COVID-19 simuation by SEIR model

covid19.py

# The preprints is available from https://www.preprints.org/manuscript/202002.0179/v1
# S Susceptible
# E Exposed
# I Infected
# R Recovery
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
from ipywidgets import interact

def dsdt(S, I, beta):
    return -beta * S * I / N

def dedt(S, I, E, beta):
    return beta * S * I / N - delta * E

def didt(E, I, delta):
    return delta * E - nu * I

def drdt(I, nu):
    return nu * I

@interact
def main(r0: (0.1,5,0.1), initial_infection: (0.1,10,0.1)):
    #r0 = 3. # basic reproduction number
    p = 10. # Infectious period(day)
    prevalence = 0.7 # patients/at-risk people
    recovery = 1.0 # recovery rate from disease
    #initial_infection = 10. # initial number of carrier

    beta = r0/p # propergation rate of infection
    delta = prevalence/p # 
    nu = recovery/p # 
    N = 1000 # Population
    D = 300 # observation days
    t = np.arange(0, D, 1)
    Ss = np.array([N])
    Es = np.array([0])
    Is = np.array([initial_infection])
    Rs = np.array([0])

    for i in t[0:D-1]:
        Ss = np.append(Ss, Ss[i] + dsdt(Ss[i], Is[i], beta))
        Es = np.append(Es, Es[i] + dedt(Ss[i], Is[i], Es[i], beta))
        Is = np.append(Is, Is[i] + didt(Es[i], Is[i], delta))
        Rs = np.append(Rs, Rs[i] + drdt(Is[i], nu))

    #print(Ss, Es, Is, Rs)
    plt.plot(t, Ss, label='S')
    plt.plot(t, Es, label='E')
    plt.plot(t, Is, label='I')
    plt.plot(t, Rs, label='R')
    plt.legend()