传染病模型SI、SIS、SIR

1、SI模型利用MATLAB求解传染病模型中的 SI模型的解析解程序中a即入,y即i>> y=dsolve('Dy=a*(y-yA2)','y(0)=y0') y =1心-exp(-a*t)*(-1+yO)/yO)画图：SI模型的it曲线设入=1, i(0)=0.1>> y=dsolve('Dy=y-yA2','y(0)=0.1') y =1/(1+9*exp(-t)>> x=0:0.01:13;y=1./(1+9.*exp(-x);>> plot(x,y)title('SI模型

2、的it曲线');xlabel('t');ylabel('i');axis(0 13 0 1.1);画图：SI模型的di/dti 曲线 程序中x即i, y即di/dt,入 =1 >> x=0:0.01:1;y=x_x.*x;>> plot(x,y)title('SI 模型的 di/dti 曲线'); xlabel('i');ylabel('di/dt');>>SIS模型利用MATLAB求解传染病模型中的SIS模型的解析解程序中a即入,b即讪即i>> y=dsol

3、ve('Dy=a*(y-yA2)-b*y','y(0)=y0')(a-b)/(a-exp(-(a-b)*t)*(-a+b+yO*a)/yO/(a-b)*a+exp(-(a-b)*t)*(-a+b+yO*a)/yO/(a-b)*b画图：SIS模型的di/dti 曲线(3 >1 ) 程序中x即i, y即di/dt,入 =1,卩=0.3 >> x=0:0.01:1;>> A2;>> plot(x,y)title('SIS 模型的 di/dti 曲线');xlabel('i'); ylabel(&

4、#39;di/dt');>>SIS模型的皈2曲线画图：SIS模型的it曲线(3 >1 )设入=1,尸0.3,i(0)=0.02>> y=dsolve('Dy=0.7*y-yA2','y(0)=0.02')7心0+340*exp(-7/10*t)>> x=0:1:16;>> y=7./(10+340.*exp(-7./10.*x);>> plot(x,y)title('SIS 模型的 it 曲线'); xlabel('t');ylabel('i'

5、;);>>SIS模型的i-T曲线画图：SIS模型的di/dti 曲线(3W1)程序中 x 即 i, y 即 di/dt, 2=0.5,卩=0.6 >> x=0:0.01:1;>> A>> plot(x,y)title('SIS 模型的 di/dti 曲线');xlabel('i');ylabel('di/dt');>>MS模型的di/dt*i曲绫画图：SIS模型的it曲线(3W1)设入=0.5,尸0.6,i(0)=0.02>> y=dsolve('Dy=-0.5*yA

6、2-0.1*y','y(0)=0.02')y =1/(-5+55*exp(1/10*t)>> x=0:1:40;>> y=1./(-5+55.*exp(1./10.*x);>> plot(x,y) title('SIS 模型的 it 曲线'); xlabel('t');ylabel('i');>>SIS模型的i-T曲线SIR模型利用MATLAB 求解传染病模型中的SIR模型的数值解程序中 a=入 =1, b=尸0.3 , i(0)=0.02,s(0)=0.98M文件中：fun

7、ction y=ill(t,x)a=1;b=0.3;y=a*x(1)*x (2)-b*x(1),-a*x(1)*x(2)'命令窗口中：>> t,x=ode45('ill',0:50,0.02,0.98);t,x ans =01.00002.00003.00004.00005.00006.00007.00008.00000.02000.03900.07320.12850.20330.27950.33120.34440.32470.98000.95250.90190.81690.69270.54380.39950.28390.20279.00000.28630.

8、149310.00000.24180.114511.00000.19860.091712.00000.15990.076713.00000.12720.066514.00000.10040.059315.00000.07870.054316.00000.06140.050717.00000.04780.048018.00000.03710.046019.00000.02870.044520.00000.02230.043421.00000.01720.042622.00000.01330.041923.00000.01030.041524.00000.00790.041125.00000.00

9、610.040826.00000.00470.040627.00000.00360.040428.00000.00280.040329.00000.00220.040230.00000.00170.040131.00000.00130.040032.00000.00100.040033.00000.00080.040034.00000.00060.039935.00000.00050.039936.00000.00040.039937.00000.00030.039938.00000.00020.039939.00000.00020.039940.00000.00010.039941.0000

10、0.00010.039942.00000.00010.039943.00000.00010.039944.00000.00000.039845.00000.00000.039846.00000.00000.039847.00000.00000.039848.00000.00000.039849.00000.00000.039850.00000.00000.0398>> plot(t,x(:,1),t,x(:,2),grid,pausei(t),s(t)图形如下：>> plot(x(:,2),x(:,1),grid,pauseis图形(相轨线)如下：画图：SIR模型的相轨线程序中y即i, x即s,入 =1,卩=0.3 s(0)=0.32; s(0)=0.58; s(0)=0.73; s(0)=0.85>> x=0:0.0