传染病模型拟合五个代码

以下是五个传染病模型拟合的代码示例：

1. SI模型拟合代码：

import numpy as np
from scipy.integrate import odeint
from scipy.optimize import minimize

def SI_model(init_vals, t, beta, N):
    S, I = init_vals
    dSdt = -beta * S * I / N
    dIdt = beta * S * I / N
    return dSdt, dIdt

def loss_fn_SI(params, t, data):
    N = 100000 # 总人口
    init_vals = 0.99*N, 0.01*N # 初始值
    beta = params[0]
    sol = odeint(SI_model, init_vals, t, args=(beta, N))
    return np.mean((sol[:, 1] - data)**2)

data = np.array([2, 5, 10, 20, 50, 100, 200, 400, 800, 1600, 3200]) # 感染人数
t = np.arange(len(data)) # 时间
res = minimize(loss_fn_SI, [0.001], args=(t, data), method='L-BFGS-B', bounds=[(0, 1)]) # 拟合
beta = res.x[0] # 拟合参数
print('beta: ', beta)

2. SIR模型拟合代码：

import numpy as np
from scipy.integrate import odeint
from scipy.optimize import minimize

def SIR_model(init_vals, t, beta, gamma, N):
    S, I, R = init_vals
    dSdt = -beta * S * I / N
    dIdt = beta * S * I / N - gamma * I
    dRdt = gamma * I
    return dSdt, dIdt, dRdt

def loss_fn_SIR(params, t, data):
    N = 100000 # 总人口
    init_vals = 0.99*N, 0.01*N, 0 # 初始值
    beta, gamma = params
    sol = odeint(SIR_model, init_vals, t, args=(beta, gamma, N))
    return np.mean((sol[:, 1] - data)**2)

data = np.array([2, 5, 10, 20, 50, 100, 200, 400, 800, 1600, 3200]) # 感染人数
t = np.arange(len(data)) # 时间
res = minimize(loss_fn_SIR, [0.001, 0.001], args=(t, data), method='L-BFGS-B', bounds=[(0, 1), (0, 1)]) # 拟合
beta, gamma = res.x # 拟合参数
print('beta: ', beta)
print('gamma: ', gamma)

3. SEIR模型拟合代码：

import numpy as np
from scipy.integrate import odeint
from scipy.optimize import minimize

def SEIR_model(init_vals, t, beta, sigma, gamma, N):
    S, E, I, R = init_vals
    dSdt = -beta * S * I / N
    dEdt = beta * S * I / N - sigma * E
    dIdt = sigma * E - gamma * I
    dRdt = gamma * I
    return dSdt, dEdt, dIdt, dRdt

def loss_fn_SEIR(params, t, data):
    N = 100000 # 总人口
    init_vals = 0.99*N, 0.01*N, 0, 0 # 初始值
    beta, sigma, gamma = params
    sol = odeint(SEIR_model, init_vals, t, args=(beta, sigma, gamma, N))
    return np.mean((sol[:, 2] - data)**2)

data = np.array([2, 5, 10, 20, 50, 100, 200, 400, 800, 1600, 3200]) # 感染人数
t = np.arange(len(data)) # 时间
res = minimize(loss_fn_SEIR, [0.001, 0.001, 0.001], args=(t, data), method='L-BFGS-B', bounds=[(0, 1), (0, 1), (0, 1)]) # 拟合
beta, sigma, gamma = res.x # 拟合参数
print('beta: ', beta)
print('sigma: ', sigma)
print('gamma: ', gamma)

4. SIS模型拟合代码：

import numpy as np
from scipy.integrate import odeint
from scipy.optimize import minimize

def SIS_model(init_vals, t, beta, gamma, N):
    S, I = init_vals
    dSdt = -beta * S * I / N + gamma * I
    dIdt = beta * S * I / N - gamma * I
    return dSdt, dIdt

def loss_fn_SIS(params, t, data):
    N = 100000 # 总人口
    init_vals = 0.99*N, 0.01*N # 初始值
    beta, gamma = params
    sol = odeint(SIS_model, init_vals, t, args=(beta, gamma, N))
    return np.mean((sol[:, 1] - data)**2)

data = np.array([2, 5, 10, 20, 50, 100, 200, 400, 800, 1600, 3200]) # 感染人数
t = np.arange(len(data)) # 时间
res = minimize(loss_fn_SIS, [0.001, 0.001], args=(t, data), method='L-BFGS-B', bounds=[(0, 1), (0, 1)]) # 拟合
beta, gamma = res.x # 拟合参数
print('beta: ', beta)
print('gamma: ', gamma)

5. SEIRS模型拟合代码：

import numpy as np
from scipy.integrate import odeint
from scipy.optimize import minimize

def SEIRS_model(init_vals, t, beta, sigma, gamma, xi, N):
    S, E, I, R, D = init_vals
    dSdt = -beta * S * I / N
    dEdt = beta * S * I / N - sigma * E
    dIdt = sigma * E - (1 - xi) * gamma * I - xi * D
    dRdt = (1 - xi) * gamma * I
    dDdt = xi * gamma * I
    return dSdt, dEdt, dIdt, dRdt, dDdt

def loss_fn_SEIRS(params, t, data):
    N = 100000 # 总人口
    init_vals = 0.99*N, 0.01*N, 0, 0, 0 # 初始值
    beta, sigma, gamma, xi = params
    sol = odeint(SEIRS_model, init_vals, t, args=(beta, sigma, gamma, xi, N))
    return np.mean((sol[:, 2] - data)**2)

data = np.array([2, 5, 10, 20, 50, 100, 200, 400, 800, 1600, 3200]) # 感染人数
t = np.arange(len(data)) # 时间
res = minimize(loss_fn_SEIRS, [0.001, 0.001, 0.001, 0.001], args=(t, data), method='L-BFGS-B', bounds=[(0, 1), (0, 1), (0, 1), (0, 1)]) # 拟合
beta, sigma, gamma, xi = res.x # 拟合参数
print('beta: ', beta)
print('sigma: ', sigma)
print('gamma: ', gamma)
print('xi: ', xi)

上述代码中，分别使用了SI、SIR、SEIR、SIS和SEIRS五种常见的传染病模型进行拟合，并输出了拟合参数。实际应用中，可以根据不同的疾病特性和数据情况选择合适的模型进行拟合。