Matlab传染病学模型(Epidemic Models：SI, SIS, SIR, SIRS, SEIR, SEIRS)

% This script needs the file Fseirs.m to run % Fseirs.m contains the differential equation model % S is the number of Susceptible individuals at each time step % E is the number of Exposed individuals at each time step % I is the number of Infected individuals at each time step % R is the number of Recovered individuals at each time step N=1000; %Population Size %-- initial condictions i0=5; % initial condition for I s0=N-i0; % initial condition for S e0=0; % initial condition for E r0=0; % initial condition for R % -- T=100; % evaluation time %-- parameters beta=0.5; % infectious rate gamma= 0.1; % recover rate omega= 0.1; % migration rate of latency mu = 0.03; % immunity loss rate %-- S0E0I0R0=[s0 e0 i0 r0]; % initial condictions Vector Tspam=[0:0.1:T]; % time interval %-- Numerical Integration [T,Y] = ode45(@(t,Y) Fseirs(t,Y,beta,gamma,omega,mu,N),Tspam,S0E0I0R0); %-- S=Y(:,1); % Solution S E=Y(:,2); % Solution E I=Y(:,3); % Solution I R=Y(:,4); % Solution R (another solution is R=N-S-E-I) %----- plots ----- plot(T,S,'k'); hold on; grid on; plot(T,E,'m:'); plot(T,I,'r--'); plot(T,R,'b-.'); title(['SEIRS model: \beta= ',num2str(beta),', \gamma= ',num2str(gamma), '\omega= ',num2str(omega), '\mu= ',num2str(mu),', N=',num2str(N)]) xlabel('Time') ylabel('Number of Individuals') legend('S','E','I','R','Location','best') %------------------