Aggregation and classification of spatial dynamics of vector-borne disease in advective heterogeneous environment

Abstract

In this paper, we formulate and analyze a reaction-diffusion-advection vector-borne disease model with spatial heterogeneity. We find the aggregation phenomenon of endemic equilibrium and classify possible dynamics for the model, including the asymptotic profiles and monotonicity of basic reproduction ratio R0 with respect to the diffusion and advection rates of infected hosts and vectors. More importantly, we obtain some crucial and interesting phenomena by classifying the level set of R0. Specifically, there exist unique critical surfaces to separate the dynamics, namely, the disease-free equilibrium is stable on one side of the surface and unstable on the other side. The resulting aggregation phenomenon shows that the infected individuals will aggregate in the downstream end if their advection rates are sufficiently large relative to dispersal. To the best of our knowledge, the conclusions of the paper complement the results of vector-borne disease in non-advective environments for the first time and provide new perspectives for the investigation and control of the disease.