An eco-epidemiological model with social predation subject to a component Allee effect - Wang, Lisha; Qiu, Zhipeng; Feng, Tao; Kang, Yun (Applied Mathematical Modelling, 2022)
•An eco-epidemiological model with component Allee effect is formulated.•The predator is subject to cooperative hunting (social behavior) and mating limitation (low-density dependence).•Theoretical and simulation techniques are provided to explore the complex dynamics of the proposed model.•Results suggest that disease, cooperative hunting, and mating limitation can jointly regulate community development. Allee effect plays important roles in social species’ survival, invasion and evolution. The dynamical characteristics of populations incorporating component Allee effect and infectious disease remain unclear. In this paper, we propose an eco-epidemiological model of prey and predator interactions with assumptions that (1) The predator has cooperative social behavior in hunting prey; (2) The predator experiences component Allee effect generated from limited mating; (3) The disease can spread among predators. Our proposed model is novel to study the joint effects of cooperative behavior, mating limitation and disease in predator. We first investigate the dynamics of the disease-free model in four cases based on whether predators have mate limitation or cooperation as well as one- and two-parameter bifurcations. Analytical results show that the introduction of mate limitation generates a strong Allee effect and Hopf bifurcation. It is found that increasing mate limitation in a reasonable region stabilizes the system, but excessive limiting strength would lead the coexistence equilibrium to go extinction. We also study the dynamics of the predator-prey model in presence of disease. The theoretical result shows that the model always has a predator-extinction equilibrium which is always locally stable. We then explore how mate limitation affect the transmissibility of disease among cooperative predators. The results show that mating limitation can save the predator from disease-driven extinction and lead the disease to disappear from the system when the cooperation coefficient is large, while it drives the predators to die out if the cooperation coefficient is small. Our results indicate that the proposed model incorporating component Allee effect exhibits rich and complex dynamic behaviors. The interesting findings provide more perspectives on protection and disease control of populations in complex communities.