@Article{JNMA-3-301,
author = {Liu , MengliZhu , Min and Song , Xiaofei},
title = {Modeling the Transmission of West Nile Virus with ${\it Wolbachia}$ in a Heterogeneous Environment},
journal = {Journal of Nonlinear Modeling and Analysis},
year = {2021},
volume = {3},
number = {2},
pages = {301--319},
abstract = {<p style="text-align: justify;">${\it Wolbachia}$ are maternally transmitted endosymbiotic bacteria. To investigate the effect of ${\it Wolbachia}$ on the spreading and vanishing of West Nile virus, we construct a reaction-diffusion model associated with the ${\it Wolbachia}$ parameter in a heterogeneous environment, which has nonlinear infectious disease parameters. Based on the spectral radius of next infection operator and the related eigenvalue problem, we present a corresponding explicit expression describing the basic reproduction number. Furthermore, utilizing this number, we not only give out the stability of disease-free equilibrium, but also analyze the uniqueness and globally asymptotic behavior of endemic equilibrium. Our theoretical results and numerical simulations indicate that only if ${\it Wolbachia}$ reach a certain magnitude in mosquitoes, it can be effective in the control of West Nile virus.</p>},
issn = {2562-2862},
doi = {https://doi.org/10.12150/jnma.2021.301},
url = {http://global-sci.org/intro/article_detail/jnma/18792.html}
}