Pieter Trapman: Markov SIR epidemics with demography in structured populations

We consider a Markov Susceptible, Infectious, Recovered (SIR) epidemic in a structured population (e.g. the individuals might be the vertices of a graph, where "friendships" are the edges). In addition to the usual SIR epidemics, individuals are replaced by susceptible ones according to independent Poisson Processes. 

If the recovery rate of individuals is 0, then this process corresponds to the contact process on a graph, while if the replacement rates is 0, then the model can be analysed using percolation theory. However, many basic questions are still open in case neither of those parameters is 0.  In particular, is the probability of extinction of the epidemic decrease if the infectivity of infectious individuals increases and is there a critical infectivity, above which survival has positive probability and below which it does not have so? In this talk I will discuss these questions further and give further background.