Matlab SEIR infectious disease model prediction

1. SEIR Model

Applicable to those who are susceptible 、 Exposed person 、 The sick and the convalescent 4 Quasi population , Have incubation period 、 Diseases that get lifelong immunity after cure , Such as herpes zoster 、 Chicken pox .

The model assumes

Suppose that the susceptible person becomes the exposed person after effective contact with the sick person , The exposed person becomes ill after the average incubation period , The sick can be cured and become a convalescent , The convalescent is no longer susceptible to lifelong immunity ; Take one day as the minimum time unit of the model .

The total number is N, Regardless of the birth and death of the population , Move in and out , This total number remains unchanged .

2. Demo1

N=330000000; % Population 
load America.mat
% The first column is the cumulative number of confirmed cases , The second column is the cumulative number of deaths , The third column is the cumulative number of cured 
E=0;% Lurker 
D=0;% Number of dead patients 
I=1;% Number of people infected 
S=N-I;% Number of susceptible people 
R=0;% Number of convalescents 
r=17;% Number of infected people exposed 
% r=19;
B=0.602;% The probability of infection 
% a=0.17;% Probability of latent person turning into infected person 
% a=0.175;
a=0.18;% Probability of latent person turning into infected person 
% r2=8;% Number of contacts of lurks 
r2=15;% Number of contacts of lurks 
% B2=0.03;% The probability of a latent person infecting a normal person 
B2=0.05;
y=0.000316893;% Rehabilitation probability 
k=0.01;% Daily mortality 
B3=0.001;% Negative conversion rate 
%  T=1:200;
T=1:180;
for idx=1:length(T)-1
    % The time for the government to issue the call for control and the response delay in various places , Here the 11 Days later is the critical point ,
    % amount to 11 Days later , The mobility and medical allocation of infected and latent people have changed significantly , Specifically, the number of contacts 
    if idx>=14
        r=0.20;% Number of infected people exposed 
        r2=1.8;% The number of infected people contacting 
        y=0.15;% The recovery rate rises 
        a=0.12;% Probability of latent person turning into infected person 
        k=0.0001;% The daily mortality rate remains unchanged 
    end
    if idx<11
        S(idx+1)=S(idx)-r*B*S(idx)*I(idx)/N-r2*B2*S(idx)*E(idx)/N;% Iteration of susceptible people 
        E(idx+1)=E(idx)+r*B*S(idx)*I(idx)/N-a*E(idx)+r2*B2*S(idx)*E(idx)/N;% Lurker iteration 
        I(idx+1)=I(idx)+a*E(idx)-(k+y)*I(idx);% The number of infected people iterates 
        R(idx+1)=R(idx)+0.05*I(idx);% Number of rehabilitated patients 
        D(idx+1)=R(idx)+k*I(idx);% Number of dead patients 
    else
        S(idx+1)=S(idx)-r*B*S(idx)*I(idx)/N-r2*B2*S(idx)*E(idx)/N+B3*E(idx-10);% Iteration of susceptible people 
        E(idx+1)=E(idx)+r*B*S(idx)*I(idx)/N-a*E(idx)+r2*B2*S(idx)*E(idx)/N-B3*E(idx-10);% Lurker iteration 
        I(idx+1)=I(idx)+a*E(idx)-(k+y)*I(idx);% The number of infected people iterates 
        % Y There is a problem with the parameters 
        R(idx+1)=R(idx)+0.045*I(idx-9);% Number of rehabilitated patients 
        D(idx+1)=R(idx)+k*I(idx);% Number of dead patients 
    end
end
B={
    '01-19','02-08','02-28','03-19','04-08','04-28','05-18','06-07','06-27','07-17','08-06'};
% plot(1:1:102,huibei(:,1)-huibei(:,2)-huibei(:,3),'r*');hold on
plot(1:1:133,America(:,1)-America(:,2)-America(:,3),'g-');hold on
plot(1:1:133,America(:,3),'k-');hold on
% legend(' Actual illness ',' Actual rehabilitation ')
% xlabel(' Days ');
% ylabel(' The number of ');
% legend(' Actual illness ')
plot(T,R,'b',T,I,'r');
grid on;
hold on;
plot([7 7],[0 1000]);
set(gca,'XTickLabel',B)
xlabel(' date ');
ylabel(' The number of ');
legend(' Actual illness ',' Actual rehabilitation ',' Predict the rehabilitation ',' Predict patients ');
title(' Taking isolation measures SEIR Model ');

