A Periodic West Nile Virus Transmission Model with Stage-Structured Host Population

In this paper, we study an avian (host) stage-structured West Nile virus model, which incorporates seasonality as well as stage-specific mosquito biting rates. We first introduce the basic reproduction number for this model and then show that the disease-free periodic solution is globally asymptotically stable when , while there exists at least one positive periodic solution and that the disease is uniformly persistent if . In the case where all coefficients are constants, for a special case, we obtain the global stability of the disease-free equilibrium, the uniqueness of the endemic equilibrium, and the permanence of the disease in terms of the basic reproduction number . Numerical simulations are carried out to verify the analytic result. Some sensitivity analysis of is performed. Our finding shows that an increase in juvenile exposure will lead to more severe transmission. Moreover, we find that the ignorance of the seasonality may result in underestimation of the basic reproduction number .