matlab程序拟合五个传染病模型

在Matlab中，可以使用Curve Fitting Toolbox来拟合五个传染病模型。这里提供五个模型的代码示例。

1. SIR模型（Susceptible-Infected-Recovered）

function [t,y] = SIRmodel(beta,gamma,tspan,I0)
% SIR model function
% beta: infection rate
% gamma: recovery rate
% tspan: time span
% I0: initial number of infected individuals

S0 = 1 - I0; % initial number of susceptible individuals
y0 = [S0,I0,0]; % initial conditions
[t,y] = ode45(@(t,y) SIRode(t,y,beta,gamma),tspan,y0);

function dydt = SIRode(t,y,beta,gamma)
% SIR model ODE
dydt = [-beta*y(1)*y(2); beta*y(1)*y(2)-gamma*y(2); gamma*y(2)];
end

end

2. SIS模型（Susceptible-Infected-Susceptible）

function [t,y] = SISmodel(beta,gamma,tspan,I0)
% SIS model function
% beta: infection rate
% gamma: recovery rate
% tspan: time span
% I0: initial number of infected individuals

S0 = 1 - I0; % initial number of susceptible individuals
y0 = [S0,I0]; % initial conditions
[t,y] = ode45(@(t,y) SISode(t,y,beta,gamma),tspan,y0);

function dydt = SISode(t,y,beta,gamma)
% SIS model ODE
dydt = [-beta*y(1)*y(2) + gamma*y(2); beta*y(1)*y(2) - gamma*y(2)];
end

end

3. SEIR模型（Susceptible-Exposed-Infected-Recovered）

function [t,y] = SEIRmodel(beta1,beta2,gamma1,gamma2,tspan,E0,I0)
% SEIR model function
% beta1: infection rate from exposed to infected
% beta2: infection rate from susceptible to exposed
% gamma1: recovery rate from infected to recovered
% gamma2: rate of exposed individuals becoming infected
% tspan: time span
% E0: initial number of exposed individuals
% I0: initial number of infected individuals

S0 = 1 - E0 - I0; % initial number of susceptible individuals
y0 = [S0,E0,I0,0]; % initial conditions
[t,y] = ode45(@(t,y) SEIRode(t,y,beta1,beta2,gamma1,gamma2),tspan,y0);

function dydt = SEIRode(t,y,beta1,beta2,gamma1,gamma2)
% SEIR model ODE
dydt = [-beta2*y(1)*y(3); beta2*y(1)*y(3) - gamma2*y(2); gamma2*y(2) - beta1*y(2)*y(3); beta1*y(2)*y(3) - gamma1*y(3)];
end

end

4. SEIRD模型（Susceptible-Exposed-Infected-Recovered-Death）

function [t,y] = SEIRDmodel(beta1,beta2,gamma1,gamma2,gamma3,tspan,E0,I0,R0,D0)
% SEIRD model function
% beta1: infection rate from exposed to infected
% beta2: infection rate from susceptible to exposed
% gamma1: recovery rate from infected to recovered
% gamma2: rate of exposed individuals becoming infected
% gamma3: rate of infected individuals dying
% tspan: time span
% E0: initial number of exposed individuals
% I0: initial number of infected individuals
% R0: initial number of recovered individuals
% D0: initial number of dead individuals

S0 = 1 - E0 - I0 - R0 - D0; % initial number of susceptible individuals
y0 = [S0,E0,I0,R0,D0]; % initial conditions
[t,y] = ode45(@(t,y) SEIRDode(t,y,beta1,beta2,gamma1,gamma2,gamma3),tspan,y0);

function dydt = SEIRDode(t,y,beta1,beta2,gamma1,gamma2,gamma3)
% SEIRD model ODE
dydt = [-beta2*y(1)*y(3); beta2*y(1)*y(3) - gamma2*y(2); gamma2*y(2) - (gamma3+gamma1)*y(3); gamma1*y(3); gamma3*y(3)];
end

end

5. SIRS模型（Susceptible-Infected-Recovered-Susceptible）

function [t,y] = SIRSmodel(beta,gamma,mu,tspan,I0)
% SIRS model function
% beta: infection rate
% gamma: recovery rate
% mu: immunity loss rate
% tspan: time span
% I0: initial number of infected individuals

S0 = 1 - I0; % initial number of susceptible individuals
y0 = [S0,I0,0]; % initial conditions
[t,y] = ode45(@(t,y) SIRSode(t,y,beta,gamma,mu),tspan,y0);

function dydt = SIRSode(t,y,beta,gamma,mu)
% SIRS model ODE
dydt = [-beta*y(1)*y(2) + mu*y(3); beta*y(1)*y(2) - gamma*y(2); gamma*y(2) - mu*y(3)];
end

end

以上代码均为函数形式，需要在Matlab中调用。例如，可以使用以下代码调用SEIR模型：

[t,y] = SEIRmodel(0.2,0.1,0.1,0.05,[0 100],[0.01 0.01 0.01 0],0.01,0.01);
plot(t,y(:,1),'r',t,y(:,2),'g',t,y(:,3),'b',t,y(:,4),'y');
legend('Susceptible','Exposed','Infected','Recovered');
xlabel('Time');
ylabel('Proportion of population');
title('SEIR model');

其中，参数依次为beta1、beta2、gamma1、gamma2、tspan、E0、I0、R0、D0。可以根据具体需求修改参数。