SIR_SIMULATION
Simulation of Disease Propagation with the SIR Model


SIR_SIMULATION is a MATLAB program which simulates the spread of a disease through a hospital room of M by N beds, using the SIR (Susceptible/Infected/Recovered) model.

We consider the evolution of a disease in a hospital in which patients are arranged on an array of beds.

We assume that the beds form an array of M rows and N columns, so that there are a total of M * N patients.

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

We set up an M by N array A to represent the patients. A(I,J) contains information on the patient in row I, column J. A(I,J) will be

The rules for transmission of the disease essentially update the patient array once a day. If patient A(I,J) was:

Quantities of interest include an animation of the day to day status of patients in the hospital (the "geometry") and the values of S, I, and R, that is, the total number of patients in each category, as it evolves over time.

Since this problem contains a probabilistic element in the transmission of disease, the outcome of any single run has limited meaning. It is much more valuable to run many simulations, and thus to get both average or "expected" values, as well as a feeling for the variance of the data from these averages.

Usage:

sir = sir_simulation ( m, n, a, k, tau, t_max )
where

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

SIR_SIMULATION is available in a MATLAB version.

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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:

Examples and Tests:

As the SIR_SIMULATION program runs, it displays a plot of the hospital room, with susceptibles in green, infecteds in shades of red, and recovereds in gray. Here is an example:

Using the command

      plot ( 1:t_max, sir(1,:), 'g', 1:t_max, sir(2,:), 'r', 1:t_max, sir(3,:), 'k' )
      
we can make line plots of the S, I and R populations. For M = N = 10, a single infected patient at A(5,5), K = 4, TAU = 0.2, and T_MAX = 50, we did this several times:

Using the commands

      h = areas ( sir' );
      set ( h(1), 'FaceColor', [ 0, 1, 0 ] );
      set ( h(2), 'FaceColor', [ 1, 0, 0 ] );
      set ( h(3), 'FaceColor', [ 0.8, 0.8, 0.8 ] );
      
we can make an area plot of the S, I and R populations. For M = N = 10, a single infected patient at A(5,5), K = 4, TAU = 0.2, and T_MAX = 50, we did this:

You can go up one level to the MATLAB source codes.


Last revised on 09 November 2009.