An epidemic model using GW trees and coupon collectors

We describe a model for information or viral transmission on the complete graph $\mathbb{K}_n$.
Each node is an individual which may be susceptible, infected or recovered.
This model has been introduced by Comets et al. with the main goal of studying the asymptotic behavior, as $n$ goes to infinity, of the duration of the infection and of the proportion of infected individuals in the population.
The results rely on two interesting stochastic processes: the GW process and the coupon collector process.
We discuss some extensions of this problem