SEIR病毒模型动态模拟及理论曲线

由

SEIR模型

\( \frac{\mathrm{d}}{\mathrm{d}t}E=r\beta I\frac{S}{N}-\alpha E \\ \frac{\mathrm{d}}{\mathrm{d}t}S=-r\beta I\frac{S}{N} \\ \frac{\mathrm{d}}{\mathrm{d}t}R=\gamma I \\\frac{\mathrm{d}}{\mathrm{d}t}I=\alpha E-\gamma I\)

查看所有模型及说明：点击病毒传染的动态扩散模拟及数学模型

clear
figure
N = 100;        %人口总数
E = 0;          %潜伏者state==3
I = 1;          %传染者state==1
S = N - I;      %易感者state==0
R = 0;          %康复者state==2
 
r = 2;          %感染者接触易感者的人数
B = 0.2;        %传染概率
a = 0.1;        %潜伏者转化为感染者概率
y = 0.1;        %康复概率

days = 150;
Dynamic = false;  %设置为true显示动态模拟过程


state=zeros(1,N);
index=randperm(N,I);
state(index)=1;
if Dynamic
    axis([0 N 0 N]);
    hold on
end
for i=1:days
    xpos=randperm(N);
    ypos=randperm(N);
    for j=1:N
        if state(j)==1
            if rand()<=y
                state(j)=2;
                continue
            end
            dis=sqrt((xpos-xpos(j)).^2+(ypos-ypos(j)).^2);
            l=0;
            for k=1:N
                if state(k)==1 || state(k)==2 || state(k)==3
                    continue
                end
                l=l+1;
                peo(l).dis=dis(k);
                peo(l).num=k;
            end
            T = struct2table(peo);
            sortedT = sortrows(T,'dis');
            sortedS = table2struct(sortedT);
            tp=sortedT{1:r,2};
            for k=1:length(tp)
                if rand()<=B
                    state(tp(k))=3;
                end
            end
        elseif state(j)==3
            if rand()<=a
                state(j)=1;
            end
        end
        
    end
    Idata(i)=length(find(state==1));
    Sdata(i)=length(find(state==0));
    Rdata(i)=length(find(state==2));
    Edata(i)=length(find(state==3));
    %a=-8;
    %b=8;
    %xpos=xpos+ a + (b-a).*rand(1,N);
    %ypos=ypos+ a + (b-a).*rand(1,N);
    if Dynamic && rem(i,10)==0
        phd=scatter(xpos,ypos,[],state,"filled");
        title(['第' num2str(i) '天'])
        drawnow
        delete(phd)
    end
end

figure
set(gcf,'visible',true)
days=length(Sdata);
plot(1:days,Sdata,1:days,Idata,1:days,Rdata,1:days,Edata)
hold on
T = 1:days+50;
for idx = 1:length(T)-1
    if S(idx)<0
        S(idx)=0;
    elseif S(idx)>N
        S(idx)=N;
    end
    if E(idx)<0
        E(idx)=0;
    elseif E(idx)>N
        E(idx)=N;
    end
    if I(idx)<0
        I(idx)=0;
    elseif I(idx)>N
        I(idx)=N;
    end
    if R(idx)<0
        R(idx)=0;
    elseif R(idx)>N
        R(idx)=N;
     end
    S(idx+1) = S(idx) - r*B*S(idx)*I(idx)/N;
    E(idx+1) = E(idx) + r*B*S(idx)*I(idx)/N-a*E(idx);
    I(idx+1) = I(idx) + a*E(idx) - y*I(idx);
    R(idx+1) = R(idx) + y*I(idx);
end
 
plot(T,S,T,E,T,I,T,R);
legend('模拟易感者','模拟传染者','模拟康复者','模拟潜伏者','易感者','潜伏者','传染者','康复者')
xlabel('天');ylabel('人数')
title('SEIR模型')Code language: Matlab (matlab)

模拟最终截图如下（动态过程未给出）：

留下评论