Analysis of an Eco-Epidemic Predator-Prey Model with Nonlinear Prey Refuges and Predator Harvesting - Islam, Md Sarijul; Sarwardi, Sahabuddin (Journal of Applied Nonlinear Dynamics, 2026)
In this article, we have studied a mathematical model for one prey and two predator with disease in predator. Here the total population is divided into three classes, namely, prey, sound predator and infected predator. We consider two different nonlinear prey refuge coefficients against the sound predator and infected predator respectively. Also both the sound predator and infected predator are harvested in the proposed dynamical system. The possibility of existence of bionomic equilibrium has been considered. The optimal harvesting policy is studied by using Pontryagin’s maximal principle. The optimal harvesting efforts corresponding to the optimal solution have been derived. The positive invariance and boundedness of the solutions of the system are shown. The existence of feasible equilibria and their stability analyses are performed. It is found that the zero equilibrium point is unstable, while other equilibrium points are asymptotically stable under certain conditions. We have investigated that harvesting parameters bear an important role to control the spread of infection. Moreover, the increment of predation rates of sound and infected predator change the stability of prey only equilibrium point to infected predator-free equilibrium point and sound predator-free equilibrium point respectively. Suitable graphical representation with proper discussions are performed in the Numerical simulation section to support the proposed dynamical system.