Analysis of a Prey-Predator Model with Disease in Prey (Communications in Mathematical Research, 2021)
In this paper, a system of reaction-diffusion equations arising in eco-epidemiological systems is investigated. The equations model a situation in which apredator species and a prey species inhabit the same bounded region and the predatoronly eats the prey with transmissible diseases. Local stability of the constant positivesolution is considered. A number of existence and non-existence results about the non-constant steady states of a reaction diffusion system are given. It is proved that ifthe diffusion coefficient of the prey with disease is treated as a bifurcation parameter,non-constant positive steady-state solutions may bifurcate from the constant steady-state solution under some conditions.