Abstract
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 R0 for this model and then show that the disease-free periodic solution is globally asymptotically stable when R0<1, while there exists at least one positive periodic solution and that the disease is uniformly persistent if R0>1. 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 R0. Numerical simulations are carried out to verify the analytic result. Some sensitivity analysis of R0 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 R0.
Highlights
West Nile virus (WNV) is a flavivirus commonly found in Africa, West Asia, and the Middle East. e virus can infect humans, birds, mosquitoes, horses, and some other mammals
Mathematical models have played a significant role in understanding and analyzing the WNV transmission dynamics
It is clear that system (46) always has two equilibria P0 0((,mN0∗T,+A, 0μ∗T,),020,FA0∗T,∗T,M0,∗0b,m,0A,20∗T/)(,0μ,(w0m,h0+e,r0eμ,)02)N), ∗Taan nddbM/(∗mP 1+ (μK()(,Nr∗TF−,∗T0μ, M0,)b)Fm/∗Tr/., In order to find any endemic equilibrium of system (46), we introduce the basic reproduction number R0
Summary
West Nile virus (WNV) is a flavivirus commonly found in Africa, West Asia, and the Middle East. e virus can infect humans, birds, mosquitoes, horses, and some other mammals. Wonham et al [5] presented a single-season susceptible-infectious-removed (SIR) model for WNV transmission in the mosquito-bird population. In a more recent work by Fan et al [11], they formulated and analyzed a single-season model for the transmission of WNV between vector mosquitoes and avian hosts, and their model incorporated maturation delay for mosquitoes. Seasonality is strongly influenced by climatic factors Due to these reason, in [18], Robertson and Caillou€et [18] developed a host-vector model for WNV transmission dynamics across a single season, which incorporated the host stage-structure as well as stage-specific biting rates of vectors on avian hosts. By taking into account the seasonality, the avian stage-structure and within-species heterogeneity, we derive a periodic model to describe the dynamics of WNV transmission.
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