Stochastic analysis of control parameter influences in an eco-epidemiological model with predator infection

This study investigates the impact of control parameters on the dynamics of a stochastic eco-epidemiological model, in which a predator population is affected by an infectious disease. The model consists of three stochastic differential equations representing susceptible prey, susceptible predators, and infected predators, integrating predation processes, competition, and disease transmission under environmental fluctuations. Fundamental analytical properties, including existence, boundedness, and persistence, are examined to ensure biological relevance and validity. Both local and global stability of equilibrium points are studied to understand deterministic and noise-driven transitions in system behavior. Numerical simulations reveal a diverse range of dynamical outcomes, including oscillations, bi-stability, noise-induced transitions, and chaotic-like fluctuations, driven by parameters such as predation efficiency, conversion rates, transmission intensity, and mortality factors. Results show that higher predator attack rates and conversion efficiencies may destabilize population dynamics, while increased disease transmission or infected predator mortality can enhance system stability. Sensitivity analysis reveals critical threshold conditions governing disease persistence, extinction, or coexistence of all populations. The impacts of various control strategies such as culling, treatment, and transmission reduction are evaluated, demonstrating their potential to suppress disease, stabilize predator populations, and maintain ecological balance. Overall, this study provides important insights into stochastic eco-epidemiological interactions and offers practical guidance for ecosystem management and disease control in predator–prey systems.