Integrating behavioral dynamics and allee effect in eco-epidemiological model: A comprehensive approach to disease impact.

Predator-prey models in ecology typically focus on direct predation without considering other interactions, such as hunting behaviors on qualitative impact and numerous diseases, which has led researchers to explore the intersection of ecology and mathematics, resulting in the development of mathematical models. This paper introduces a novel eco-epidemiological model that integrates the dynamics of infectious diseases within predator-prey interactions, factoring in direct predation, the roles of infected prey, and the influence of behavioral dynamics. By utilizing evolutionary game theory, this study explores the effects of cooperation and non-cooperation strategies on disease spread and population stability. Numerical simulations reveal that disease transmission rates and the Allee effect significantly impact population stability. Low transmission rates favor stability, while higher rates provoke periodic oscillations that can destabilize the population. The associated controlling cost reduces the risk of infection in prey populations, affecting the predator population. Moreover, the Allee effect exacerbates prey vulnerability, increasing the risk of predator extinction unless disease transmission is curtailed. Findings underscore the importance of considering behavioral dynamics and epidemic factors in conserving species and managing infectious diseases, offering valuable insights into the complex interactions that govern ecosystem health and stability.