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

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

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

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

Attempt:

So I would assume $\displaystyle \beta = 0.0005$

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

How do I calculate $\displaystyle \gamma$. 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