Threshold dynamics of an age-space structure vector-borne disease model with multiple transmission pathways

Abstract

This paper aims to study threshold dynamics of an age-space structured vector-borne epidemic model with multiple transmission pathways. We develop a model in a bounded space, and demonstrate the well-posedness by proving the global existence of the solution and the model admits a global attractor with using the theory of fixed point problem, Picard sequences and iteration. In the special case of homogenous space, the explicit formula of basic reproduction number $ R_{0} $ is established, which can be used to discuss whether a disease is persistent or extinct. The local and global stability of steady states are achieved by analyzing the distribution of characteristic roots of characteristic equations and designing Lyapunov functions. These theoretical results are illustrated by numerical simulations. Besides, sensitive analysis on $ R_{0} $ reveals that certain parameters are more effective to impact the $ R_{0} $. We find that the PRCC indexes of solutions can be time-dependent, and the relative importance of parameters can also depend on time. Relying on this analysis and exhaustive numerical simulations, we suggest that insecticides and mosquito nets should be used in a timely manner to disinfect vectors and reduce the contact between vectors and hosts, and that ignoring the horizontal transmission in the host underestimates the risk of disease transmission.