传染病模型SI、SIS、SIR

1、标准实用SI模型利用MATLABt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('

2、;SI 模型的it曲线')；xlabel('t');ylabel('i');axis(0 13 0 1.1);S模型的E曲线文案大全画图：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');>>S模型的d岫、曲线SIS模型利用MATLABt解传染病*II型中的SIS模型的解析解：程

3、序中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/dti 曲线(S>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/dti

4、 曲线')；xlabel('i');ylabel('di/dt');>>SIS模型的曲线画图：SIS模型的it曲线(8 >1)设入=1,科=0.3,i(0)=0.02>> y=dsoke('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.*exp(-7./10.*x);>> plot(x,y)title('SIS模型的 it 曲线)；xlab

5、el('t');ylabel('i');>>SIS模型的7曲线画图：SIS模型的di/dti 曲线(SW1)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');ylabel('di/dt');>>SIS模型的d冏卜i曲线画图：SIS模型的it曲线(SW1)设入=0.5,科=0.6

6、,i(0)=0.02>> y=dsoke('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 it 曲线');xlabel('t');ylabel('i');>>SIS模型的Z曲线SIR模型利用MATLABt解传染病*II型中的SIR模型的数值解程序中 2=入=1

7、, b=科=0.3, i(0)=0.02,s(0)=0.98 M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 0.98001.00000.03900.95252.00000.07320.90193.00000.12850.81694.00000.20330.69275.00000.27950.54386.00000.33120.39957.00000.344

8、40.28398.00000.32470.20279.00000.28630.149310.00000.24180.114511.00000.19860.091712.00000.15990.076713.00000.12720.066514.00000.10040.059315.00000.07870.054316.00000.06140.050717.00000.04780.048018.00000.03710.046019.00000.02870.044520.00000.02230.043421.00000.01720.042622.00000.01330.041923.00000.0

9、1030.041524.00000.00790.041125.00000.00610.040826.00000.00470.040627.00000.00360.040428.00000.00280.040329.00000.00220.040230.00000.00170.040131.0000 0.0013 0.040032.0000 0.0010 0.040033.0000 0.0008 0.040034.0000 0.0006 0.039935.0000 0.0005 0.039936.0000 0.0004 0.039937.0000 0.0003 0.039938.0000 0.0

10、002 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 0.039850.0000 0.0000 0.0398>> plot(t,x(:,1),t,x(:,2),grid,p

11、ausei(t),s(t) 图形如下：1IIIII1II1DViiii1IIii、11111!1H|iHH1111111RHn iiiihi|hU.S11T'11I1fF1n 1 IT n rtY11|i1HVFIH11h1blihIkiiii|i|ii|Ii|i|jiijif|ipp111111RliHHU 0T - -Huh- 1 - u b bb - -hiiii1|ii|hliIIIIirItn 71111*111HliM口I 11liillihhfekL_ . ._ , _ _ _J.一一_1r_工一一1 11V巾PV|II111141R|iHH1r|.jLI.I.Ln 6

12、11V1P|I|I1|l1hIIIiIIhIk1iii|ii1|1III1VIPtn c«1V'I!1H|iMHll1hillbhhibu iiiipjiipfI1i|p|p|i|1|j.K|j|11illiillbhlifeba_'au11iim11U 411V'1!1Hli11I 11Ihilibhhib11|iijiPPli1V1 / 11I!>1!1fiF11Jn of , >>kr>kfllVVI1)li1ff1E111Hh11/I1'*!i、|ii|i|u zj v tii/ I 1.11*hhIkJiiiki<

13、;iin 1/j.1'L 1 Ji 一 1>1 iUB I/i1|11111111H/r.Il1ii/ii-fppiiip/iihIriirrn'iiiV- - iiiiu05101520253035404550>> 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,=0.3 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.