Dynamics of an Eco-Epidemiological Model with Harvesting and Constant Prey Refuge

This study developed an eco-epidemiological model incorporating constant prey refuge, predator disease transmission, and anthropogenic harvesting to explore the coupled dynamical behaviors of ecological populations under natural infection and human interference. All feasible equilibrium points of the proposed system were solved, and the local stability of the boundary equilibria and threshold conditions for transcritical bifurcations were systematically analyzed. The global asymptotic stability of the positive coexistence equilibrium was verified by constructing the appropriate Lyapunov functions. Furthermore, a parameter sensitivity analysis was performed to identify the dominant parameters governing population persistence and system stability. To balance ecological sustainability and economic benefits, an optimal harvesting control problem was investigated, and time-dependent optimal harvesting efforts were obtained by applying optimal control theory. Numerical simulations demonstrated that the optimal harvesting strategy can dynamically adjust the harvesting intensity to maximize long-term discounted economic profit while maintaining stable population coexistence. The theoretical and numerical results provide reliable theoretical guidance for the sustainable exploitation and ecological management of infected predator–prey ecosystems.