Dynamical analysis of a heterogeneous spatial diffusion Zika model with vector-bias and environmental transmission

Abstract

In this study, we formulate a reaction-diffusion Zika model which incorporates vector-bias, environmental transmission and spatial heterogeneity. The main question of this paper is the analysis of the threshold dynamics. For this purpose, we establish the mosquito reproduction number $ R_{1} $ and basic reproduction number $ R_{0} $. Then, we analyze the dynamical behaviors in terms of $ R_{1} $ and $ R_{0} $. Numerically, we find that the ignorance of the vector-bias effect will underestimate the infection risk of the Zika disease, ignorance of the spatial heterogeneity effect will overestimate the infection risk, and the environmental transmission is indispensable.

Keywords

• zika
• reaction-diffusion
• vector-bias
• environmental transmission
• spatial heterogeneity
• reproduction number
• threshold dynamics