传染病模型SI、SIS、SIR40945

1、SI模型利用MATLAB解传染病*II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/(1-exp(-a*t)*(-1+y0)/y0)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

2、型的i-t曲线')；xlabel('t');ylabel('i');axis(0 13 0 1.1);5模型的E曲战精品画图：SI模型的di/dt-i 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/dt-i 曲线'); xlabel('i');ylabel('di/dt');>>印模型的的k曲战精品SIS模型利用MATLAB解传染病*II型中的SIS模型的解析解：程序

3、中a即入，b即科,y即i>> y=dsolve('Dy=a*(y-yA2)-b*y','y(0)=y0')y =(a-b)/(a-exp(-(a-b)*t)*(-a+b+y0*a)/y0/(a-b)*a+exp(-(a-b)*t)*(-a+b+y0*a)/y0/(a-b)*b)画图：SIS模型的di/dt-i 曲线(8 >1) 程序中x即i , y即di/dt,4=1,=0.3 >> x=0:0.01:1;>> y=0.7.*x-x.A2;>> plot(x,y)title('SIS 模型的 di/d

4、t-i 曲线')； xlabel('i');ylabel('di/dt');>>81s模型的Mdki曲线0.1S010.050005-01-0.20 300 10 20 30 40.50 6070 30 91精品画图：SIS模型的it曲线(8 >1)设入=1=0.3,i(0)=0.02>> y=dsolve('Dy=0.7*y-yA2','y(0)=0.02') y =7/(10+340*exp(-7/10*t)>> x=0:1:16;>> y=7./(10+340.*

5、exp(-7./10.*x);>> plot(x,y)title('SIS 模型的 i-t 曲线');xlabel('t');ylabel('i');>>日瀚型的i-t曲线精品画图：SIS模型的di/dti 曲线（SW 1）精品程序中x即i , y即di/dt,入=0.5,科=0.6> > x=0:0.01:1;> > y=-0.5.*x.A2-0.1.*x;> > plot(x,y)title('SIS 模型的 di/dti 曲线')；xlabel('i'

6、;);ylabel('di/dt');>>画图：SIS模型的it曲线（SW 1）精品设入=0.5, = =0.6,i(0)=0.02精品>> y=dsolve('Dy=-0.5*yA2-0.1*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 i-t 曲线');xlabel('t');ylabe

7、l('i');>>SIR模型精品利用MATLAB解传染病*II型中的SIR模型的数值解程序中 2=入=1, b=科=0.3, i(0)=0.02,s(0)=0.98M文件中：function 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,xans =0 0.0200 0.98001.00000.03900.95252.00000.07320.90193.00000.12850.8169

8、4.00000.20330.69275.00000.27950.54386.00000.33120.39957.00000.34440.28398.00000.32470.20279.00000.28630.149310.00000.24180.114511.00000.19860.091712.00000.15990.076713.00000.12720.066514.00000.10040.059315.00000.07870.054316.00000.06140.050717.00000.04780.048018.00000.03710.046019.00000.02870.044520

9、.00000.02230.043421.00000.01720.042622.00000.01330.041923.00000.01030.041524.00000.00790.041125.00000.00610.040826.00000.00470.040627.00000.00360.040428.00000.00280.040329.00000.00220.040230.00000.00170.040131.00000.00130.040032.00000.00100.0400精品33.0000 0.0008 0.040034.0000 0.0006 0.039935.0000 0.0

10、005 0.039936.0000 0.0004 0.039937.0000 0.0003 0.039938.0000 0.0002 0.039939.0000 0.0002 0.039940.0000 0.0001 0.039941.0000 0.0001 0.039942.0000 0.0001 0.039943.0000 0.0001 0.039944.0000 0.0000 0.039845.0000 0.0000 0.039846.0000 0.0000 0.039847.0000 0.0000 0.039848.0000 0.0000 0.039849.0000 0.0000 0.

11、039850.0000 0.0000 0.0398>> 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：精品0.35030.25020 15010.05i111. 1j4 1 I1 i aLn:K；I.111 r J1 IJiII 1 1 * 1 V 11 1 i1 ji1iIiit1iIi)1 H11 Jq jI14一J111 i1111 1 . 1 11 ii飞0.10.20.30.40.50.60.7080 91画图：SIR模型的相轨线程序中y即i, x 即s,入=1,=0.3精品 s(0)=0.32; s(0)=0.58; s(0)=0.73; s(0)=0.85>> x=0:0.01:1;>> y=1-x;>> y1=1-x+0.3.*(log(x)-log(0.32);>> y2=1-x+0.3.*(log(x)-log(0.58);>> y3=1-x+0.3.*(log(x)-log(0.73);