Observable Python SIR

import numpy as np

import matplotlib.pyplot as plt

from scipy.integrate import odeint

N = 1       # Size of the population (so everything in proportions)

I0 = 0.01   # Initial proportion of the population infected

S0 = N - I0 # Initial proportion of the population susceptible

R0 = 0.0    # Initial proportion of the population recovered

maxT = 25   # max number of periods in simulation

beta = 0.5  # transmission rate

gamma = 0.1 # recovery rate

def SIR(y, t, beta, gamma):

    '''the SIR model'''

    S, I, R = y

    dSdt = -beta*S*I

    dIdt = beta*S*I - gamma*I

    dRdt = gamma*I

    return([dSdt, dIdt, dRdt])

def plotSIR(beta = beta, gamma = gamma, maxT = maxT):

    '''Solve differential equations in SIR and plot'''

    t = np.linspace(0, maxT, 1000)

    soln = odeint(SIR, [S0,I0,R0], t, args=(beta, gamma))

    soln = np.array(soln)

    plt.figure(figsize=[8,6])

    plt.plot(t, soln[:,0], linewidth=3, label = 'S(t)')

    plt.plot(t, soln[:,1], linewidth=3, label = 'I(t)')

    plt.plot(t, soln[:,2], linewidth=3, label = 'R(t)')

    plt.title("SIR model")

    plt.xlabel("Time"); plt.ylabel("proportions")

    plt.grid(); plt.legend()

from IPython.display import display, HTML

# display(HTML("<h1>hello</h1>"))

123

plotSIR(Beta:
0.5, Gamma:
0.5, MaxT:
55)

Generators.input(controls.beta)

Generators.input(controls.gamma)

Generators.input(controls.maxt)