Compiling model graph 132 | #> Resolving undeclared variables 133 | #> Allocating nodes 134 | #> Graph information: 135 | #> Observed stochastic nodes: 60 136 | #> Unobserved stochastic nodes: 37 137 | #> Total graph size: 1873 138 | #> 139 | #> Initializing model 140 | res.exp$plot_infection 141 | ``` 142 | 143 | ![](man/figures/README-model1-4.png) 144 | 145 | ``` r 146 | res.exp$spaghetti_plot 147 | ``` 148 | 149 | ![](man/figures/README-model1-5.png) 150 | 151 | ``` r 152 | #res.exp$plot_removed 153 | 154 | ### without pi(t), the standard state-space SIR model without intervention 155 | res.nopi <- tvt.eSIR(Y,R,begin_str="01/13/2020",death_in_R = 0.4,T_fin=200, casename="Hubei_nopi",save_files = F,save_plot_data = F, 156 | M=5e3,nburnin = 2e3) 157 | #> The follow-up is from 01/13/20 to 07/30/20 and the last observed date is 02/11/20. 158 | #> Running without pi(t) 159 | #> Compiling model graph 160 | #> Resolving undeclared variables 161 | #> Allocating nodes 162 | #> Graph information: 163 | #> Observed stochastic nodes: 60 164 | #> Unobserved stochastic nodes: 37 165 | #> Total graph size: 1873 166 | #> 167 | #> Initializing model 168 | res.nopi$plot_infection 169 | ``` 170 | 171 | ![](man/figures/README-model1-6.png) 172 | 173 | ``` r 174 | res.nopi$spaghetti_plot 175 | ``` 176 | 177 | ![](man/figures/README-model1-7.png) 178 | 179 | ``` r 180 | #res.nopi$plot_removed 181 | ``` 182 | 183 | 模型2 `qh.eSIR()`: 具有随时间变化的隔离的SIR，遵循Dirac Delta函数 184 | ------------------------------------------------------------------------------------------------- 185 | 通过引入向量`phi`及其对应的变化点`change_time`，我们引入了依赖于Dirac delta函数 *ϕ**t* ∈ \[0, 1\]。换句话说，仅在`change_time`定义的时间点，我们才将某些风险（易感）对象的某些部分移至隔离阶段。 该模型与以前的时变传输模型的不同之处在于，我们不允许传输率发生变化，而只是让易感对象的比例降低。 186 | 187 | ![Standard SIR](man/figures/model2.png) 188 | 189 | ![phi](man/figures/phi_functions.png) 190 | 191 | ``` r 192 | set.seed(20192020) 193 | NI_complete <- c( 41,41,41,45,62,131,200,270,375,444,549, 729, 194 | 1052,1423,2714,3554,4903,5806,7153,9074,11177, 195 | 13522,16678,19665,22112,24953,27100,29631,31728,33366) 196 | RI_complete <- c(1,1,7,10,14,20,25,31,34,45,55,71,94,121,152,213, 197 | 252,345,417,561,650,811,1017,1261,1485,1917,2260, 198 | 2725,3284,3754) 199 | N=58.5e6 200 | R <- RI_complete/N 201 | Y <- NI_complete/N- R #Jan13->Feb 11 202 | 203 | change_time <- c("01/23/2020","02/04/2020","02/08/2020") 204 | phi0 <- c(0.1,0.4,0.4) 205 | res.q <- qh.eSIR (Y,R,begin_str="01/13/2020",death_in_R = 0.4, 206 | phi0=phi0,change_time=change_time,casename="Hubei_q", 207 | save_files = T,save_mcmc = F,save_plot_data = F, 208 | M=5e3,nburnin = 2e3) 209 | #> The follow-up is from 01/13/20 to 07/30/20 and the last observed date is 02/11/20. 210 | #> Running for qh.eSIR 211 | #> Compiling model graph 212 | #> Resolving undeclared variables 213 | #> Allocating nodes 214 | #> Graph information: 215 | #> Observed stochastic nodes: 60 216 | #> Unobserved stochastic nodes: 37 217 | #> Total graph size: 2676 218 | #> 219 | #> Initializing model 220 | res.q$plot_infection 221 | ``` 222 | 223 | ![](man/figures/README-model2-1.png) 224 | 225 | ``` r 226 | #res.q$plot_removed 227 | 228 | #res.noq <- qh.eSIR (Y,R,begin_str="01/13/2020",death_in_R = 0.4, 229 | # T_fin=200,casename="Hubei_noq", 230 | # M=5e3,nburnin = 2e3) 231 | #res.noq$plot_infection 232 | ``` 233 | 如果在`qh.eSIR`中设置`save_file = T`，除了traceplots和summary表之外，还将获得以下图表。 蓝色垂直线表示开始日期，而其他三个灰色线表示三个更改点。 234 | 235 | ![Standard SIR](man/figures/Hubei_qthetaQ_plot.png) 236 | 237 | 结果和汇总表 238 | ------------------------- 239 | 要保存所有图（包括轨迹图）和汇总表，请设置`save_files = T`，并在可能的情况下通过设置`file_add="YOUR/FAVORITE/FOLDER"`提供位置。否则，轨迹图和其他中间图将不会保存，但是您仍然可以使用`res.step$forecast_infection`和`res.step$out_table`来找到它们。 此外，如果您有兴趣自己绘制图形，可以设置`save_mcmc = T`，以便所有MCMC图形也都保存在`.RData`文件中。 240 | 241 | 有关详细信息，请直接浏览我们的软件包。我们有准备完整的`.rd`文件，请使用`?(tvt.eSIR)`或`help(qh.eSIR)`查找它们。 242 | 243 | 参考文献 244 | ---------- 245 | 246 | 1. Song, P. X., Wang, L., Zhou, Y., He, J., Zhu, B., Wang, F., ... & Eisenberg, M. (2020). An epidemiological forecast model and software assessing interventions on COVID-19 epidemic in China. medRxiv. 247 | 248 | 2. Osthus, D., Hickmann, K. S., Caragea, P. C., Higdon, D., & Del Valle, S. Y. (2017). Forecasting seasonal influenza with a state-space SIR model. The annals of applied statistics, 11(1), 202. 249 | 250 | 3. Mkhatshwa, T., & Mummert, A. (2010). Modeling super-spreading events for infectious diseases: case study SARS. arXiv preprint arXiv:1007.0908. 251 | -------------------------------------------------------------------------------- /data/USA_state_N.rda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/lilywang1988/eSIR/2a1f0c36afd0d77b55642102780d852d2354fe46/data/USA_state_N.rda -------------------------------------------------------------------------------- /data/confirmed.rda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/lilywang1988/eSIR/2a1f0c36afd0d77b55642102780d852d2354fe46/data/confirmed.rda -------------------------------------------------------------------------------- /data/death.rda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/lilywang1988/eSIR/2a1f0c36afd0d77b55642102780d852d2354fe46/data/death.rda 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-------------------------------------------------------------------------------- https://raw.githubusercontent.com/lilywang1988/eSIR/2a1f0c36afd0d77b55642102780d852d2354fe46/install_pkg/eSIR_0.3.3.tgz -------------------------------------------------------------------------------- /man/eSAIR.Rd: -------------------------------------------------------------------------------- 1 | % Generated by roxygen2: do not edit by hand 2 | % Please edit documentation in R/eSAIR.R 3 | \name{eSAIR} 4 | \alias{eSAIR} 5 | \title{Extended state-space SIR with a subset of the population showing antibody positivity} 6 | \usage{ 7 | eSAIR( 8 | Y, 9 | R, 10 | alpha0 = NULL, 11 | change_time = NULL, 12 | begin_str = "01/13/2020", 13 | T_fin = 200, 14 | nchain = 4, 15 | nadapt = 10000, 16 | M = 500, 17 | thn = 10, 18 | nburnin = 200, 19 | dic = FALSE, 20 | death_in_R = 0.02, 21 | casename = "eSAIR", 22 | beta0 = 0.2586, 23 | gamma0 = 0.0821, 24 | R0 = beta0/gamma0, 25 | gamma0_sd = 0.1, 26 | R0_sd = 1, 27 | file_add = character(0), 28 | add_death = FALSE, 29 | save_files = FALSE, 30 | save_mcmc = FALSE, 31 | save_plot_data = FALSE, 32 | eps = 1e-10 33 | ) 34 | } 35 | \arguments{ 36 | \item{Y}{the time series of daily observed infected compartment proportions.} 37 | 38 | \item{R}{the time series of daily observed removed compartment proportions, including death and recovered.} 39 | 40 | \item{alpha0}{a vector of values of the dirac delta function \eqn{\alpha_t}. Each entry denotes the proportion that will be immunized at each change time point. Note that all the entries lie between 0 and 1, its default is \code{NULL}.} 41 | 42 | \item{change_time}{the change points over time corresponding to \code{alpha0}, to formulate the dirac delta function \eqn{\alpha_t}; its defalt value is \code{NULL}.} 43 | 44 | \item{begin_str}{the character of starting time, the default is "01/13/2020".