3. Demo2

% hypothesis 1 month 15 The first confirmed case began to appear on the th ,1 month 23 The city was closed on the th , At this time, other provinces and cities also respond to isolation measures , About distance 15 After 11 Government control plays an obvious role 
N=1395380000;  % Population 
load quanguo1.mat
% The first column is the cumulative number of confirmed cases , The second column is the cumulative number of deaths , The third column is the cumulative number of cured 
E=0;% Lurker 
D=0;% Number of dead patients 
I=1;% Number of people infected 
S=N-I;% Number of susceptible people 
R=0;% Number of convalescents 
r=17;% Number of infected people exposed 
% r=19;
B=0.602;% The probability of infection 
% a=0.17;% Probability of latent person turning into infected person 
% a=0.175;
a=0.298;% Probability of latent person turning into infected person 
% r2=8;  % Number of contacts of lurks 
r2=15;% Number of contacts of lurks 
% B2=0.03;% The probability of a latent person infecting a normal person 
B2=0.05;
y=0.05;% Rehabilitation probability 
k=0.0001;% Daily mortality 
B3=0.1;% Negative conversion rate 
%  T=1:200;
T=1:180;
for idx=1:length(T)-1
    % If the 1 month 18 Japan is the starting point of the epidemic , The time for the government to issue the call for control and the response delay in various places , Here the 11 Days later is the critical point ,
    % amount to 11 Days later , The mobility and medical allocation of infected and latent people have changed significantly , Specifically, the number of contacts 
    if idx>=11
        r=0.20;% Number of infected people exposed 
        r2=1.8;% The number of infected people contacting 
        y=0.15;% The recovery rate rises 
        a=0.12;% Probability of latent person turning into infected person 
        k=0.0001;% The daily mortality rate remains unchanged 
    end
    if idx<11
        S(idx+1)=S(idx)-r*B*S(idx)*I(idx)/N-r2*B2*S(idx)*E(idx)/N;% Iteration of susceptible people 
        E(idx+1)=E(idx)+r*B*S(idx)*I(idx)/N-a*E(idx)+r2*B2*S(idx)*E(idx)/N;% Lurker iteration 
        I(idx+1)=I(idx)+a*E(idx)-(k+y)*I(idx);% The number of infected people iterates 
        R(idx+1)=R(idx)+0.05*I(idx);% Number of rehabilitated patients 
        D(idx+1)=R(idx)+k*I(idx);% Number of dead patients 
    else
        S(idx+1)=S(idx)-r*B*S(idx)*I(idx)/N-r2*B2*S(idx)*E(idx)/N+B3*E(idx-10);% Iteration of susceptible people 
        E(idx+1)=E(idx)+r*B*S(idx)*I(idx)/N-a*E(idx)+r2*B2*S(idx)*E(idx)/N-B3*E(idx-10);% Lurker iteration 
        I(idx+1)=I(idx)+a*E(idx)-(k+y)*I(idx);% The number of infected people iterates 
        % Y There is a problem with the parameters 
        R(idx+1)=R(idx)+0.045*I(idx-9);% Number of rehabilitated patients 
        D(idx+1)=R(idx)+k*I(idx);% Number of dead patients 
    end
end
B={
    '01-19','02-08','02-28','03-19','04-08','04-28','05-18','06-07','06-27','07-17','08-06'};
% plot(1:1:102,huibei(:,1)-huibei(:,2)-huibei(:,3),'r*');hold on
plot(1:1:137,quanguo1(:,1)-quanguo1(:,2)-quanguo1(:,3),'g-');hold on
plot(1:1:137,quanguo1(:,3),'k-');hold on
% legend(' Actual illness ',' Actual rehabilitation ')
% xlabel(' Days ');
% ylabel(' The number of ');
% legend(' Actual illness ')
plot(T,R,'b',T,I,'r');
grid on;
hold on;
plot([7 7],[0 1000]);
set(gca,'XTickLabel',B)
xlabel(' date ');
ylabel(' The number of ');
legend(' Actual illness ',' Actual rehabilitation ',' Predict the rehabilitation ',' Predict patients ');
title(' Taking isolation measures SEIR Model ');

4. data

1. America.mat
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2. quanguo1.mat
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