Complex Dynamics of Ecoepidemiological Model of Fear-Induced Infected Prey and Predator

Ecoepidemiology is a discipline within biomathematics that investigates and analyzes the dynamics of infectious disease transmission, emphasizing on the interactions among species and tackling both ecological and epidemiological issues. For many years, a multitude of studies has concentrated on exploring the effects of disease in predator–prey dynamics. Recent field experiments on prey–predator interactions demonstrate that the subtle impact of predator species over prey may be more significant, potentially overshadowing the more evident, direct effects of predators in influencing the dynamics of these interactions. The intricate interplay between direct and indirect effects has been highlighted, especially concerning the fear response to predators. This suggests that the intensity of fear serves as a stabilizing element within the dynamics of the system. This study seeks to investigate the ecological issues related to the fear response in susceptible prey, considering both scenarios of predation and nonpredation, utilizing the Holling Type II functional response framework. The mathematical criteria for the presence of equilibrium points of the model have been established, and the local asymptotic stability at each equilibrium point has been analyzed. Additionally, we identified criteria that guarantee the system's stability on a global scale obtained Hopf bifurcation. Furthermore, it has been shown that the system may exhibit instability at the interior equilibrium point in either scenario if the fear factor surpasses the threshold value. Bifurcation analyses with respect to the conversion coefficient θ, predation rate β, and infection transmission rate λ revealed that the system undergoes bifurcation as these parameters increase.