# Math Help - Setting Up Epidemic SIR Model

1. ## 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

2. ## 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?

3. ## Re: Setting Up Epidemic SIR Model

Originally Posted by Len
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.)