傳染病模型SI、SIS、SIR

1、標(biāo)準(zhǔn)實(shí)用SI模型利用MATLABt解傳染病*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)畫圖：SI模型的it曲線設(shè)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曲線')；xlabel('t');ylabel('i');axis(0 13 0 1.1);S模型的E曲線文案大全畫圖：SI模型的di/dti 曲線程序中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 曲線');xlabel('i');ylabel('di/dt');>>S模型的d岫、曲線SIS模型利用MATLABt解傳染病*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)畫圖：SIS模型的di/dti 曲線(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、 曲線')；xlabel('i');ylabel('di/dt');>>SIS模型的曲線畫圖：SIS模型的it曲線(8 >1)設(shè)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 曲線)；xlab

5、el('t');ylabel('i');>>SIS模型的7曲線畫圖：SIS模型的di/dti 曲線(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 曲線')；xlabel('i');ylabel('di/dt');>>SIS模型的d冏卜i曲線畫圖：SIS模型的it曲線(SW1)設(shè)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 曲線');xlabel('t');ylabel('i');>>SIS模型的Z曲線SIR模型利用MATLABt解傳染病*II型中的SIR模型的數(shù)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) 圖形如下：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圖形(相軌線)如下：畫圖：SIR模型的相軌線程序中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.