Abstract
We formulate a multi-group and multi-vector epidemic model in which hosts' dynamics is captured by staged-progression SEIR framework and the dynamics of vectors is captured by an SI framework. The proposed model describes the evolution of a class of zoonotic infections where the pathogen is shared by m host species and transmitted by p arthropod vector species. In each host, the infectious period is structured into n stages with a corresponding infectiousness parameter to each vector species. We determine the basic reproduction number R02(m, n, p) and investigate the dynamics of the systems when this threshold is less or greater than one. We show that the dynamics of the multi-host, multi-stage, and multi-vector system is completely determined by the basic reproduction number and the structure of the host-vector network configuration. Particularly, we prove that the disease-free equilibrium is globally asymptotically stable (GAS) whenever R02(m, n, p) < 1 , and a unique strongly endemic equilibrium exists and is GAS if R02(m, n, p) > 1 and the host-vector configuration is irreducible. That is, either the disease dies out or persists in all hosts and all vector species.