base_sir_model_w_sd_factor_viz.py

%matplotlib inline

import numpy as np
from scipy.integrate import odeint
import matplotlib.pyplot as plt

# Total population, N.
N = 1339200000

# Initial number of infected and recovered individuals, I0 and R0.
I0, R0 = 296, 23

# Everyone else, S0, is susceptible to infection initially.
S0 = N - I0 - R0

# Contact rate, beta, and mean recovery rate, gamma, (in 1/days).
beta, gamma = 1.75, 1./8 

# Social distancing factor
rho = 1.0

# New beta now becomes a multiplicative factor of rho
beta = rho*beta

# A grid of time points (in days)
t = np.linspace(0, 100, 100)

# The SIR model differential equations.
def deriv(y, t, N, beta, gamma):
    S, I, R = y
    dSdt = -beta * S * I / N
    dIdt = beta * S * I / N - gamma * I
    dRdt = gamma * I
    return dSdt, dIdt, dRdt

# Initial conditions vector
y0 = S0, I0, R0

# Integrate the SIR equations over the time grid, t.
ret = odeint(deriv, y0, t, args=(N, beta, gamma))
S, I, R = ret.T

# Plot the data on three separate curves for S(t), I(t) and R(t)
fig = plt.figure(facecolor='w')
ax = fig.add_subplot(111, axisbelow=True)
ax.plot(t, S/1000000000, 'b', alpha=0.5, lw=2, label='Susceptible')
ax.plot(t, I/1000000000, 'r', alpha=0.5, lw=2, label='Infected')
ax.plot(t, R/1000000000, 'g', alpha=0.5, lw=2, label='Recovered with immunity')
ax.set_xlabel('Time /days')
ax.set_ylabel('Number (100 Crores)')
ax.set_ylim(0,1.5)
ax.yaxis.set_tick_params(length=0)
ax.xaxis.set_tick_params(length=0)
ax.grid(b=True, which='major', c='w', lw=2, ls='-')
legend = ax.legend()
legend.get_frame().set_alpha(0.5)

for spine in ('top', 'right', 'bottom', 'left'):
    ax.spines[spine].set_visible(False)

plt.show()