We consider a stochastic model for the spread of an epidemic in a population split into m groups in which both infective and susceptible individuals are able to move between groups. Using a coupling argument similar to those applied to various other epidemic models by previous authors, we show that as the initial susceptible population becomes large, the process of infectives in this epidemic model converges to a multitype birth-and-death process with time-dependent birth rates. The behavior of this limiting process is then considered, in particular, the conditions under which extinction is almost certain.
"Strong approximations for mobile population epidemic models." Ann. Appl. Probab. 6 (3) 883 - 895, August 1996. https://doi.org/10.1214/aoap/1034968231