sir_ode

sir_ode, a Python code which sets up the ordinary differential equations (ODE) which simulate the spread of a disease using the Susceptible/Infected/Recovered (SIR) model.

We consider the evolution of a disease epidemic in a population of N people.

We assume that the patients can be classified as Susceptible, Infected or Recovering, with the properties that:

• Susceptible: A patient who has never been infected with the disease. A susceptible patient can become infected, with an infectivity coefficient alpha.
• Infected: A patient who was susceptible, and has now contracted the disease. Infected patients can spread the disease to susceptible patients. An infected patient can become recovered, with recovery coefficient beta.
• Recovered: A patient who was infectious, but has recovered. Such patients cannot contract the disease, and cannot transmit it. A recovered patient can become susceptible, with susceptibility coefficient gamma.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

sir_ode is available in a MATLAB version and an Octave version and a Python version..

Related Data and codes:

python_ode, Python codes which sets up various systems of ordinary differential equations (ODE).

Reference:

1. Dianne OLeary,
   Models of Infection: Person to Person,
   Computing in Science and Engineering,
   Volume 6, Number 1, January/February 2004.
2. Dianne OLeary,
   Scientific Computing with Case Studies,
   SIAM, 2008,
   ISBN13: 978-0-898716-66-5,
   LC: QA401.O44.

Source Code:

• sir_ode.py, the source code.
• sir_ode.sh, runs all the tests.
• sir_ode.txt, the output file.

• sir_solve_ivp.png, a time history plot.
• sir_solve_ivp_conservation.png, a plot of S+I+R, should be constant.