Hasan S. Panigoro, Emli Rahmi, Abadi, Dian Savitri, Olumuyiwa James Peter
We investigate the eco-epidemic predator-prey model based on a SIS epidemic model for the prey and a Gause-type for the predator-prey interaction. The birth rate of the prey decreases as the impact of fear and the predation process is influenced by environmental protection for prey, the resistance of prey, and the level of competition between predators in hunting prey which can be determined by Beddington-DeAngelis functional response. The Caputo fractional-order derivative is employed to include the memory effect in the model. Three types of equilibrium points are obtained namely the susceptible-prey only, the predator-free, and the co-existence points. All local stability properties are identified using Matignon's condition and the generalized Routh-Hurwitz criterion. Some numerical simulations are organized to show the impact of the fear, the infection rate, and the memory effect on the dynamical behaviors of the model. We have demonstrated numerically the occurrence of Hopf bifurcations driven by those three biological parameters. © 2025 Author(s).
Biomathematics Research Group, Department of Mathematics, Universitas Negeri Gorontalo, Bone Bolango, 96554, Indonesia; Departement of Mathematics, Universitas Negeri Surabaya, Surabaya, 60231, Indonesia; Department of Mathematical and Computer Sciences, University of Medical Sciences, Ondo State, Ondo City, Nigeria
