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?