Abstract In this paper, we propose a general ratio-dependent prey-predator model with disease in predator subject to the strong Allee effect in prey. We obtain the complete dynamics of both models: (a) full model with Allee effect; (b) full model without Allee effect. Model (a) may have more than one interior equilibrium point, but model (b) has only one interior equilibrium point. Numerical results reveal that the coexistence of all the populations at the endemic state is possible for both the models. But for the model with Allee effect, the coexistence can be destroyed by an increased supply of alternative food for the predators. It can also be proved that for the full model with Allee effect, the disease can be suppressed under certain parametric conditions. Also by comparing models (a) and (b), we conclude that Allee effect can create or destroy the interior attractor. Finally, we have studied the disease free-submodel (prey and susceptible predator model) with and without Allee effect. The comparative study between these two submodels leads to the following conclusions: 1) In the presence of Allee effect, the number of interior equilibrium points can change from zero to two whereas the submodel without Allee effect has unique interior equilibrium point; 2) Both with and without Allee effect, initial conditions play an important role on the survival and extinction of prey as well as its corresponding predator; 3) In the presence of Allee effect, bi-stability occurs with stable or periodic coexistence of prey and susceptible predator and the extinction of prey and susceptible predator; 4) Allee effect can generate or destroy the interior equilibrium points.

中文翻译：

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Allee 效应对生态流行病学系统的影响

摘要 在本文中，我们提出了一种受捕食者强 Allee 效应影响的捕食者疾病的一般比例依赖的猎物-捕食者模型。我们获得了两个模型的完整动态：（a）具有 Allee 效应的完整模型；(b) 没有 Allee 效应的完整模型。模型（a）可能有多个内部平衡点，但模型（b）只有一个内部平衡点。数值结果表明，两种模型都有可能在流行状态下所有种群共存。但是对于具有 Allee 效应的模型，增加捕食者的替代食物供应可能会破坏共存。也可以证明，对于具有 Allee 效应的完整模型，在一定的参数条件下可以抑制疾病。同样通过比较模型（a）和（b），我们得出结论，Allee 效应可以创建或破坏内部吸引子。最后，我们研究了有和没有 Allee 效应的无病子模型（猎物和易感捕食者模型）。通过对这两个子模型的对比研究，得出以下结论： 1）存在 Allee 效应时，内部平衡点的数量可以从 0 变为 2，而没有 Allee 效应的子模型具有唯一的内部平衡点；2）无论有无阿利效应，初始条件对猎物及其相应捕食者的生存和灭绝都起着重要作用；3）在Allee效应存在下，猎物与易感捕食者稳定或周期性共存，猎物与易感捕食者灭绝，出现双稳态；