} 45 | 46 | \item{T_fin}{the end of follow-up time after the beginning date \code{begin_str}, the default is 200.} 47 | 48 | \item{nchain}{the number of MCMC chains generated by \code{\link[rjags]{rjags}}, the default is 4.} 49 | 50 | \item{nadapt}{the iteration number of adaptation in the MCMC. We recommend using at least the default value 1e4 to obtained fully adapted chains.} 51 | 52 | \item{M}{the number of draws in each chain, with no thinning. The default is M=5e2 but suggest using 5e5.} 53 | 54 | \item{thn}{the thinning interval between mixing. The total number of draws thus would become \code{round(M/thn)*nchain}. The default is 10.} 55 | 56 | \item{nburnin}{the burn-in period. The default is 2e2 but suggest 2e5.} 57 | 58 | \item{dic}{logical, whether compute the DIC (deviance information criterion) for model selection.} 59 | 60 | \item{death_in_R}{the numeric value of average of cumulative deaths in the removed compartments. The default is 0.4 within Hubei and 0.02 outside Hubei.} 61 | 62 | \item{casename}{the string of the job's name. The default is "eSAIR".} 63 | 64 | \item{beta0}{the hyperparameter of average transmission rate, the default is the one estimated from the SARS first-month outbreak (0.2586).} 65 | 66 | \item{gamma0}{the hyperparameter of average removed rate, the default is the one estimated from the SARS first-month outbreak (0.0821).} 67 | 68 | \item{R0}{the hyperparameter of the mean reproduction number R0. The default is thus the ratio of \code{beta0/gamma0}, which can be specified directly.} 69 | 70 | \item{gamma0_sd}{the standard deviation for the prior distrbution of the removed rate \eqn{\gamma}, the default is 0.1.} 71 | 72 | \item{R0_sd}{the standard deviation for the prior disbution of R0, the default is 1.} 73 | 74 | \item{file_add}{the string to denote the location of saving output files and tables.} 75 | 76 | \item{add_death}{logical, whether add the approximate death curve to the plot, default is false.} 77 | 78 | \item{save_files}{logical, whether to save plots to file.} 79 | 80 | \item{save_mcmc}{logical, whether save (\code{TRUE}) all the MCMC outputs or not (\code{FALSE}).The output file will be an \code{.RData} file named by the \eqn{casename}. We include arrays of prevalence values of the three compartments with their matrices of posterior draws up to the last date of the collected data as \code{theta_p[,,1]} and afterwards as \code{theta_pp[,,1]} for \eqn{\theta_t^S}, \code{theta_p[,,2]} and \code{theta_pp[,,2]} for \eqn{\theta_t^I}, and \code{theta_p[,,3]} and \code{theta_pp[,,3]} for \eqn{\theta_t^R}. The posterior draws of the prevalence process of the antibody-immunized compartment can be obtained via \code{thetaA_p} and \code{thetaA_pp}. Moreover, the input and predicted proportions \code{Y}, \code{Y_pp}, \code{R} and \code{R_pp} can also be retrieved. The prevalence and prediceted proportion matrices have rows for MCMC replicates, and columns for days. The MCMC posterior draws of other parameters including \code{beta}, \code{gamma}, \code{R0}, and variance controllers \code{k_p}, \code{lambdaY_p}, \code{lambdaR_p} are also available.} 81 | 82 | \item{save_plot_data}{logical, whether save the plotting data or not.} 83 | 84 | \item{eps}{a non-zero controller so that all the input \code{Y} and \code{R} values would be bounded above 0 (at least \code{eps}). Its default value is 1e-10} 85 | } 86 | \value{ 87 | \item{casename}{the predefined \code{casename}.} 88 | \item{incidence_mean}{mean cumulative incidence, the mean prevalence of cumulative confirmed cases at the end of the study.} 89 | \item{incidence_ci}{2.5\%, 50\%, and 97.5\% quantiles of the incidences.} 90 | \item{out_table}{summary tables including the posterior mean of the prevalance processes of the 3 states compartments (\eqn{\theta_t^S,\theta_t^I,\theta_t^R,\theta_t^H}) at last date of data collected ((\eqn{t^\prime}) decided by the lengths of your input data \code{Y} and \code{R}), and their respective credible inctervals (ci); the respective means and ci's of the reporduction number (R0), removed rate (\eqn{\gamma}), transmission rate (\eqn{\beta}).} 91 | \item{plot_infection}{plot of summarizing and forecasting for the infection compartment, in which the vertial blue line denotes the last date of data collected (\eqn{t^\prime}), the vertial darkgray line denotes the deacceleration point (first turning point) that the posterior mean first-derivative of infection prevalence \eqn{\dot{\theta}_t^I} achieves the maximum, the vertical purple line denotes the second turning point that the posterior mean first-derivative infection proportion \eqn{\dot{\theta}_t^I} equals zero, the darkgray line denotes the posterior mean of the infection prevalence \eqn{\theta_t^I} and the red line denotes its posterior median. } 92 | \item{plot_removed}{plot of summarizing and forecasting for the removed compartment with lines similar to those in the \code{plot_infection}. The vertical lines are identical, but the horizontal mean and median correspond to the posterior mean and median of the removed process \eqn{\theta_t^R}. An additional line indicates the estimated death prevalence from the input \code{death_in_R}.} 93 | \item{spaghetti_plot}{20 randomly selected MCMC draws of the first-order derivative of the posterior prevalence of infection, namely \eqn{\dot{\theta}_t^I}. The black curve is the posterior mean of the derivative, and the vertical lines mark times of turning points corresponding respectively to those shown in \code{plot_infection} and \code{plot_removed}. Moreover, the 95\% credible intervals of these turning points are also highlighted by semi-transparent rectangles. } 94 | \item{first_tp_mean}{the date t at which \eqn{\ddot{\theta}_t^I=0}, calculated as the average of the time points with maximum posterior first-order derivatives \eqn{\dot{\theta}_t^I}; this value may be slightly different from the one labeled by the "darkgreen" lines in the two plots \code{plot_infection} and \code{plot_removed}, which indicate the stationary point such that the first-order derivative of the averaged posterior of \eqn{\theta_t^I} reaches its maximum.} 95 | \item{first_tp_mean}{the date t at which \eqn{\ddot{\theta}_t^I=0}, calculated as the average of the time points with maximum posterior first-order derivatives \eqn{\dot{\theta}_t^I}; this value may be slightly different from the one labeled by the "darkgreen" lines in the two plots \code{plot_infection} and \code{plot_removed}, which indicate the stationary point such that the first-order derivative of the averaged posterior of \eqn{\theta_t^I} reaches its maximum.} 96 | 97 | \item{first_tp_ci}{fwith \code{first_tp_mean}, it reports the corresponding credible interval and median.} 98 | \item{second_tp_mean}{the date t at which \eqn{\theta_t^I=0}, calculated as the average of the stationary points of all of posterior first-order derivatives \eqn{\dot{\theta}_t^I}; this value may be slightly different from the one labeled by the "pruple" lines in the plots of \code{plot_infection} and \code{plot_removed}. The latter indicate stationary t at which the first-order derivative of the averaged posterior of \eqn{\theta_t^I} equals zero.