The Effects of Migration and Fear on the Stability of an Eco-Epidemiological Model with Hunting Cooperation among Predators

Abstract

Background: In the current study, we construct a 2D eco-epidemiological model in which prey populations on one hand, fear and competition among prey populations internalized, and evolution of spatial structure merit to predator (P) zone vs. protecting-shield (PRQ) in between. Individuals of the predator population can be either healthy or susceptible-infected (SI) individuals, and the disease spreads by contactbetween SIand Sindividuals. Hunting cooperation between predators and that disease propagates in the predator's population.
Methods: The proposed model incorporates the Sokol-Howell functional response to describe predator–prey interactions. The mathematical properties of the model were investigated by establishing its boundedness and uniqueness. All equilibrium points were determined, and the conditions required for their local and global stability were analyzed using appropriate mathematical techniques, including Lyapunov functions. Numerical simulations were also performed using a selected parameter set and varying initial conditions.
Results: The analysis identified all equilibrium points of the model and established the necessary conditions for their local stability. Under the corresponding conditions, all equilibrium points were shown to be locally stable. Furthermore, the global stability analysis based on suitable Lyapunov functions confirmed the stability properties of the system. Numerical simulations supported the analytical findings and demonstrated the effects of SI disease on the predator–prey dynamics .
Conclusion: The findings demonstrate that incorporating fear, internal rivalry, migration, and SI disease transmission provides a more comprehensive representation of predator–prey dynamics in protected and predator zones. The analytical and numerical results highlight the significant role of disease transmission in influencing population dynamics and support the validity of the proposed eco-epidemiological model.