Notebook

This notebook contains material from nbpages by Jeffrey Kantor (jeff at nd.edu). The text is released under the CC-BY-NC-ND-4.0 license. The code is released under the MIT license.

2.1.1.1 SIR model without vital dynamics¶

The Susceptible-Infectious-Recovered (SIR) model is an example of a compartmental model that is widely used to forecast the progress of disease epidemics.

\begin{align} \frac{dS}{dt} & = -\frac{\beta I S}{N} \\ \frac{dI}{dt} & = \frac{\beta I S}{N} - \gamma I \\ \frac{dR}{dt} & = \gamma I \end{align}

Where the basic reproduction number $R_0 = \frac{\beta}{\gamma}$

In [23]:

%matplotlib inline

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

N = 10000.0
R0 = 2.4
gamma = 1/8.0
beta = gamma*R0

def deriv(t, y):
    S, I, R = y
    dSdt = -beta*I*S/N
    dIdt = beta*I*S/N - gamma*I
    dRdt = gamma*I
    return [dSdt, dIdt, dRdt]

t = np.linspace(0, 180, 181)
y0 = [N - 1.0, 1.0, 0.0]
soln = solve_ivp(deriv, [t[0], t[-1]], y0, t_eval=t)

plt.plot(soln.t, soln.y[0], label='Susceptible')
plt.plot(soln.t, soln.y[1], label='Infectious')
plt.plot(soln.t, soln.y[2], label='Recoverd')
plt.legend()
plt.xlabel('days')
plt.grid(True)

Home Activity:

2.1.1 SIR model without vital dynamics¶

The Susceptible-Infectious-Recovered (SIR) model is an example of a compartmental model that is widely used to forecast the progress of disease epidemics.

\begin{align} \frac{dS}{dt} & = -\frac{\beta I S}{N} \\ \frac{dI}{dt} & = \frac{\beta I S}{N} - \gamma I \\ \frac{dR}{dt} & = \gamma I \end{align}

Where the basic reproduction number $R_0 = \frac{\beta}{\gamma}$

This cell has been tagged with "home-activity".

2.1.1 Tagging solutions in code cells¶

For teaching purposes, it is often useful to selecting remove code from cells a

2.1.1.1 Exercise 1.¶

In the following cell write a function that returns the square of a number.

In [6]:

# write a function that returns the square of a number

### BEGIN SOLUTION
def sqr(x):
    return x**2
### END SOLUTION

assert sqr(2) == 4
assert sqr(-1) == 1

### BEGIN HIDDEN TESTS
assert sqr(3) == 9
assert abs(sqr(3.3) - 10.89) < 0.001
### END HIDDEN TESTS

2.1 Tagging¶

2.1.1 Tagging cells¶

2.1.1.1 SIR model without vital dynamics¶

2.1 Special formatting for special tags¶

2.1.1 SIR model without vital dynamics¶

2.1.1 Tagging solutions in code cells¶

2.1.1.1 Exercise 1.¶