Mathematical analysis of a generalized reaction-diffusion model of Ebola transmission in bats

Abstract

Bats of the Pteropodidae family are believed to be the natural hosts of the Ebola virus (EV). These bats often have extensive home ranges, which can span large areas, including across countries and regions. We propose in this work to consider the mobility effect by studying a new generalized reaction-diffusion spatiotemporal system that emphasizes the transmission of Ebola virus disease (EVD) among bats. Besides transmission through direct contact with infectious bats, the model also considers infection via a contaminated environment. This transmission mechanism is characterized by two general incidence functions, encompassing various types of incidence rates. We provide evidence of the uniqueness, non-negativity, and boundedness of solutions considering the Neumann boundary conditions, indicating that the flux is zero at the boundary, and positive initial data. The stability behavior of the equilibria is demonstrated theoretically by using appropriate Lyapunov functionals and the linearization method, and numerically via some numerical simulations.