Classical disease models use a mass action term as the interaction between infected and susceptible people in separate patches. We derive the equations when this interaction is a migration of people between patches. The results model what happens when a new population is moved into a region with endemic disease.
@article{arxiv.physics/0510061,
title = {Migration induced epidemics: Dynamics of flux-based multipatch models},
author = {Larry S. Liebovitch and Ira B. Schwartz},
journal= {arXiv preprint arXiv:physics/0510061},
year = {2009}
}