} 99 | \item{second_tp_ci}{with \code{second_tp_mean}, it reports the corresponding credible interval and median.} 100 | \item{dic_val}{the output of \code{dic.samples()} in \code{\link[rjags]{dic.samples}}, computing deviance information criterion for model comparison.} 101 | \item{gelman_diag_list}{ Since version 0.3.3, we incorporated Gelman And Rubin's Convergence Diagnostic using \code{\link[coda]{gelman.diag}}. We included both the statistics and their upper C.I. limits. Values substantially above 1 indicate lack of convergence. Error messages would be printed as they are. This would be only valid for multiple chains (e.g. nchain > 1). Note that for time dependent processes, we only compute the convergence of the last observation data (\code{T_prime}), though it shows to be \code{T_prime+1}, which is due to the day 0 for initialization.} 102 | } 103 | \description{ 104 | In this function we allow it to characterize time-varying immunization among a subset of the population that have been tested positive in an antibody assessment. We expanded the SIR model by adding a time-varying antibody-positive proportion \eqn{\alpha_t}. 105 | } 106 | \examples{ 107 | \dontrun{ 108 | NI_complete <- c( 109 | 41, 41, 41, 45, 62, 131, 200, 270, 375, 444, 549, 729, 110 | 1052, 1423, 2714, 3554, 4903, 5806, 7153, 9074, 11177, 111 | 13522, 16678, 19665, 22112, 24953, 27100, 29631, 31728, 33366 112 | ) 113 | RI_complete <- c( 114 | 1, 1, 7, 10, 14, 20, 25, 31, 34, 45, 55, 71, 94, 115 | 121, 152, 213, 252, 345, 417, 561, 650, 811, 1017, 116 | 1261, 1485, 1917, 2260, 2725, 3284, 3754 117 | ) 118 | N <- 58.5e6 119 | R <- RI_complete / N 120 | Y <- NI_complete / N - R # Jan13->Feb 11 121 | change_time <- c("02/08/2020") 122 | alpha0 <- c(0.2) # 20\% of the susceptible population were found immunized 123 | res.antibody <- eSAIR(Y, R, 124 | begin_str = "01/13/2020", death_in_R = 0.4, 125 | alpha0 = alpha0, change_time = change_time, 126 | casename = "Hubei_antibody", save_files = T, save_mcmc = F, 127 | M = 5e2, nburnin = 2e2 128 | ) 129 | res.antibody$plot_infection 130 | } 131 | 132 | change_time <- c("01/16/2020") 133 | alpha0 <- c(0.2) 134 | NI_complete2 <- c(41, 45) 135 | RI_complete2 <- c(1, 1) 136 | N2 <- 1E3 137 | res3 <- eSAIR( 138 | RI_complete2 / N2, 139 | NI_complete2 / N2, 140 | begin_str = "01/13/2020", 141 | T_fin = 4, 142 | alpha0 = alpha0, 143 | change_time = change_time, 144 | dic = FALSE, 145 | casename = "Hubei_q", 146 | save_files = FALSE, 147 | save_mcmc = FALSE, 148 | save_plot_data = FALSE, 149 | M = 50, 150 | nburnin = 1 151 | ) 152 | closeAllConnections() 153 | 154 | } 155 | -------------------------------------------------------------------------------- /man/figures/BDSSM.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/lilywang1988/eSIR/2a1f0c36afd0d77b55642102780d852d2354fe46/man/figures/BDSSM.png -------------------------------------------------------------------------------- /man/figures/Hubei_qthetaQ_plot.png: 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nburnin = 200, 19 | dic = FALSE, 20 | death_in_R = 0.02, 21 | casename = "qh.eSIR", 22 | beta0 = 0.2586, 23 | gamma0 = 0.0821, 24 | R0 = beta0/gamma0, 25 | gamma0_sd = 0.1, 26 | R0_sd = 1, 27 | file_add = character(0), 28 | add_death = FALSE, 29 | save_files = FALSE, 30 | save_mcmc = FALSE, 31 | save_plot_data = FALSE, 32 | eps = 1e-10 33 | ) 34 | } 35 | \arguments{ 36 | \item{Y}{the time series of daily observed infected compartment proportions.} 37 | 38 | \item{R}{the time series of daily observed removed compartment proportions, including death and recovered.} 39 | 40 | \item{phi0}{a vector of values of the dirac delta function \eqn{\phi_t}. Each entry denotes the proportion that will be qurantined at each change time point. Note that all the entries lie between 0 and 1, its default is \code{NULL}.} 41 | 42 | \item{change_time}{the change points over time corresponding to \code{phi0}, to formulate the dirac delta function \eqn{\phi_t}; its defalt value is \code{NULL}.} 43 | 44 | \item{begin_str}{the character of starting time, the default is "01/13/2020".} 45 | 46 | \item{T_fin}{the end of follow-up time after the beginning date \code{begin_str}, the default is 200.} 47 | 48 | \item{nchain}{the number of MCMC chains generated by \code{\link[rjags]{rjags}}, the default is 4.} 49 | 50 | \item{nadapt}{the iteration number of adaptation in the MCMC. We recommend using at least the default value 1e4 to obtained fully adapted chains.} 51 | 52 | \item{M}{the number of draws in each chain, with no thinning. The default is M=5e2 but suggest using 5e5.} 53 | 54 | \item{thn}{the thinning interval between mixing. The total number of draws thus would become \code{round(M/thn)*nchain}. The default is 10.} 55 | 56 | \item{nburnin}{the burn-in period. The default is 2e2 but suggest 2e5.} 57 | 58 | \item{dic}{logical, whether compute the DIC (deviance information criterion) for model selection.} 59 | 60 | \item{death_in_R}{the numeric value of average of cumulative deaths in the removed compartments. The default is 0.4 within Hubei and 0.02 outside Hubei.} 61 | 62 | \item{casename}{the string of the job's name. The default is "qh.eSIR".} 63 | 64 | \item{beta0}{the hyperparameter of average transmission rate, the default is the one estimated from the SARS first-month outbreak (0.2586).} 65 | 66 | \item{gamma0}{the hyperparameter of average removed rate, the default is the one estimated from the SARS first-month outbreak (0.0821).} 67 | 68 | \item{R0}{the hyperparameter of the mean reproduction number R0. The default is thus the ratio of \code{beta0/gamma0}, which can be specified directly.} 69 | 70 | \item{gamma0_sd}{the standard deviation for the prior distrbution of the removed rate \eqn{\gamma}, the default is 0.1.} 71 | 72 | \item{R0_sd}{the standard deviation for the prior disbution of R0, the default is 1.} 73 | 74 | \item{file_add}{the string to denote the location of saving output files and tables.} 75 | 76 | \item{add_death}{logical, whether add the approximate death curve to the plot, default is false.} 77 | 78 | \item{save_files}{logical, whether to save plots to file.} 79 | 80 | \item{save_mcmc}{logical, whether save (\code{TRUE}) all the MCMC outputs or not (\code{FALSE}).The output file will be an \code{.RData} file named by the \eqn{casename}. We include arrays of prevalence values of the three compartments with their matrices of posterior draws up to the last date of the collected data as \code{theta_p[,,1]} and afterwards as \code{theta_pp[,,1]} for \eqn{\theta_t^S}, \code{theta_p[,,2]} and \code{theta_pp[,,2]} for \eqn{\theta_t^I}, and \code{theta_p[,,3]} and \code{theta_pp[,,3]} for \eqn{\theta_t^R}. The posterior draws of the prevalence process of the quarantine compartment can be obtained via \code{thetaQ_p} and \code{thetaQ_pp}. Moreover, the input and predicted proportions \code{Y}, \code{Y_pp}, \code{R} and \code{R_pp} can also be retrieved. The prevalence and prediceted proportion matrices have rows for MCMC replicates, and columns for days. The MCMC posterior draws of other parameters including \code{beta}, \code{gamma}, \code{R0}, and variance controllers \code{k_p}, \code{lambdaY_p}, \code{lambdaR_p} are also available.