The effect of harvesting policy on an eco-epidemiological model

Abstract

Considering to the high extent spread of epidemics in the general of individuals of the distressed communities, which the cause of extinction, we suggest and investigate an eco-epidemiological system consisting two different (SIS and SI) infectious diseases in prey population. Such diseases are transmitted within prey species by contact, as well as, the selection of optimal harvesting on predator species is proposed and analyzed. The mathematical model involves four first-order nonlinear ordinary differential equations, which characterize the interaction among the susceptible prey, infected prey, and predator. The predator feeding depends on predation prey according to Holling type-II functional response as well as, the nonlinear incidence for describing the transition of infectious diseases is used. The existence of bionomic equilibria, uniqueness, boundedness of the system solution and the optimal proportionate harvesting policy are discussed.Considering to the high extent spread of epidemics in the general of individuals of the distressed communities, which the cause of extinction, we suggest and investigate an eco-epidemiological system consisting two different (SIS and SI) infectious diseases in prey population. Such diseases are transmitted within prey species by contact, as well as, the selection of optimal harvesting on predator species is proposed and analyzed. The mathematical model involves four first-order nonlinear ordinary differential equations, which characterize the interaction among the susceptible prey, infected prey, and predator. The predator feeding depends on predation prey according to Holling type-II functional response as well as, the nonlinear incidence for describing the transition of infectious diseases is used. The existence of bionomic equilibria, uniqueness, boundedness of the system solution and the optimal proportionate harvesting policy are discussed.