Complex dynamics in an eco-epidemiological model with the cost of anti-predator behaviors

• Published in: Nonlinear dynamics Vol. 107; no. 3; pp. 3127 - 3141
• Main Authors: Tan, Yiping, Cai, Yongli, Yao, Ruoxia, Hu, Maolin, Wang, Weiming
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.02.2022; Springer Nature B.V
• Subjects: Automotive Engineering; Behavior; Birth rate; Classical Mechanics; Control; Disease; Dynamical Systems; Endangered & extinct species; Engineering; Epidemiology; Equilibrium; Extinction; Fear; Hopf bifurcation; Mechanical Engineering; Ordinary differential equations; Original Paper; Population; Population density; Predators; Stability; Vibration; Eco-epidemiological model; Hopf bifurcation; Extinction; Fear factor
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-021-07133-4

In this paper, we investigate the complex dynamics of a predator–prey model with disease in the prey, which is characterized by the reduction of prey growth rate due to the anti-predator behavior. The value of this study lies in two aspects: Mathematically, it provides the existence and the stability of the equilibria and gives the existence of Hopf bifurcation. And epidemiologically, we find that the influence of the fear factor is complex: (i) The level of the population density decreases with the increasing of the fear factor; (ii) the cost of fear can destabilize the stability and benefit the emergency of the periodic behavior; and (iii) the high level of fear can induce the extinction of the predator. These results may enrich the dynamics of the eco-epidemiological systems.