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2.2.2 SEIDR_V2t.py
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2.2.2 SEIDR_V2t.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_V2(y, t, alpha, beta0, beta1, beta2, gamma0, gamma1, gamma2, delta0, delta1, delta2, lamda, v1, v2):
s0, s1, s2, e0, e1, e2, i0, i1, i2, d0, d1, d2, r = y
n = s0 + s1 + s2 + e0 + e1 + e2 + i0 + i1 + i2 + d0 + d1 + d2 + r
if t < 20: # 20天后开始接种第一针
v1 = 0
v2 = 0
elif t < 50: # 50天后开始接种第二针
v2 = 0
i_e = i0 + i1 + i2 + e0 + e1 + e2
ds0_dt = - lamda * beta0 * s0 * i_e / n - v1 * s0
ds1_dt = - lamda * beta1 * s1 * i_e / n + v1 * s0 - v2 * s1
ds2_dt = - lamda * beta2 * s2 * i_e / n + v2 * s1
de0_dt = lamda * beta0 * s0 * i_e / n - alpha * e0
de1_dt = lamda * beta1 * s1 * i_e / n - alpha * e1
de2_dt = lamda * beta2 * s2 * i_e / n - alpha * e2
di0_dt = alpha * e0 - gamma0 * i0 - delta0 * i0
di1_dt = alpha * e1 - gamma1 * i1 - delta1 * i1
di2_dt = alpha * e2 - gamma2 * i2 - delta2 * i2
dd0_dt = delta0 * i0
dd1_dt = delta1 * i1
dd2_dt = delta2 * i2
dr_dt = gamma0 * i0 + gamma1 * i1 + gamma2 * i2
return np.array([ds0_dt, ds1_dt, ds2_dt, de0_dt, de1_dt, de2_dt, di0_dt, di1_dt, di2_dt, dd0_dt, dd1_dt, dd2_dt, dr_dt])
def draw_SEIDR(ySEIR):
plt.figure(figsize=(16, 9))
plt.plot(t, ySEIR[:, 0] + ySEIR[:, 1] + ySEIR[:, 2], '--', label='s(t)--SEIR')
plt.plot(t, ySEIR[:, 3] + ySEIR[:, 4] + ySEIR[:, 5], '-.', label='e(t)--SEIR')
plt.plot(t, ySEIR[:, 6] + ySEIR[:, 7] + ySEIR[:, 8], '-', label='i(t)--SEIR')
plt.plot(t, ySEIR[:, 9] + ySEIR[:, 10] + ySEIR[:, 11], '.', label='d(t)--SEIR')
plt.plot(t, ySEIR[:, 12], '--', label='r(t)--SEIR')
plt.legend()
# plt.show()
plt.savefig('./img/' + '2.2.2 SEIDR_V2t_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)
v1 = 0.02 # Vaccination coverage rates of first dose 第一针疫苗接种率
v2 = 0.02 # Vaccination coverage rates of second dose 第二针疫苗接种率
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
beta2 = 0.005 # 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
gamma2 = 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
delta2 = 0.0008 # Death rate of vaccinated infected persons 接种了疫苗的感染者的死亡率
s0 = 9990 # Number of unvaccinated people 未接种疫苗人群
s1 = 0 # The number of people who receive one dose of vaccine 接种一针疫苗人群
s2 = 0 # The number of people who receive two doses of vaccine 接种两针疫苗人群
e0 = 0 # The latent people who do not receive vaccine 未接种疫苗的潜伏人群
e1 = 0 # The latent people who receive one dose of vaccine 接种一针疫苗的潜伏人群
e2 = 0 # The latent people who receive two doses of vaccine 接种两针疫苗的潜伏人群
i0 = 10 # The infected people who do not receive vaccine 未接种疫苗的感染人群
i1 = 0 # The infected people who receive one dose of vaccine 接种一针疫苗的感染人群
i2 = 0 # The infected people who receive two doses of vaccine 接种两针疫苗的感染人群
d0 = 0 # The dead people who do not receive vaccine 未接种疫苗的死亡人群
d1 = 0 # The dead people who receive one dose of vaccine 接种一针疫苗的死亡人群
d2 = 0 # The dead people who receive two doses of vaccine 接种两针疫苗的感染人群
Y0 = (s0, s1, s2, e0, e1, e2, i0, i1, i2, d0, d1, d2, r)
ySEIR = odeint(dySEIDR_V2, Y0, t, args=(alpha, beta0, beta1, beta2, gamma0, gamma1, gamma2, delta0, delta1, delta2, lamda, v1, v2))
draw_SEIDR(ySEIR)