Mitigating infection in prey through cooperative behavior under fear-induced defense

Abstract

This study investigates an eco-epidemiological model that incorporates disease dynamics in prey populations while considering the impact of predator-induced fear on prey species. A pairwise evolutionary game theory model, which incorporates prey species behavior to mitigate infection, is also examined. Prey individuals can employ two behavioral tactics, cooperation, and defection, to reduce infection. The behavioral changes in prey are described using a game dynamic model based on replicator equations, where the gain depends on pairwise dyadic interactions. Without predator species, the prey population is assumed to grow logistically, with the disease affecting only the prey. The prey population is divided into susceptible prey and infected prey. Predators, which are not infected by the disease, feed on both susceptible and infected prey. The presence of predators induces fear in the prey, making them more vigilant and reducing their contact with infected individuals. This decreased contact lowers the chance of infection among susceptible prey. Infected prey, being more watchful, are unaffected by the fear of predators. The equilibrium points of the system and their stability are analyzed. As the level of fear increases, the system shifts from limit cycle oscillations to a steady state. While increasing fear levels do not eradicate the disease, they do reduce the amplitude of the infected prey population. The system's stability changes with varying infection rates, leading to predator extinction when the infection rate in prey is sufficiently high despite predators not being infected. This study reveals that fear and behavioral control strategies can contribute to eradicating the disease. Increasing levels of fear have a passive effect on reducing the infected population, while control behavior has an active impact, highlighting a critical insight that strengthens the model. These findings enhance the understanding of the system's dynamic behavior.