Dynamics of a prey-predator model involving a prey refuge and disease in the predator

In this paper, a mathematical model consisting of a prey-predator involving a prey refuge and infectious disease in the predator has been proposed and analyzed. Two types of functional responses are used to describe the feeding of the predator on the available prey. The existence, uniqueness and boundedness of the solution of the system are discussed. The dynamical behavior of the system has been investigated locally as well as globally using suitable Lyapunov function. The persistence conditions of the system are established. Local bifurcation near the equilibrium points has been investigated. The Hopf bifurcation conditions around the positive equilibrium point are derived. Finally, numerical simulations are carried out to specify the control parameters and confirm the obtained results Keywords: Prey-Predator, Disease, Refuge, Stability, Bifurcation

Order and Chaos in a Prey-Predator Model Incorporating Refuge, Disease, and Harvesting

In this paper, a mathematical model consisting of a prey-predator system incorporating infectious disease in the prey has been proposed and analyzed. It is assumed that the predator preys upon the nonrefugees prey only according to the modified Holling type-II functional response. There is a harvesting process from the predator. The existence and uniqueness of the solution in addition to their bounded are discussed. The stability analysis of the model around all possible equilibrium points is investigated. The persistence conditions of the system are established. Local bifurcation analysis in view of the Sotomayor theorem is carried out. Numerical simulation has been applied to investigate the global dynamics and specify the effect of varying the parameters. It is observed that the system has a chaotic dynamics