Modeling of an Eco-Epidemiological system Involving Various Epidemic Diseases with Optimal Harvesting

Abstract

This paper aims to study and analyze the effect of optimal harvesting on the dynamical behavior of an eco-epidemiological model dealing with a field of wheat (Host species) and assailant species (Locust insect). The host species contain two different (SIS and SI) epidemic diseases, which transmitted via contact among its members. The interaction of the susceptible and infected species with assailant species is characterized by a system of four nonlinear ordinary differential equations of the first order. According to the response of Holling type2 functional, the assailant feeding is depending on predation host species. Besides, infectious diseases are described by nonlinear incidence. The dynamical behavior of the solution of the proposed model in terms of equilibrium, uniqueness, boundedness is discussed. Finally, the stability analysis of all possible equilibrium points of the proposed system is studied and analyzed. The effect of the interpretation for the proportional harvest on the proposed system is also presented.