Section: New Results

Analysis of the dynamics of some models for vector-borne diseases with host circulation

In this work 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 $R_0$ 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, $R_0$, is greater that unity. We are also able to show that the DFE is globally asymptotically stable, if $R_0\le 1$. If $R_0>1$, the dynamics is uniformly persistent and, with further assumptions on the contact network structure, we also show that the endemic equilibrium (EE) is globally asymptotically stable [17] .