A Branching Process Approximation of the Final Size of a Multitype Collective Reed-Frost Model

We consider the asymptotic behavior of the final size of a multitype collective Reed-Frost process. This type of models was introduced by [9] and include most known epidemic models of the type SIR (Susceptible, Infected, Removed) as special cases. Under certain conditions, we show that, when the initial number of susceptible is very large and the initial number of infected individuals is finite, the infection process behaves as a multitype Galton-Watson process. This fact is proved using a simple argument based on Bernstein polynomials. We use this result to study the final size of the epidemic