Modeling the Transmission of West Nile Virus with ${\it Wolbachia}$ in a Heterogeneous Environment

Modeling the Transmission of West Nile Virus with ${\it Wolbachia}$ in a Heterogeneous Environment

Year:    2021

Author:    Mengli Liu, Min Zhu, Xiaofei Song

Journal of Nonlinear Modeling and Analysis, Vol. 3 (2021), Iss. 2 : pp. 301–319

Abstract

${\it Wolbachia}$ 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.12150/jnma.2021.301

Journal of Nonlinear Modeling and Analysis, Vol. 3 (2021), Iss. 2 : pp. 301–319

Published online:    2021-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    West Nile virus model ${\it Wolbachia}$ Basic reproduction number Stability.

Author Details

Mengli Liu

Min Zhu

Xiaofei Song