├── README.md ├── sir_recovery_step.m ├── LICENSE ├── example.m ├── sir_infection_step.m ├── sir_simulation.m └── test_network.txt /README.md: -------------------------------------------------------------------------------- 1 | # SIR_simulation [MATLAB] 2 | ## Susceptible Infected Recovered (SIR) model simulation on a network 3 | The code takes any network in form of an adjacency matrix and performs a simulation of the SIR infectious model. The user can define the starting node(s), transmission rate, recovery rate... It is an agent-based simulation and user can observe the behavior of the system in each time step. 4 | 5 | The main file is sir_simulation.m and it requires sir_infection_step.m and sir_recovery_step.m. There is an example file example.m which loads the example network test_network.txt 6 | -------------------------------------------------------------------------------- /sir_recovery_step.m: -------------------------------------------------------------------------------- 1 | function [nA,nr] = sir_recovery_step(A,z,r) 2 | %A - adjacency matrix 3 | %z - list of infected nodes 4 | %r - rate of recovery - the probability the node will recover in this time step (independently) 5 | 6 | %nA - new adjacency matrix with removed recovered nodes 7 | %nr - "newly recovered" - the list of nodes recovered/removed in this iteration 8 | 9 | remove = times(z',rand(size(z,2),1)); 10 | remove(remove > 1-r) = 1; 11 | remove(remove <= 1-r) = 0; 12 | A(remove == 1,:) = 0; 13 | A(:,remove == 1) = 0; 14 | nA = A; 15 | nr = remove; 16 | end -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | MIT License 2 | 3 | Copyright (c) 2017 Goran Muric 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | -------------------------------------------------------------------------------- /example.m: -------------------------------------------------------------------------------- 1 | clear; 2 | %the network 3 | A = load ('test_network.txt'); 4 | 5 | 6 | %simulation parameters 7 | num_of_steps = 2000; %maximum number of iterations. If all the nodes get recovered before that, the simulation will stop 8 | prob = 0.8; %the probability that the node will be infected from already infected neighboring node 9 | r = 0.3; %the recovery rate 10 | parent_node = 1; %the ID of the node where infection starts. If parent_node is an array of IDs, 11 | %the infection will start in all of the nodes listed in parent_node. For 12 | %example: parent_node = [1 5 7] means the infection will start in nodes 1 5 and 7 13 | immunized = []; %the custom probability of virus transmission to certain nodes could be specified if needed. 14 | %For custom transmission probabilities, the vector "immunized" should have the size of number of nodes where 15 | %each entry is the customized probability of transmission to certain node. If left empty, the p is the same 16 | %for all nodes. For example, if network has 5 nodes and we want to 17 | %customize the probabilities of transmission, then immunized vector should 18 | %have the following form: immunized = [0.5 0.5 0.7 0.5 0.9] 19 | 20 | %Start of the simulation 21 | 22 | 23 | [inf,nisum,rec,infsum] = sir_simulation(A,parent_node,prob,immunized,r,num_of_steps); 24 | 25 | %Plotting the results of the simulation 26 | figure 27 | subplot(4,1,1); 28 | plot(inf, 'b*:'); 29 | ylabel('Infected nodes'); 30 | grid on 31 | 32 | subplot(4,1,2); 33 | plot(infsum,'b*:'); 34 | ylabel('Sum of infected nodes'); 35 | grid on 36 | 37 | subplot(4,1,3); 38 | plot(nisum,'b*:'); 39 | ylabel('Infected nodes at each time step'); 40 | grid on 41 | 42 | subplot(4,1,4); 43 | plot(rec,'b*:'); 44 | ylabel('Recovered nodes'); 45 | grid on 46 | 47 | 48 | 49 | -------------------------------------------------------------------------------- /sir_infection_step.m: -------------------------------------------------------------------------------- 1 | function [z,ni] = sir_infection_step(A,x0,p) 2 | 3 | %A - Adjacency matrix 4 | %x0 - vector which describes infected nodes in time step before running function where each element represents infected/non infected node. The