We study the dynamics of a vector-borne disease on a metapopulation model that accounts for host circulation. For such models, the movement network topology gives rise to a contact network topology, corresponding to a bipartite graph. Under the assumption that the contact network is strongly connected, we can define the basic reproductive number R0 and show that this system has only two equilibria: the so called disease free equilibrium (DFE); and a unique interior equilibrium that exists if, and only if, the basic reproduction number, R0, is greater that unity. We also  show that the DFE is globally asymptotically stable, if R0 ≤ 1. If R0 > 1, the dynamics is uniformly persistent and, with further assumptions on the contact network, the EE is globally asymptotically stable. This is joint work with Abedarrhaman  Iggidr and Gauthier Sallet.

References

A Iggidr, G Sallet & MO Souza, Analysis of the dynamics of a class of models for vector-borne diseases with host circulation. Submitted. Preprint available at HAL 00905926.