} 81 | 82 | \item{save_plot_data}{logical, whether save the plotting data or not.} 83 | 84 | \item{eps}{a non-zero controller so that all the input \code{Y} and \code{R} values would be bounded above 0 (at least \code{eps}). Its default value is 1e-10} 85 | } 86 | \value{ 87 | \item{casename}{the predefined \code{casename}.} 88 | \item{incidence_mean}{mean cumulative incidence, the mean prevalence of cumulative confirmed cases at the end of the study.} 89 | \item{incidence_ci}{2.5\%, 50\%, and 97.5\% quantiles of the incidences.} 90 | \item{out_table}{summary tables including the posterior mean of the prevalence processes of the 3 states compartments (\eqn{\theta_t^S,\theta_t^I,\theta_t^R,\theta_t^H}) at last date of data collected ((\eqn{t^\prime}) decided by the lengths of your input data \code{Y} and \code{R}), and their respective credible intervals (ci); the respective means and ci's of the reproduction number (R0), removed rate (\eqn{\gamma}), transmission rate (\eqn{\beta}).} 91 | \item{plot_infection}{plot of summarizing and forecasting for the infection compartment, in which the vertical blue line denotes the last date of data collected (\eqn{t^\prime}), the vertical darkgray line denotes the deacceleration point (first turning point) that the posterior mean first-derivative of infection prevalence \eqn{\dot{\theta}_t^I} achieves the maximum, the vertical purple line denotes the second turning point that the posterior mean first-derivative infection proportion \eqn{\dot{\theta}_t^I} equals zero, the darkgray line denotes the posterior mean of the infection prevalence \eqn{\theta_t^I} and the red line denotes its posterior median. } 92 | \item{plot_removed}{plot of summarizing and forecasting for the removed compartment with lines similar to those in the \code{plot_infection}. The vertical lines are identical, but the horizontal mean and median correspond to the posterior mean and median of the removed process \eqn{\theta_t^R}. An additional line indicates the estimated death prevalence from the input \code{death_in_R}.} 93 | \item{spaghetti_plot}{20 randomly selected MCMC draws of the first-order derivative of the posterior prevalence of infection, namely \eqn{\dot{\theta}_t^I}. The black curve is the posterior mean of the derivative, and the vertical lines mark times of turning points corresponding respectively to those shown in \code{plot_infection} and \code{plot_removed}. Moreover, the 95\% credible intervals of these turning points are also highlighted by semi-transparent rectangles. } 94 | \item{first_tp_mean}{the date t at which \eqn{\ddot{\theta}_t^I=0}, calculated as the average of the time points with maximum posterior first-order derivatives \eqn{\dot{\theta}_t^I}; this value may be slightly different from the one labeled by the "darkgreen" lines in the two plots \code{plot_infection} and \code{plot_removed}, which indicate the stationary point such that the first-order derivative of the averaged posterior of \eqn{\theta_t^I} reaches its maximum.} 95 | \item{first_tp_mean}{the date t at which \eqn{\ddot{\theta}_t^I=0}, calculated as the average of the time points with maximum posterior first-order derivatives \eqn{\dot{\theta}_t^I}; this value may be slightly different from the one labeled by the "darkgreen" lines in the two plots \code{plot_infection} and \code{plot_removed}, which indicate the stationary point such that the first-order derivative of the averaged posterior of \eqn{\theta_t^I} reaches its maximum.} 96 | 97 | \item{first_tp_ci}{fwith \code{first_tp_mean}, it reports the corresponding credible interval and median.} 98 | \item{second_tp_mean}{the date t at which \eqn{\theta_t^I=0}, calculated as the average of the stationary points of all of posterior first-order derivatives \eqn{\dot{\theta}_t^I}; this value may be slightly different from the one labeled by the "pruple" lines in the plots of \code{plot_infection} and \code{plot_removed}. The latter indicate stationary t at which the first-order derivative of the averaged posterior of \eqn{\theta_t^I} equals zero.} 99 | \item{second_tp_ci}{with \code{second_tp_mean}, it reports the corresponding credible interval and median.} 100 | \item{dic_val}{the output of \code{dic.samples()} in \code{\link[rjags]{dic.samples}}, computing deviance information criterion for model comparison.} 101 | \item{gelman_diag_list}{ Since version 0.3.3, we incorporated Gelman And Rubin's Convergence Diagnostic using \code{\link[coda]{gelman.diag}}. We included both the statistics and their upper C.I. limits. Values substantially above 1 indicate lack of convergence. Error messages would be printed as they are. This would be only valid for multiple chains (e.g. nchain > 1). Note that for time dependent processes, we only compute the convergence of the last observation data (\code{T_prime}), though it shows to be \code{T_prime+1}, which is due to the day 0 for initialization.} 102 | } 103 | \description{ 104 | Fit an extended state-space SIR model being reduced by in-home hospitalization. 105 | } 106 | \details{ 107 | In this function we allow it to characterize time-varying proportions of susceptible due to government-enforced stringent in-home isolation. We expanded the SIR model by adding a quarantine compartment with a time-varying rate of quarantine \eqn{\phi_t}, the chance of a susceptible person being willing to take in-home isolation at time t. 108 | } 109 | \examples{ 110 | \dontrun{ 111 | NI_complete <- c( 112 | 41, 41, 41, 45, 62, 131, 200, 270, 375, 444, 549, 729, 113 | 1052, 1423, 2714, 3554, 4903, 5806, 7153, 9074, 11177, 114 | 13522, 16678, 19665, 22112, 24953, 27100, 29631, 31728, 33366 115 | ) 116 | RI_complete <- c( 117 | 1, 1, 7, 10, 14, 20, 25, 31, 34, 45, 55, 71, 94, 121, 152, 213, 118 | 252, 345, 417, 561, 650, 811, 1017, 1261, 1485, 1917, 2260, 119 | 2725, 3284, 3754 120 | ) 121 | N <- 58.5e6 122 | R <- RI_complete / N 123 | Y <- NI_complete / N - R # Jan13->Feb 11 124 | 125 | change_time <- c("01/23/2020", "02/04/2020", "02/08/2020") 126 | phi0 <- c(0.1, 0.4, 0.4) 127 | res.q <- qh.eSIR(Y, R, 128 | begin_str = "01/13/2020", death_in_R = 0.4, 129 | phi0 = phi0, change_time = change_time, 130 | casename = "Hubei_q", save_files = T, save_mcmc = F, 131 | M = 5e2, nburnin = 2e2 132 | ) 133 | res.q$plot_infection 134 | # res.q$plot_removed 135 | 136 | res.noq <- qh.eSIR(Y, R, 137 | begin_str = "01/13/2020", death_in_R = 0.4, 138 | T_fin = 200, casename = "Hubei_noq", 139 | M = 5e2, nburnin = 2e2 140 | ) 141 | res.noq$plot_infection 142 | } 143 | 144 | change_time <- c("01/16/2020") 145 | phi0 <- c(0.1) 146 | NI_complete2 <- c(41, 45) 147 | RI_complete2 <- c(1, 1) 148 | N2 <- 1E3 149 | res2 <- qh.eSIR( 150 | RI_complete2 / N2, 151 | NI_complete2 / N2, 152 | begin_str = "01/13/2020", 153 | T_fin = 4, 154 | phi0 = phi0, 155 | change_time = change_time, 156 | dic = FALSE, 157 | casename = "Hubei_q", 158 | save_files = FALSE, 159 | save_mcmc = FALSE, 160 | save_plot_data = FALSE, 161 | M = 50, 162 | nburnin = 1 163 | ) 164 | closeAllConnections() 165 | 166 | } 167 | -------------------------------------------------------------------------------- /man/tvt.eSIR.Rd: -------------------------------------------------------------------------------- 1 | % Generated by roxygen2: do not edit by hand 2 | % Please edit documentation in R/tvt.eSIR.R 3 | \name{tvt.eSIR} 4 | \alias{tvt.eSIR} 5 | \title{Fit extended state-space SIR model with time-varying transmission rates} 6 | \usage{ 7 | tvt.eSIR( 8 | Y, 9 | R, 10 | pi0 = NULL, 11 | change_time = NULL, 12 | exponential = FALSE, 13 | lambda0 = NULL, 14 | begin_str = "01/13/2020", 15 | T_fin = 200, 16 | nchain = 4, 17 | nadapt = 10000, 18 | M = 500, 19 | thn = 10, 20 | nburnin = 200, 21 | dic = FALSE, 22 | death_in_R = 0.02, 23 | beta0 = 0.2586, 24 | gamma0 = 0.0821, 25 | R0 = beta0/gamma0, 26 | gamma0_sd = 0.1, 27 | R0_sd = 1, 28 | casename = "tvt.eSIR", 29 | file_add = character(0), 30 | add_death = FALSE, 31 | save_files = FALSE, 32 | save_mcmc = FALSE, 33 | save_plot_data = FALSE, 34 | eps = 1e-10 35 | ) 36 | } 37 | \arguments{ 38 | \item{Y}{the time series of daily observed infected compartment proportions.} 39 | 40 | \item{R}{the time series of daily observed removed compartment proportions, including death and recovered.} 41 | 42 | \item{pi0}{the time-dependent transmission rate modifier \eqn{\pi(t)} between 0 and 1.} 43 | 44 | \item{change_time}{the change points over time for step function pi, defalt value is \code{NULL}.} 45 | 46 | \item{exponential}{logical, whether \eqn{\pi(t)} is exponential \eqn{\exp(-\lambda_0t)} or not; the default is \code{FALSE}.} 47 | 48 | \item{lambda0}{the rate of decline in the exponential survival function in \eqn{\exp(-\lambda_0t)}.} 49 | 50 | \item{begin_str}{the character of starting time, the default is "01/13/2020".} 51 | 52 | \item{T_fin}{the end of follow-up time after the beginning date \code{begin_str}, the default is 200.} 53 | 54 | \item{nchain}{the number of MCMC chains generated by \code{\link[rjags]{rjags}}, the default is 4.} 55 | 56 | \item{nadapt}{the iteration number of adaptation in the MCMC. We recommend using at least the default value 1e4 to obtained fully adapted chains.} 57 | 58 | \item{M}{the number of draws in each chain, with no thinning. The default is M=5e2 but suggest using 5e5.} 59 | 60 | \item{thn}{the thinning interval between mixing. The total number of draws thus would become \code{round(M/thn)*nchain}. The default is 10.} 61 | 62 | \item{nburnin}{the burn-in period. The default is 2e2 but suggest 2e5.} 63 | 64 | \item{dic}{logical, whether compute the DIC (deviance information criterion) for model selection.} 65 | 66 | \item{death_in_R}{the numeric value of average of cumulative deaths in the removed compartments. The default is 0.4 within Hubei and 0.02 outside Hubei.} 67 | 68 | \item{beta0}{the hyperparameter of average transmission rate, the default is the one estimated from the SARS first-month outbreak (0.2586).} 69 | 70 | \item{gamma0}{the hyperparameter of average removed rate, the default is the one estimated from the SARS first-month outbreak (0.0821).} 71 | 72 | \item{R0}{the hyperparameter of the mean reproduction number R0. The default is thus the ratio of \code{beta0/gamma0}, which can be specified directly.} 73 | 74 | \item{gamma0_sd}{the standard deviation for the prior distrbution of the removed rate \eqn{\gamma}, the default is 0.1.} 75 | 76 | \item{R0_sd}{the standard deviation for the prior disbution of R0, the default is 1.} 77 | 78 | \item{casename}{the string of the job's name. The default is "tvt.eSIR".} 79 | 80 | \item{file_add}{the string to denote the location of saving output files and tables.} 81 | 82 | \item{add_death}{logical, whether add the approximate death curve to the plot, default is false.} 83 | 84 | \item{save_files}{logical, whether to save plots to file.} 85 | 86 | \item{save_mcmc}{logical, whether save (\code{TRUE}) all the MCMC outputs or not (\code{FALSE}).The output file will be an \code{.RData} file named by the \eqn{casename}. We include arrays of prevalence values of the three compartments with their matrices of posterior draws up to the last date of the collected data as \code{theta_p[,,1]} and afterwards as \code{theta_pp[,,1]} for \eqn{\theta_t^S}, \code{theta_p[,,2]} and \code{theta_pp[,,2]} for \eqn{\theta_t^I}, and \code{theta_p[,,3]} and \code{theta_pp[,,3]} for \eqn{\theta_t^R}. Moreover, the input and predicted proportions \code{Y}, \code{Y_pp}, \code{R} and \code{R_pp} can also be retrieved. The prevalence and predicted proportion matrices have rows for MCMC replicates, and columns for days. The MCMC posterior draws of other parameters including \code{beta_p}, \code{gamma_p}, \code{R0_p}, and variance controllers \code{k_p}, \code{lambdaY_p}, \code{lambdaR_p} are also available.} 87 | 88 | \item{save_plot_data}{logical, whether save the plotting data or not.} 89 | 90 | \item{eps}{a non-zero controller so that all the input \code{Y} and \code{R} values would be bounded above 0 (at least \code{eps}). Its default value is 1e-10} 91 | } 92 | \value{ 93 | \item{casename}{the predefined \code{casename}.} 94 | \item{incidence_mean}{mean cumulative incidence, the mean prevalence of cumulative confirmed cases at the end of the study.} 95 | \item{incidence_ci}{2.5\%, 50\%, and 97.5\% quantiles of the incidences.} 96 | \item{out_table}{summary tables including the posterior mean of the prevalance processes of the 3 states compartments (\eqn{\theta_t^S,\theta_t^I,\theta_t^R}) at last date of data collected ((\eqn{t^\prime}) decided by the lengths of your input data \code{Y} and \code{R}), and their respective credible inctervals (ci); the respective means and ci's of the reporduction number (R0), removed rate (\eqn{\gamma}), transmission rate (\eqn{\beta}).} 97 | \item{plot_infection}{plot of summarizing and forecasting for the infection compartment, in which the vertial blue line denotes the last date of data collected (\eqn{t^\prime}), the vertial darkgray line denotes the deacceleration point (first turning point) that the posterior mean first-derivative of infection prevalence \eqn{\dot{\theta}_t^I} achieves the maximum, the vertical purple line denotes the second turning point that the posterior mean first-derivative infection proportion \eqn{\dot{\theta}_t^I} equals zero, the darkgray line denotes the posterior mean of the infection prevalence \eqn{\theta_t^I} and the red line denotes its posterior median. } 98 | \item{plot_removed}{plot of summarizing and forecasting for the removed compartment with lines similar to those in the \code{plot_infection}. The vertical lines are identical, but the horizontal mean and median correspond to the posterior mean and median of the removed process \eqn{\theta_t^R}. An additional line indicates the estimated death prevalence from the input \code{death_in_R}.