SIR_assignment_2/Problem 2 at master · pjetroque/SIR_assignment_2 · GitHub

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import numpy as np
import random
from scipy.integrate import odeint
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt
import statistics


# Define starting conditions
N1 = 1000
S1 = 995
I1 = 5
R1 = N1-S1-I1

N2 = 1000
S2 = 1000
I2 = 0
R2 = N2-S2-I2

days = 100
t = 0.0
t_old = 0
time_step = 0.1
N_populations = 2
interaction_matrix = np.array([[1, 0.01], [0.01, 1]])
value_matrix = np.array([[S1, I1, R1], [S2, I2, R2]])
time = np.arange((t + time_step), (days + time_step), time_step)

N_list = [[N1],[N2]]
S_list = [[S1],[S2]]
I_list = [[I1],[I2]]
R_list = [[R1],[R2]]
t_list = [[t],[t]]

N_smooth_list = [[N1],[N2]]
S_smooth_list = [[S1],[S2]]
I_smooth_list = [[I1],[I2]]
R_smooth_list = [[R1],[R2]]

mu = 0.01
beta = [[1.2], [1.2]]
gamma = [[0.8], [0.8]]

# Defining all events, changes in [S, I, R]
E1 = [1, 0, 0]     #birth
E2 = [-1, 1, 0]    #infection
E3 = [0, -1, 1]    #recovery
E4 = [-1, 0, 0]    #deathS
E5 = [0, -1, 0]    #deathI
E6 = [0, 0 , -1]   #deathR

e_list = [E1, E2, E3, E4, E5, E6]
#e_list = [E2, E3]

for interval in time:
    #find the most recent numbers and calculate N's of every population

    value_matrix = np.array([[S_smooth_list[0][-1], I_smooth_list[0][-1], R_smooth_list[0][-1]], [S_smooth_list[1][-1], I_smooth_list[1][-1], R_smooth_list[1][-1]]])
    N_vector = value_matrix @ np.array([[1], [1], [1]])

    #calculate beta/N
    beta_N = beta / N_vector
    first_matrix = np.identity(2) * beta_N
    infecteds = np.array([value_matrix[:,1]]).T
    susceptebles = np.array([value_matrix[:,0]]).T
    recoverds = np.array([value_matrix[:,2]]).T

    #calculate lambdas
    lapda = first_matrix @ (interaction_matrix @ infecteds)

    #Event rates are calculated for all populations
    r_b = mu * N_vector.T[0]
    r_i = (lapda * susceptebles).T[0]
    r_r = (gamma * infecteds).T[0]
    r_ds = mu * susceptebles.T[0]
    r_di = mu * infecteds.T[0]
    r_dr = mu * recoverds.T[0]
    r_list = np.array([r_b, r_i, r_r, r_ds, r_di, r_dr]).T
    r_t = r_list @ np.array([[1], [1], [1], [1], [1], [1]])

    for pop in range(0,N_populations):
        #find specific time in that population and numbers
        t = t_list[pop][-1]
        S = S_list[pop][-1]
        I = I_list[pop][-1]
        R = I_list[pop][-1]
        r_list_pop = r_list[pop]
        r_t_pop = r_t[pop]

        #if the time falls within this interval event happens
        while interval > t:

            #calculate the step in time untill next event
            dt = -(1/r_t_pop) * np.log(random.uniform(0, 1))
            p = r_t_pop * random.uniform(0, 1)

            #update the time of the event
            t += dt
            p0 = 0
            i = 0

            #find the event that happens
            while p0 < p:
                p0 += r_list_pop[i]
                if p0 > p:
                    break
                i += 1

            #find changes in S I and R and recalculate N
            S += e_list[i][0]
            I += e_list[i][1]
            R += e_list[i][2]
            N = S + I + R

            S_list[pop].append(S)
            I_list[pop].append(I)
            R_list[pop].append(R)
            N_list[pop].append(N)
            t_list[pop].append(t)

        #after new events within the time interval are calculated update the smooth list of that population
        S_smooth_list[pop].append(S)
        I_smooth_list[pop].append(I)
        R_smooth_list[pop].append(R)
        N_smooth_list[pop].append(N)

t = 0.0
t_old = 0
time_step = 0.1
time_plot = np.arange(t, (days + time_step), time_step)
plt.figure(1)
plt.title('For β= '+str(beta)+' and γ = '+str(gamma))
plt.plot(time_plot, S_smooth_list[0], label='S1')
plt.plot(time_plot, S_smooth_list[1], label='S2')
plt.plot(time_plot, I_smooth_list[0], label='I1')
plt.plot(time_plot, I_smooth_list[1], label='I2')
plt.plot(time_plot, R_smooth_list[0], label='R1')
plt.plot(time_plot, R_smooth_list[1], label='R2')
plt.ylim(0, 1200)
plt.xlim(0, 100)
plt.ylabel('Amount of people')
plt.xlabel('Amount of days')
plt.legend()
plt.show()