Dynamics of a periodic West Nile virus model with mosquito demographics

Abstract

<p style='text-indent:20px;'>In this paper, we propose a time-delayed model of West Nile virus with periodic extrinsic incubation period (EIP) and mosquito demographics including stage-structure, pair formation and intraspecific competition. We define two quantities <inline-formula><tex-math id="M1">\begin{document}$ \mathcal{R}_{\rm min} $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}$ \mathcal{R}_{\rm max} $\end{document}</tex-math></inline-formula> for mosquito population and the basic reproduction number <inline-formula><tex-math id="M3">\begin{document}$ \mathcal{R}_0 $\end{document}</tex-math></inline-formula> for our model. It is shown that the threshold dynamics are determined by these three parameters: (ⅰ) if <inline-formula><tex-math id="M4">\begin{document}$ \mathcal{R}_{\rm max}\leq 1 $\end{document}</tex-math></inline-formula>, the mosquito population will not survive; (ⅱ) if <inline-formula><tex-math id="M5">\begin{document}$ \mathcal{R}_{\rm min}&gt;1 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M6">\begin{document}$ \mathcal{R}_0&lt;1 $\end{document}</tex-math></inline-formula>, then WNv disease will go extinct; (ⅲ) if <inline-formula><tex-math id="M7">\begin{document}$ \mathcal{R}_{\rm min}&gt;1 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M8">\begin{document}$ \mathcal{R}_0&gt;1 $\end{document}</tex-math></inline-formula>, then the disease will persist. Numerically, we simulate the long-term behaviors of solutions and reveal the influences of key model parameters on the disease transmission. A new finding is that <inline-formula><tex-math id="M9">\begin{document}$ \mathcal{R}_0 $\end{document}</tex-math></inline-formula> is non-monotone with respect to the fraction of the aquatic mosquitoes maturing into adult male mosquitoes, which can help us implement more effective control strategies. Besides we observe that using the time-averaged EIP has the possibility of underestimating the infection risk.</p>