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.

Allee 效应在社会物种的生存、入侵和进化中起着重要作用。结合成分 Allee 效应和传染病的种群动态特征尚不清楚。在本文中，我们提出了一种猎物和捕食者相互作用的生态流行病学模型，假设：（1）捕食者在狩猎猎物时具有合作社会行为；(2)捕食者经历有限交配产生的成分Allee效应；(3) 该病可在捕食者之间传播。我们提出的模型对于研究捕食者的合作行为、交配限制和疾病的联合影响是新颖的。我们首先根据捕食者是否具有配偶限制或合作以及一参数和二参数分叉来研究四种情况下无病模型的动力学。分析结果表明，引入配对限制会产生强烈的 Allee 效应和 Hopf 分叉。发现在合理区域内增加配对限制可以稳定系统，但过度的限制强度会导致共存平衡消失。我们还研究了存在疾病时捕食者-猎物模型的动力学。理论结果表明，该模型始终具有局部稳定的捕食者-灭绝平衡。然后，我们探讨了配偶限制如何影响合作捕食者之间疾病的传播。结果表明，当合作系数较大时，交配限制可以使捕食者免于疾病驱动的灭绝，并使疾病从系统中消失，而如果合作系数小，则会驱使捕食者死亡。我们的结果表明，所提出的包含组件 Allee 效应的模型表现出丰富而复杂的动态行为。有趣的发现为复杂社区中人群的保护和疾病控制提供了更多视角。