SIR模型實現（matlab）

 

 

 

matlab代碼

 

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);

%畫圖
subplot(2,2,1);
plot(t,y(:,1),'-o',t,y(:,2),'-.',t,r,'g');
hold on;
legend('生病人數:i(t)','健康人數:s(t)','移除人數:r(t)','Location','Best');
ylabel('占人口比例%');
xlabel('時間t');
str = ['接觸數λ/μ:',num2str(A/B),' 初始生病人數:',num2str(I),',初始健康人數:',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('生病人數:i(t)','健康人數:s(t)','移除人數:r(t)','Location','Best');
ylabel('占人口比例%');
xlabel('時間t');
str = ['接觸數λ/μ:',num2str(A/B),' 初始生病人數:',num2str(I),',初始健康人數:',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 = ['生病人數對比圖i(t), 誤差:',num2str(diff)];
title(str1);
legend('euler','ode','Location','Best');
ylabel('占人口比例%');
xlabel('時間t');

subplot(2,2,4);
plot(t_0,y_s,'r-',t,y(:,2),'-.');
diff = sum(abs(y_s - y(:,2)));
str1 = ['健康人數對比圖s(t), 誤差:',num2str(diff)];
title(str1);
legend('euler','ode','Location','Best');
ylabel('占人口比例%');
xlabel('時間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

結果