1、傳染病模型實(shí)驗(yàn)實(shí)驗(yàn)?zāi)康模豪斫鈧魅静〉乃念惸Ｐ停瑢W(xué)會(huì)利用Matlab軟件求解微分方程(組)。實(shí)驗(yàn)題目：利用Matlab求解傳染病的SIS微分方程模型，并繪制教材P139頁(yè)圖3-圖6。SIS模型假設(shè)：(1) 、t時(shí)刻人群分為易感者(占總?cè)藬?shù)比例的s(t)和已感染者(占總?cè)藬?shù)比例的i(t)。、每個(gè)病人每天有效接觸的平均人數(shù)是常數(shù)，稱為日接觸率，當(dāng)健康者與病人接觸時(shí)，健康者受感染成為病人。1、病人每天被治愈的占病人總數(shù)的比例為，稱為日治愈率，顯然為這種傳染病的平均傳染期。則建立微分方程模型為：di77=*(10演，*(°)=at令則模型可寫作分別作圖：當(dāng)sigma>1時(shí)Step1先定義

2、函數(shù)functiony=pr1(i,lambda,sigma)y=-lambda.*i.*(i-(1-1./sigma)step2作圖lambda=0.3;sigma=2;i=0:0.01:1;y=pr1(i,lambda,sigma)plot(i,y)當(dāng)sigma<1時(shí)Step1先定義函數(shù)functiony=pr1(i,lambda,sigma)y=-lambda.*i.*(i-(1-1./sigma)step2作圖lambda=0.3;sigma=0.5;i=0:0.01:1;y=pr1(i,lambda,sigma)plot(i,y)-0.6-0.1-0.2-0.3-0.4-0.5

3、-0.700.10.20.30.40.50.60.70.80.91當(dāng)sigma=1時(shí)Step1先定義函數(shù)functiony=pr1(i,lambda,sigma)y=-lambda.*i.*(i-(1-1./sigma)step2作圖lambda=0.3;sigma=1;i=0:0.01:1;y=pr1(i,lambda,sigma)plot(i,y)0-0.05-0.1-0.15-0.2-0.25-0.3-0.3500.10.20.30.40.50.60.70.80.9當(dāng)sigma>1時(shí)Step1先定義函數(shù)functiondi=crb(t,i,lambda,sigma)di=-lamb

4、da*i*(i-(1-1/sigma)%step2求解并作圖clcclearlambda=0.01;sigma=2;t,i1=ode45(crb,0,1000,0.9,lambda,sigma);t,i2=ode45(crb,0,1000,0.2,lambda,sigma);plot(t,i1,t,i2,t,1/2)legend('sigma>1')當(dāng)sigma=1時(shí)Step1先定義函數(shù)functiondi=crb(t,i,lambda,sigma)di=-lambda*i*(i-(1-1/sigma)%step2求解并作圖clcclearlambda=0.01;sigm

5、a=1t,i1=ode45(crb,0,1000,0.9,lambda,sigma);plot(t,i1)legend('sigma=1')10.90.80.70.60.50.40.30.20.1001002003004005006007008009001000當(dāng)sigma<1時(shí)Step1先定義函數(shù)functiondi=crb(t,i,lambda,sigma)di=-lambda*i*(i-(1-1/sigma)%step2求解并作圖clcclearlambda=0.01;sigma=0.5;t,i1=ode45(crb,0,1000,0.9,lambda,sigma)

6、;plot(t,i1)legend('sigma<1')1.210.80.60.40.20-0.2<101002003004005006007008009001000利用matlab求解上面SIS模型.提示(畫圖5程序):Step1先定義函數(shù)functiony=pr1(i,lambda,sigma)y=-lambda.*i.*(i-(1-1./sigma)step2作圖lambda=0.3;sigma=2;i=0:0.01:1;y=pr1(i,lambda,sigma)plot(i,y)提示(畫圖6程序):Step1先定義函數(shù)functiondi=crb(t,i,lambda,sigma)di=-lambda*i*(i-(1-1/sigma)%step2求解并作圖clcclearlambda=0.01;sigma=0.2;t,i=ode45(crb,0,100,0.9,lambda,sigma);plot(t,i)legend('sigma<1')實(shí)驗(yàn)指導(dǎo)書：利用matlab求下面定解問(wèn)題