SIR 模型实施（matlab）

clc clear close all; A = 0.4; B = 0.1; I = 0.4; S = 0.5; %ode tspan = [0 50]; y0 = [I S]; [t, y] = ode45(@(t,y)odefun(t,y,A,B), tspan, y0); r = 1-y(:,1)-y(:,2); %euler n = size(r,1); h = 50 / (n-1); t_0 = [0:h:50]'; y_i = zeros(n,1); y_s = zeros(n,1); y_i(1) = I; y_s(1) = S; for i = 1:n-1 y_i(i+1) = h*[A*y_i(i)*y_s(i) - B*y_i(i)]+y_i(i); y_s(i+1) = h*[-A*y_i(i)*y_s(i)]+y_s(i); end r_0 = 1 - y_i(:,1) - y_s(:,1); %画图 subplot(2,2,1); plot(t,y(:,1),'-o',t,y(:,2),'-.',t,r,'g'); hold on; legend('生病人数:i(t)','健康人数:s(t)','移除人数:r(t)','Location','Best'); ylabel('占人口比例%'); xlabel('时间t'); str = ['接触数λ/μ:',num2str(A/B),' 初始生病人数:',num2str(I),',初始健康人数:',num2str(S)]; text(15,0.4,str,'FontSize',10); title('SIR模型(ode)'); subplot(2,2,2); plot(t_0,y_i,'-o',t_0,y_s,'-.',t_0,r_0,'g'); hold on; legend('生病人数:i(t)','健康人数:s(t)','移除人数:r(t)','Location','Best'); ylabel('占人口比例%'); xlabel('时间t'); str = ['接触数λ/μ:',num2str(A/B),' 初始生病人数:',num2str(I),',初始健康人数:',num2str(S)]; text(15,0.4,str,'FontSize',10); title('SIR模型(euler)'); subplot(2,2,3); plot(t_0,y_i,'r-',t,y(:,1),'-.'); diff = sum(abs(y_i - y(:,1))); str1 = ['生病人数对比图i(t), 误差:',num2str(diff)]; title(str1); legend('euler','ode','Location','Best'); ylabel('占人口比例%'); xlabel('时间t'); subplot(2,2,4); plot(t_0,y_s,'r-',t,y(:,2),'-.'); diff = sum(abs(y_s - y(:,2))); str1 = ['健康人数对比图s(t), 误差:',num2str(diff)]; title(str1); legend('euler','ode','Location','Best'); ylabel('占人口比例%'); xlabel('时间t'); function dydt = odefun(t,y,A,B) dydt = zeros(2,1); dydt(1) = A*y(1)*y(2) - B*y(1); dydt(2) = -A*y(1)*y(2); end