} 99 | \item{spaghetti_plot}{20 randomly selected MCMC draws of the first-order derivative of the posterior prevalence of infection, namely \eqn{\dot{\theta}_t^I}. The black curve is the posterior mean of the derivative, and the vertical lines mark times of turning points corresponding respectively to those shown in \code{plot_infection} and \code{plot_removed}. Moreover, the 95\% credible intervals of these turning points are also highlighted by semi-transparent rectangles. } 100 | \item{first_tp_mean}{the date t at which \eqn{\ddot{\theta}_t^I=0}, calculated as the average of the time points with maximum posterior first-order derivatives \eqn{\dot{\theta}_t^I}; this value may be slightly different from the one labeled by the "darkgreen" lines in the two plots \code{plot_infection} and \code{plot_removed}, which indicate the stationary point such that the first-order derivative of the averaged posterior of \eqn{\theta_t^I} reaches its maximum.} 101 | 102 | \item{first_tp_ci}{fwith \code{first_tp_mean}, it reports the corresponding credible interval and median.} 103 | \item{second_tp_mean}{the date t at which \eqn{\theta_t^I=0}, calculated as the average of the stationary points of all of posterior first-order derivatives \eqn{\dot{\theta}_t^I}; this value may be slightly different from the one labeled by the "pruple" lines in the plots of \code{plot_infection} and \code{plot_removed}. The latter indicate stationary t at which the first-order derivative of the averaged posterior of \eqn{\theta_t^I} equals zero.} 104 | \item{second_tp_ci}{with \code{second_tp_mean}, it reports the corresponding credible interval and median.} 105 | \item{dic_val}{the output of \code{dic.samples()} in \code{\link[rjags]{dic.samples}}, computing deviance information criterion for model comparison.} 106 | \item{gelman_diag_list}{ Since version 0.3.3, we incorporated Gelman And Rubin's Convergence Diagnostic using \code{\link[coda]{gelman.diag}}. We included both the statistics and their upper C.I. limits. Values substantially above 1 indicate lack of convergence. Error messages would be printed as they are. This would be only valid for multiple chains (e.g. nchain > 1). Note that for time dependent processes, we only compute the convergence of the last observation data (\code{T_prime}), though it shows to be \code{T_prime+1}, which is due to the day 0 for initialization.} 107 | } 108 | \description{ 109 | Fit extended state-space SIR model with pre-specified changes in the transmission rate, either stepwise or continuous, accommodating time-varying quarantine protocols. 110 | } 111 | \details{ 112 | We fit a state-space model with extended SIR, in which a time-varying transmission rate modifier \eqn{\pi(t)} (between 0 and 1) is introduced to model. This allows us to accommodate quarantine protocol changes and ignored resources of hospitalization. The form of reducing rate may be a step-function with jumps at times of big policy changes or a smooth exponential survival function \eqn{\exp(-\lambda_0t)}. The parameters of the function and change points, if any, should be predefined. 113 | } 114 | \examples{ 115 | \dontrun{ 116 | NI_complete <- c( 117 | 41, 41, 41, 45, 62, 131, 200, 270, 375, 444, 549, 729, 118 | 1052, 1423, 2714, 3554, 4903, 5806, 7153, 9074, 11177, 119 | 13522, 16678, 19665, 22112, 24953, 27100, 29631, 31728, 33366 120 | ) 121 | RI_complete <- c( 122 | 1, 1, 7, 10, 14, 20, 25, 31, 34, 45, 55, 71, 94, 121, 152, 213, 123 | 252, 345, 417, 561, 650, 811, 1017, 1261, 1485, 1917, 2260, 124 | 2725, 3284, 3754 125 | ) 126 | N <- 58.5e6 127 | R <- RI_complete / N 128 | Y <- NI_complete / N - R # Jan13->Feb 11 129 | ### Step function of pi(t) 130 | change_time <- c("01/23/2020", "02/04/2020", "02/08/2020") 131 | pi0 <- c(1.0, 0.9, 0.5, 0.1) 132 | res.step <- tvt.eSIR(Y, R, 133 | begin_str = "01/13/2020", death_in_R = 0.4, 134 | T_fin = 200, pi0 = pi0, change_time = change_time, dic = T, 135 | casename = "Hubei_step", save_files = T, 136 | save_mcmc = F, M = 5e2, nburnin = 2e2 137 | ) 138 | res.step$plot_infection 139 | res.step$plot_removed 140 | res.step$dic_val 141 | 142 | ### continuous exponential function of pi(t) 143 | res.exp <- tvt.eSIR(Y, R, 144 | begin_str = "01/13/2020", death_in_R = 0.4, 145 | T_fin = 200, exponential = TRUE, dic = F, lambda0 = 0.05, 146 | casename = "Hubei_exp", save_files = F, save_mcmc = F, 147 | M = 5e2, nburnin = 2e2 148 | ) 149 | res.exp$plot_infection 150 | # res.exp$plot_removed 151 | 152 | ### without pi(t), the standard state-space SIR model without intervention 153 | res.nopi <- tvt.eSIR(Y, R, 154 | begin_str = "01/13/2020", death_in_R = 0.4, 155 | T_fin = 200, casename = "Hubei_nopi", save_files = F, 156 | M = 5e2, nburnin = 2e2 157 | ) 158 | res.nopi$plot_infection 159 | # res.nopi$plot_removed 160 | } 161 | 162 | change_time <- c("01/18/2020") 163 | pi0<- c(1.0, 0.9) 164 | NI_complete2 <- c(41, 45, 62, 131) 165 | RI_complete2 <- c(1, 1, 7, 10) 166 | N2 <- 1E3 167 | res1 <- tvt.eSIR( 168 | RI_complete2 / N2, 169 | (NI_complete2 - RI_complete2) / N2, 170 | begin_str = "01/10/2020", 171 | T_fin =10, 172 | pi0 = pi0, 173 | change_time = change_time, 174 | dic = FALSE, 175 | casename = "Hubei_step", 176 | save_files = FALSE, 177 | save_mcmc = FALSE, 178 | save_plot_data = FALSE, 179 | M = 50, 180 | nburnin = 1 181 | ) 182 | closeAllConnections() 183 | 184 | } 185 | -------------------------------------------------------------------------------- /man/tvt.eSIR2.Rd: -------------------------------------------------------------------------------- 1 | % Generated by roxygen2: do not edit by hand 2 | % Please edit documentation in R/tvt.eSIR2.R 3 | \name{tvt.eSIR2} 4 | \alias{tvt.eSIR2} 5 | \title{Fit extended state-space SIR model with time-varying transmission rates} 6 | \usage{ 7 | tvt.eSIR2( 8 | Y, 9 | R, 10 | pi0 = NULL, 11 | change_time = NULL, 12 | exponential = FALSE, 13 | lambda0 = NULL, 14 | begin_str = "01/13/2020", 15 | T_fin = 200, 16 | nchain = 4, 17 | nadapt = 10000, 18 | M = 500, 19 | thn = 10, 20 | nburnin = 200, 21 | dic = FALSE, 22 | death_in_R = 0.02, 23 | beta0 = 0.2586, 24 | gamma0 = 0.0821, 25 | R0 = beta0/gamma0, 26 | gamma0_sd = 0.1, 27 | R0_sd = 1, 28 | casename = "tvt.eSIR2", 29 | file_add = character(0), 30 | add_death = FALSE, 31 | save_files = FALSE, 32 | save_mcmc = FALSE, 33 | save_plot_data = FALSE, 34 | eps = 1e-10, 35 | time_unit = 1 36 | ) 37 | } 38 | \arguments{ 39 | \item{Y}{the time series of daily observed infected compartment proportions.} 40 | 41 | \item{R}{the time series of daily observed removed compartment proportions, 42 | including death and recovered.} 43 | 44 | \item{pi0}{the time-dependent transmission rate modifier \eqn{\pi(t)} between 45 | 0 and 1.} 46 | 47 | \item{change_time}{the change points over time for step function pi, defalt 48 | value is \code{NULL}.} 49 | 50 | \item{exponential}{logical, whether \eqn{\pi(t)} is exponential 51 | \eqn{\exp(-\lambda_0t)} or not; the default is \code{FALSE}.} 52 | 53 | \item{lambda0}{the rate of decline in the exponential survival function in 54 | \eqn{\exp(-\lambda_0t)}.} 55 | 56 | \item{begin_str}{the character of starting time, the default is "01/13/2020".} 57 | 58 | \item{T_fin}{the end of follow-up time after the beginning date 59 | \code{begin_str}, the default is 200. This value must be longer than the 60 | length of your input observed time series data.