Global threshold dynamics of a spatial chemotactic mosquito-borne disease model

Abstract

It is natural that mosquitoes move toward high human population density and environmental heterogeneity plays a pivotal role on disease transmission, and thus we formulate and analyze a mosquito-borne disease model with chemotaxis and spatial heterogeneity. The global existence and boundedness of solutions are proven to guarantee the solvability of the model and is challenging due to the model complexity. Under appropriate conditions, we demonstrate the disease-free equilibrium is globally asymptotically stable provided that the basic reproduction number $\mathcal {R}_0$ is less than one, and the system is uniformly persistent and admits at least one endemic equilibrium if $\mathcal {R}_0$ is greater than one. Furthermore, we numerically explore the impacts of chemotactic effect, spatial heterogeneity and dispersal rates of infected individuals to provide a clear picture on disease severity. In particular, the mosquito chemotaxis causes disease mild in some regions but severe in others, which suggests developing targeted strategies to control mosquitoes in specific locations and achieves a deep understanding on the chemotaxis.