SEIR是属于遗传病学的经典算法,

SUSCEPTIBLES–those able to contract the disease
EXPOSED–those who have been infected but are not yet
infectious
INFECTIVES–those capable of transmitting the disease
RECOVERED–those who have become immune

S： 易感人群

E：潜伏人群

I： 感染者

R：恢复健康者。

在这个模型中，可以分成许多子模型：

1.潜伏期人群是否有 传染能力？delay or not？

2. 潜伏期是否有时间限制?  infinite or not?

3.恢复健康者是否有抗体？

这个其实早就有论文了，参考最原始的：Seasonality and Period-doubling Bifurcation in an Epidemic Model

func_SEIR.m

function dy=func_SEIR(~,y)
global alpha beta0 beta1 gamma mu 
S = y(1);
E = y(2);
I = y(3);
tt = y(4);
x=beta0*(cos(2*pi*tt)*beta1+1);
dS = mu-x*S*I-mu*S;
dE = x*S*I-(mu + alpha)*E;
dI = alpha*E-(mu+gamma)*I;
ds = 1;
dy=[dS;dE;dI;ds];
end

SEIR_main.m

global alpha beta0 beta1 gamma mu 
mu=0.02;
alpha = 31.74;
gamma = 52;
beta0 = 1095;
beta1 = 0.05;

options = odeset('MaxStep',0.01);
[T,Y] = ode45(@func_SEIR, [0,50], [0.0658 0.0007 0.0002 0.00], options);  

figure(1)
plot(T,Y(:,3),'k','LineWidth',2);
xlabel('t/ yr');
ylabel('I/ people');

%figure(2);
%plot(Y(:,1),Y(:,3));
%xlabel('-ln(S)');
%ylabel('-ln(I)');

figure(2);
%options = odeset('MaxStep',0.01);
%[T,Y] = ode45('func_SEIR',[0 50],[0.0658 0.0007 0.0002 0.0],options);  
T=T(1:450);
 T=T(1:8.6:end);
YY=Y(1:450,3);
 YY=YY(1:8.6:end)
 plot(T,YY,'k','LineWidth',2);
 xlabel('t /yr');
 ylabel('I/ people');
 hold on;