value is 1 for infected, and 0 for non infected node 5 | %p - the probability that succeptible node will be infected. The probability is the same for all nodes if the p is scalar. If p is the vector, it represents the probabilities of infection for each node 6 | %r_tobe - "recovered to be" - the list of nodes to be recovered in this time step 7 | 8 | %z - output vector - the new state of a system. Vector consisted of 1s and 0s, where 1 is infected and 0 is not infected node 9 | %ni - "newly infected" - output vector - the difference between previous and new state of a system 10 | 11 | 12 | [~,n] = size(A); 13 | 14 | x0(x0>1) = 1; 15 | % I = find(x0 == 1) 16 | %Calculate all susceptible nodes 17 | 18 | PROB = zeros(1,n); 19 | NEWINF = zeros(1,n); 20 | 21 | %OPTIMIZED CODE 1 22 | AN = sum(A(x0==1,:),1); 23 | AN(AN>1) = 1; 24 | SUC1 = AN; 25 | %END OF OPTIMIZED CODE 1 26 | 27 | SUC = SUC1 - x0; 28 | SUC(SUC<0) = 0; 29 | 30 | %Calculate the number of infected neighboring nodes for each susceptible node 31 | %OPTIMIZED CODE 2 32 | NEIGH = zeros(1,n); 33 | for i = find(SUC==1) 34 | AN = and(A(:,i),x0'); 35 | NEIGH(i) = sum(AN); 36 | end 37 | %END OF THE OPTIMIZED CODE 38 | 39 | %Calculate the probability of infection for each node 40 | if size(p,1)==1 41 | for i = 1:n 42 | PROB(i) = 1-(1-p)^NEIGH(i); 43 | end 44 | else 45 | for i = 1:n 46 | PROB(i) = 1-(1-p(i))^NEIGH(i); 47 | end 48 | end 49 | 50 | 51 | %Calculate new infected nodes 52 | for i = 1:n 53 | format long 54 | r = rand; 55 | if r <= PROB(i) 56 | NEWINF(i) = 1; 57 | end 58 | end 59 | ni = NEWINF; 60 | %The new vector z with all infected nodes 61 | z = NEWINF + x0; 62 | 63 | %remove the nodes 64 | 65 | 66 | 67 | end -------------------------------------------------------------------------------- /sir_simulation.m: -------------------------------------------------------------------------------- 1 | function[inf,nisum,rec,infsum] = sir_simulation(A,parent_node,prob,immunized,r,num_of_steps) 2 | %OUTPUT 3 | %inf - number of infected 4 | %nisum - number of infected nodes in each iteration 5 | %rec - number of recovered nodes in each iteration 6 | %infsum - total number of infected 7 | 8 | 9 | %INPUT 10 | % num_of_steps - maximum number of iterations. If all the nodes get recovered before that, the simulation will stop 11 | % prob - the probability that the node will be infected from already infected neighboring node 12 | % r - the recovery rate 13 | % parent_node - the ID of the node where infection starts. If parent_node is an array of IDs, 14 | %the infection will start in all of the nodes listed in parent_node. For 15 | %example: parent_node = [1 5 7] means the infection will start in nodes 1 5 and 7 16 | % immunized - the custom probability of virus transmission to certain nodes could be specified if needed. 17 | %For custom transmission probabilities, the vector "immunized" should have the size of number of nodes where 18 | %each entry is the customized probability of transmission to certain node. If left empty, the p is the same 19 | %for all nodes. For example, if network has 5 nodes and we want to 20 | %customize the probabilities of transmission, then immunized vector should 21 | %have the following form: immunized = [0.5 0.5 0.7 0.5 0.9] 22 | 23 | num_of_nodes = size(A,1); 24 | x = zeros(1,num_of_nodes); 25 | x(parent_node) = 1; 26 | 27 | all_prob = zeros(num_of_nodes,1); 28 | for i = 1:size(immunized,1) 29 | all_prob(immunized(i,1)) = immunized(i,2); 30 | end 31 | all_prob(all_prob==0)=prob; 32 | 33 | inf = []; 34 | nisum = []; 35 | r_sequence = []; 36 | 37 | for i = 1:num_of_steps 38 | if i == 1 39 | z = x; 40 | ni = zeros(1,num_of_nodes); 41 | if rand 1)=1; 51 | end 52 | inf(i) = sum(z(z==1)); 53 | nisum(i) = sum(ni(ni==1)); 54 | rec(i) = sum(recovered(recovered==1)); 55 | infsum(i) = sum(z(z==1)); 56 | inf(i) = inf(i)-rec(i); 57 | if i > 1 && inf(i) == 0 58 | break 59 | end 60 | end 61 | end 62 | 63 | 64 | -------------------------------------------------------------------------------- /test_network.txt: 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