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Math Help - Setting Up Epidemic SIR Model

  1. #1
    Len
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    Setting Up Epidemic SIR Model

    Question:

    Model a daycare that measles spreads when a sick child comes in. In this daycare, we have 100 susceptible children, and there is a recruitment rate of 5 new kids per year. The rate at which measles is transmitted from an infected child to a susceptible child is assumed to be 0.0005 per year. Also assume that infected children will recover from the disease in 2 weeks.

    Info:

    So I know


    \frac {dS}{dt} = -\beta S I

    \frac {dI}{dt}= \beta S I + \gamma I

    \frac {dR}{dt}= \gamma I

    Attempt:

    So I would assume \beta = 0.0005

    And I think S = 100 + 5t - \gamma I

    How do I calculate \gamma. I know they recover in 14 days. Would it be 14/365?

    What else am I missing?

    Any help is certainly appreciated to help me understand a little better. I have tried to read wikipedia. Thanks
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  2. #2
    A Plied Mathematician
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    Re: Setting Up Epidemic SIR Model

    Hmm. I'm not sure I would agree with your model as yet. Start with English first, and then translate to differential equations. Let S be the number of susceptibles, I be the number of infectees, and R be the number of recoverees. (Coining words there, I know.) Then I think you have the following:

    dS/dt = recruitment rate minus infection rate (since infected children are not counted as susceptible anymore).

    dI/dt = rate due to interactions between susceptibles and infectees minus recovery rate.

    dR/dt = proportional to the number of infectees

    So from this, what do you think a reasonable model would be? What are the initial conditions?
    Last edited by Ackbeet; October 3rd 2011 at 07:33 AM.
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  3. #3
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    Re: Setting Up Epidemic SIR Model

    Quote Originally Posted by Len View Post
    How do I calculate \gamma. I know they recover in 14 days. Would it be 14/365?
    Wikipedia glosses 1 / \gamma as average recovery period. (So flip your fraction.)
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