} 61 | 62 | \item{nchain}{the number of MCMC chains generated by 63 | \code{\link[rjags]{rjags}}, the default is 4.} 64 | 65 | \item{nadapt}{the iteration number of adaptation in the MCMC. We recommend 66 | using at least the default value 1e4 to obtained fully adapted chains.} 67 | 68 | \item{M}{the number of draws in each chain, with no thinning. The default is 69 | M=5e2 but suggest using 5e5.} 70 | 71 | \item{thn}{the thinning interval between mixing. The total number of draws 72 | thus would become \code{round(M/thn)*nchain}. The default is 10.} 73 | 74 | \item{nburnin}{the burn-in period. The default is 2e2 but suggest 2e5.} 75 | 76 | \item{dic}{logical, whether compute the DIC (deviance information criterion) 77 | for model selection.} 78 | 79 | \item{death_in_R}{the numeric value of average of cumulative deaths in the 80 | removed compartments. The default is 0.4 within Hubei and 0.02 outside Hubei.} 81 | 82 | \item{beta0}{the hyperparameter of average transmission rate, the default is 83 | the one estimated from the SARS first-month outbreak (0.2586).} 84 | 85 | \item{gamma0}{the hyperparameter of average removed rate, the default is the 86 | one estimated from the SARS first-month outbreak (0.0821).} 87 | 88 | \item{R0}{the hyperparameter of the mean reproduction number R0. The default 89 | is thus the ratio of \code{beta0/gamma0}, which can be specified directly.} 90 | 91 | \item{gamma0_sd}{the standard deviation for the prior distrbution of the 92 | removed rate \eqn{\gamma}, the default is 0.1.} 93 | 94 | \item{R0_sd}{the standard deviation for the prior disbution of R0, the 95 | default is 1.} 96 | 97 | \item{casename}{the string of the job's name. The default is "tvt.eSIR2".} 98 | 99 | \item{file_add}{the string to denote the location of saving output files and 100 | tables.} 101 | 102 | \item{add_death}{logical, whether add the approximate death curve to the 103 | plot, default is false.} 104 | 105 | \item{save_files}{logical, whether to save plots to file.} 106 | 107 | \item{save_mcmc}{logical, whether save (\code{TRUE}) all the MCMC outputs or 108 | not (\code{FALSE}).The output file will be an \code{.RData} file named by the 109 | \eqn{casename}. We include arrays of prevalence values of the three 110 | compartments with their matrices of posterior draws up to the last date of 111 | the collected data as \code{theta_p[,,1]} and afterwards as 112 | \code{theta_pp[,,1]} for \eqn{\theta_t^S}, \code{theta_p[,,2]} and 113 | \code{theta_pp[,,2]} for \eqn{\theta_t^I}, and \code{theta_p[,,3]} and 114 | \code{theta_pp[,,3]} for \eqn{\theta_t^R}. Moreover, the input and 115 | predicted proportions \code{Y}, \code{Y_pp}, \code{R} and \code{R_pp} can 116 | also be retrieved. The prevalence and predicted proportion matrices have 117 | rows for MCMC replicates, and columns for days. The MCMC posterior draws of 118 | other parameters including \code{beta_p}, \code{gamma_p}, \code{R0_p}, and 119 | variance controllers \code{k_p}, \code{lambdaY_p}, \code{lambdaR_p} are 120 | also available.} 121 | 122 | \item{save_plot_data}{logical, whether save the plotting data or not.} 123 | 124 | \item{eps}{a non-zero controller so that all the input \code{Y} and \code{R} 125 | values would be bounded above 0 (at least \code{eps}). Its default value is 126 | 1e-10} 127 | 128 | \item{time_unit}{numeric, newly added argument, which can be changed to an 129 | integer (ceiling) of the input to indicate the time unit for each data 130 | point. The default is one-day, i.e., we let each input time series data 131 | correspond to each day. If this value is set to be 7, each data point 132 | represents one-week's aggregated data.} 133 | } 134 | \value{ 135 | \item{casename}{the predefined \code{casename}.} 136 | \item{incidence_mean}{mean cumulative incidence, the mean prevalence of 137 | cumulative confirmed cases at the end of the study.} 138 | \item{incidence_ci}{2.5\%, 50\%, and 97.5\% quantiles of the incidences.} 139 | \item{out_table}{summary tables including the posterior mean of the 140 | prevalence processes of the 3 states compartments (\eqn{\theta_t^S, 141 | \theta_t^I,\theta_t^R}) at last date of data collected ((\eqn{t^\prime}) 142 | decided by the lengths of your input data \code{Y} and \code{R}), and their 143 | respective credible intervals (ci); the respective means and ci's of the 144 | reproduction number (R0), removed rate (\eqn{\gamma}), transmission rate 145 | (\eqn{\beta}).} 146 | \item{plot_infection}{plot of summarizing and forecasting for the infection 147 | compartment, in which the vertical blue line denotes the last date of data 148 | collected (\eqn{t^\prime}), the vertial darkgray line denotes the 149 | deacceleration point (first turning point) that the posterior mean 150 | first-derivative of infection prevalence \eqn{\dot{\theta}_t^I} achieves the 151 | maximum, the vertical purple line denotes the second turning point that 152 | the posterior mean first-derivative infection proportion 153 | \eqn{\dot{\theta}_t^I} equals zero, the darkgray line denotes the 154 | posterior mean of the infection prevalence \eqn{\theta_t^I} and the red 155 | line denotes its posterior median. } 156 | \item{plot_removed}{plot of summarizing and forecasting for the removed 157 | compartment with lines similar to those in the \code{plot_infection}. The 158 | vertical lines are identical, but the horizontal mean and median correspond 159 | to the posterior mean and median of the removed process \eqn{\theta_t^R}. 160 | An additional line indicates the estimated death prevalence from the input 161 | \code{death_in_R}.} 162 | \item{spaghetti_plot}{20 randomly selected MCMC draws of the first-order 163 | derivative of the posterior prevalence of infection, namely 164 | \eqn{\dot{\theta}_t^I}. The black curve is the posterior mean of the 165 | derivative, and the vertical lines mark times of turning points corresponding 166 | respectively to those shown in \code{plot_infection} and 167 | \code{plot_removed}. Moreover, the 95\% credible intervals of these turning 168 | points are also highlighted by semi-transparent rectangles. } 169 | \item{first_tp_mean}{the date t at which \eqn{\ddot{\theta}_t^I=0}, 170 | calculated as the average of the time points with maximum posterior 171 | first-order derivatives \eqn{\dot{\theta}_t^I}; this value may be slightly 172 | different from the one labeled by the "darkgreen" lines in the two plots 173 | \code{plot_infection} and \code{plot_removed}, which indicate the stationary 174 | point such that the first-order derivative of the averaged posterior of 175 | \eqn{\theta_t^I} reaches its maximum.} 176 | 177 | \item{first_tp_ci}{fwith \code{first_tp_mean}, it reports the corresponding 178 | credible interval and median.} 179 | \item{second_tp_mean}{the date t at which \eqn{\theta_t^I=0}, calculated as 180 | the average of the stationary points of all of posterior first-order 181 | derivatives \eqn{\dot{\theta}_t^I}; this value may be slightly different from 182 | the one labeled by the "pruple" lines in the plots of \code{plot_infection} 183 | and \code{plot_removed}. The latter indicate stationary t at which the 184 | first-order derivative of the averaged posterior of \eqn{\theta_t^I} equals 185 | zero.