Transmission dynamics of a general temporal-spatial vector-host epidemic model with an application to the dengue fever in Guangdong, China

<p style='text-indent:20px;'>Due to the nature of the spread of vector-host epidemic disease, there are many factors affecting its dynamic behaviors. In this paper, a vector-host epidemic model with two seasonal development periods and awareness control of host is proposed to investigate the multi-effects of the spatial heterogeneity, seasonal development periods, temporal periodicity and awareness control. We first address the well-posedness of the model and then derive the basic reproduction number <inline-formula><tex-math id="M1">\begin{document}$ R_0 $\end{document}</tex-math></inline-formula>. In the case where <inline-formula><tex-math id="M2">\begin{document}$ R_0&lt;1 $\end{document}</tex-math></inline-formula>, we establish the global attractivity of the disease-free periodic solution, and in the case where <inline-formula><tex-math id="M3">\begin{document}$ R_0&gt;1 $\end{document}</tex-math></inline-formula>, we show that the disease is uniformly persistent and the system admits at least one positive periodic endemic steady state, and further obtain the global attractivity of the positive endemic constant steady state for the model with constant coefficients. As a case study, we conduct numerical simulations for the dengue fever transmission in Guangdong, China, 2014. We find that the greater heterogeneity of the mosquito distribution and human population may increase the risk of disease transmission, and the stronger awareness control may lower the risk of disease transmission.</p>