TY - JOUR
T1 - Modeling the Transmission of West Nile Virus with ${\it Wolbachia}$ in a Heterogeneous Environment
AU - Liu , Mengli
AU - Zhu , Min
AU - Song , Xiaofei
JO - Journal of Nonlinear Modeling and Analysis
VL - 2
SP - 301
EP - 319
PY - 2021
DA - 2021/04
SN - 3
DO - http://doi.org/10.12150/jnma.2021.301
UR - https://global-sci.org/intro/article_detail/jnma/18792.html
KW - West Nile virus model, ${\it Wolbachia}$, Basic reproduction number,
Stability.
AB - <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>