} 186 | \item{second_tp_ci}{with \code{second_tp_mean}, it reports the corresponding 187 | credible interval and median.} 188 | \item{dic_val}{the output of \code{dic.samples()} in \code{\link[rjags]{di 189 | c.samples}}, computing deviance information criterion for model comparison.} 190 | \item{gelman_diag_list}{ Since version 0.3.3, we incorporated Gelman And 191 | Rubin's Convergence Diagnostic using \code{\link[coda]{gelman.diag}}. We 192 | included both the statistics and their upper C.I. limits. Values 193 | substantially above 1 indicate lack of convergence. Error messages would be 194 | printed as they are. This would be only valid for multiple chains 195 | (e.g. nchain > 1). Note that for time dependent processes, we only compute 196 | the convergence of the last observation data (\code{T_prime}), though it 197 | shows to be \code{T_prime+1}, which is due to the day 0 for initialization.} 198 | } 199 | \description{ 200 | Fit extended state-space SIR model with pre-specified changes in the 201 | transmission rate, either stepwise or continuous, accommodating time-varying 202 | quarantine protocols. 203 | } 204 | \details{ 205 | We fit a state-space model with extended SIR, in which a time-varying 206 | transmission rate modifier \eqn{\pi(t)} (between 0 and 1) is introduced to 207 | the model. This allows us to accommodate quarantine protocol changes and 208 | ignored resources of hospitalization. The form of reducing rate may be a step 209 | -function with jumps at times of big policy changes or a smooth exponential 210 | survival function \eqn{\exp(-\lambda_0t)}. The parameters of the function and 211 | change points, if any, should be predefined. 212 | } 213 | \examples{ 214 | \dontrun{ 215 | NI_complete <- c( 216 | 41, 41, 41, 45, 62, 131, 200, 270, 375, 444, 549, 729, 217 | 1052, 1423, 2714, 3554, 4903, 5806, 7153, 9074, 11177, 218 | 13522, 16678, 19665, 22112, 24953, 27100, 29631, 31728, 33366 219 | ) 220 | RI_complete <- c( 221 | 1, 1, 7, 10, 14, 20, 25, 31, 34, 45, 55, 71, 94, 121, 152, 213, 222 | 252, 345, 417, 561, 650, 811, 1017, 1261, 1485, 1917, 2260, 223 | 2725, 3284, 3754 224 | ) 225 | N <- 58.5e6 226 | R <- RI_complete / N 227 | Y <- NI_complete / N - R # Jan13->Feb 11 228 | ### Step function of pi(t) 229 | change_time <- c("01/23/2020", "02/04/2020", "02/08/2020") 230 | pi0 <- c(1.0, 0.9, 0.5, 0.1) 231 | res.step <- tvt.eSIR(Y, R, 232 | begin_str = "01/13/2020", death_in_R = 0.4, 233 | T_fin = 200, pi0 = pi0, change_time = change_time, dic = T, 234 | casename = "Hubei_step", save_files = T, 235 | save_mcmc = F, M = 5e2, nburnin = 2e2 236 | ) 237 | res.step$plot_infection 238 | res.step$plot_removed 239 | res.step$dic_val 240 | 241 | ### continuous exponential function of pi(t) 242 | res.exp <- tvt.eSIR(Y, R, 243 | begin_str = "01/13/2020", death_in_R = 0.4, 244 | T_fin = 200, exponential = TRUE, dic = F, lambda0 = 0.05, 245 | casename = "Hubei_exp", save_files = F, save_mcmc = F, 246 | M = 5e2, nburnin = 2e2 247 | ) 248 | res.exp$plot_infection 249 | # res.exp$plot_removed 250 | 251 | ### without pi(t), the standard state-space SIR model without intervention 252 | res.nopi <- tvt.eSIR(Y, R, 253 | begin_str = "01/13/2020", death_in_R = 0.4, 254 | T_fin = 200, casename = "Hubei_nopi", save_files = F, 255 | M = 5e2, nburnin = 2e2 256 | ) 257 | res.nopi$plot_infection 258 | # res.nopi$plot_removed 259 | } 260 | 261 | change_time <- c("01/18/2020") 262 | pi0<- c(1.0, 0.9) 263 | NI_complete2 <- c(41, 45, 62, 131) 264 | RI_complete2 <- c(1, 1, 7, 10) 265 | N2 <- 1E3 266 | res1 <- tvt.eSIR( 267 | Y = RI_complete2 / N2, 268 | R = (NI_complete2 - RI_complete2) / N2, 269 | begin_str = "01/10/2020", 270 | T_fin =10, 271 | pi0 = pi0, 272 | change_time = change_time, 273 | dic = FALSE, 274 | casename = "Hubei_step", 275 | save_files = FALSE, 276 | save_mcmc = FALSE, 277 | save_plot_data = FALSE, 278 | M = 50, 279 | nburnin = 1 280 | ) 281 | closeAllConnections() 282 | 283 | } 284 | -------------------------------------------------------------------------------- /meta/Hubei_exp2_plot_data.RData: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/lilywang1988/eSIR/2a1f0c36afd0d77b55642102780d852d2354fe46/meta/Hubei_exp2_plot_data.RData -------------------------------------------------------------------------------- /meta/Hubei_exp_plot_data.RData: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/lilywang1988/eSIR/2a1f0c36afd0d77b55642102780d852d2354fe46/meta/Hubei_exp_plot_data.RData -------------------------------------------------------------------------------- /meta/Hubei_qR0_p.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/lilywang1988/eSIR/2a1f0c36afd0d77b55642102780d852d2354fe46/meta/Hubei_qR0_p.png -------------------------------------------------------------------------------- /meta/Hubei_q_Gelman_diag.txt: -------------------------------------------------------------------------------- 1 | [[1]] 2 | Potential scale reduction factors: 3 | 4 | Point est. Upper C.I. 5 | R0 1 1.01 6 | 7 | 8 | [[2]] 9 | Potential scale reduction factors: 10 | 11 | Point est. Upper C.I. 12 | gamma 1.03 1.1 13 | 14 | 15 | [[3]] 16 | Potential scale reduction factors: 17 | 18 | Point est. Upper C.I. 19 | beta 1.02 1.06 20 | 21 | 22 | [[4]] 23 | Potential scale reduction factors: 24 | 25 | Point est. Upper C.I. 26 | theta[31,1] 1.02 1.05 27 | theta[31,2] 1.01 1.02 28 | theta[31,3] 1.07 1.21 29 | 30 | Multivariate psrf 31 | 32 | 1.07 33 | 34 | [[5]] 35 | [[5]][[1]] 36 | [1] "theta_Q: " 37 | 38 | [[5]][[2]] 39 | Potential scale reduction factors: 40 | 41 | Point est. Upper C.I. 42 | [1,] 1.01 1.02 43 | 44 | 45 | 46 | [[6]] 47 | Potential scale reduction factors: 48 | 49 | Point est. Upper C.I. 50 | lambdaY 1 1.01 51 | 52 | 53 | [[7]] 54 | Potential scale reduction factors: 55 | 56 | Point est. Upper C.I. 57 | lambdaR 1.05 1.15 58 | 59 | 60 | [[8]] 61 | Potential scale reduction factors: 62 | 63 | Point est. Upper C.I. 64 | k 1 1.01 65 | 66 | 67 | -------------------------------------------------------------------------------- /meta/Hubei_q_forecast.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/lilywang1988/eSIR/2a1f0c36afd0d77b55642102780d852d2354fe46/meta/Hubei_q_forecast.png -------------------------------------------------------------------------------- /meta/Hubei_q_forecast2.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/lilywang1988/eSIR/2a1f0c36afd0d77b55642102780d852d2354fe46/meta/Hubei_q_forecast2.png -------------------------------------------------------------------------------- /meta/Hubei_q_spaghetti.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/lilywang1988/eSIR/2a1f0c36afd0d77b55642102780d852d2354fe46/meta/Hubei_q_spaghetti.png -------------------------------------------------------------------------------- /meta/Hubei_q_summary.csv: -------------------------------------------------------------------------------- 1 | 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