An almost periodic Dengue transmission model with age structure and time-delayed input of vector in a patchy environment

Abstract

<p style='text-indent:20px;'>In this paper, we propose an almost periodic multi-patch SIR-SEI model with age structure and time-delayed input of vector. The existence of the almost periodic disease-free solution and the definition of the basic reproduction ratio <inline-formula><tex-math id="M1">\begin{document}$ R_{0} $\end{document}</tex-math></inline-formula> are given. It is shown that the disease is uniformly persistent if <inline-formula><tex-math id="M2">\begin{document}$ R_0&gt;1 $\end{document}</tex-math></inline-formula>, and it dies out if <inline-formula><tex-math id="M3">\begin{document}$ R_0&lt;1 $\end{document}</tex-math></inline-formula> under the assumptions that there exists a small invasion and the same travel rate of susceptible, infective and recovered host population in different patches. Finally, we illustrate the above results by numerical simulations. In addition, a simple example shows that the basic reproduction ratio may be underestimated or overestimated if an almost periodic coefficient is approximated by a periodic one.