In this paper, we consider an SI epidemic model incorporating additive Allee effect and time delay. The primary purpose of this paper is to study the dynamics of the above system. Firstly, for the model without time delay, we demonstrate the existence and stability of equilibria for three different cases, i.e. with weak Allee effect, with strong Allee effect, and in the critical case. We also investigate the existence and uniqueness of Hopf bifurcation and limit cycle. Secondly, for the model with time delay, the stability of equilibria and the existence of Hopf bifurcation are discussed. All the above show that both additive Allee effect and time delay have vital effects on the prevalence of the disease.

中文翻译：

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具有加性 Allee 效应和时间延迟的 SI 流行病模型的稳定性和分岔

在本文中，我们考虑了一个结合了加性 Allee 效应和时间延迟的 SI 流行病模型。本文的主要目的是研究上述系统的动力学。首先，对于没有时滞的模型，我们证明了在弱阿利效应、强阿利效应和临界情况下三种不同情况下平衡的存在性和稳定性。我们还研究了 Hopf 分岔和极限环的存在性和唯一性。其次，针对时滞模型，讨论了平衡的稳定性和Hopf分岔的存在性。综上所述，加性 Allee 效应和时间延迟对疾病的流行都有至关重要的影响。