matlab代码

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

结果

原文：https://www.cnblogs.com/shish/p/12685865.html