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2.1.2 SEIDR_Vt.py
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2.1.2 SEIDR_Vt.py
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'''
@coding: utf-8
@author: moyuweiqing
加入疫苗影响
'''
import numpy as np
import math
import matplotlib.pyplot as plt
from scipy.integrate import odeint
def dySEIDR_Vt(y, t, alpha, beta0, beta1, gamma0, gamma1, delta0, delta1, lamda, v):
s0, s1, e0, e1, i0, i1, d0, d1, r = y
n = s0 + s1 + e0 + e1 + i0 + i1 + d0 + d1 + r
if t < 20: # 20天后开始接种
v = 0
ds0_dt = - lamda * beta0 * s0 * ( i0 + i1 + e0 + e1 ) / n - v * s0
ds1_dt = - lamda * beta1 * s1 * ( i0 + i1 + e0 + e1 ) / n + v * s0
de0_dt = lamda * beta0 * s0 * ( i0 + i1 + e0 + e1 ) / n - alpha * e0
de1_dt = lamda * beta1 * s1 * ( i0 + i1 + e0 + e1 ) / n - alpha * e1
di0_dt = alpha * e0 - gamma0 * i0 - delta0 * i0
di1_dt = alpha * e1 - gamma1 * i1 - delta1 * i1
dd0_dt = delta0 * i0
dd1_dt = delta1 * i1
dr_dt = gamma0 * i0 + gamma1 * i1
return np.array([ds0_dt, ds1_dt, de0_dt, de1_dt, di0_dt, di1_dt, dd0_dt, dd1_dt, dr_dt])
def draw_SEIDR(ySEIR):
plt.figure(figsize=(16, 9))
plt.plot(t, ySEIR[:, 0] + ySEIR[:, 1], '--', label='s(t)--SEIR')
plt.plot(t, ySEIR[:, 2] + ySEIR[:, 3], '-.', label='e(t)--SEIR')
plt.plot(t, ySEIR[:, 4] + ySEIR[:, 5], '-', label='i(t)--SEIR')
plt.plot(t, ySEIR[:, 6] + ySEIR[:, 7], '.', label='d(t)--SEIR')
plt.plot(t, ySEIR[:, 8], '--', label='r(t)--SEIR')
plt.legend()
# plt.show()
plt.savefig('./img/' + '2.1.2 SEIDR_Vt_model.jpg')
if __name__ == '__main__':
number = 10000 # 模型总人数
s = 9990 # Susceptible 易感人群数量
e = 0 # Exposed 暴露者/潜伏者
i = 10 # Infected 感染者
d = 0 # Dead 死亡者
r = 0 # Recovered 康复者
alpha = 0.05 # Probability of latent people becoming infected people 潜伏期的人变成感染者的概率
beta = 0.05 # For susceptible persons, probability of becoming latent after contact with infected persons 对于易感者，与感染者接触后成为潜伏者的可能性
gamma = 0.08 # Cure rate of infected persons 感染者的治愈率
delta = 0.02 # Death rate of infected persons 感染者的死亡率
lamda = 5 # Number of susceptible persons exposed by infected persons per unit time 单位时间内受感染者接触的易受感染人数
tEnd = 300 # 300天
t = np.arange(0, tEnd, 1)
v = 0.02 # Vaccination coverage rates 疫苗接种率
beta0 = 0.05 # The probability of becoming latent in unvaccinated population 未打疫苗人群的患病概率
beta1 = 0.01 # The probability of becoming latent in vaccinated population 已打疫苗人群的感染率
gamma0 = 0.08 # Cure rates of unvaccinated infected persons 未接种疫苗的感染者的治愈率
gamma1 = 0.10 # The cure rate of vaccinated infected people 接种了疫苗的感染者的治愈率
delta0 = 0.02 # Death rate of unvaccinated infected persons 未接种疫苗的感染者的死亡率
delta1 = 0.001 # Death rate of vaccinated infected persons 接种了疫苗的感染者的死亡率
s0 = 9990
s1 = 0
e0 = 0
e1 = 0
i0 = 10
i1 = 0
d0 = 0
d1 = 0
Y0 = (s0, s1, e0, e1, i0, i1, d0, d1, r)
ySEIR = odeint(dySEIDR_Vt, Y0, t, args=(alpha, beta0, beta1, gamma0, gamma1, delta0, delta1, lamda, v))
draw_SEIDR(ySEIR)