It has been reported that COVID-19 patients had an increased neutrophil count and a decreased lymphocyte count in the severe phase and neutrophils may contribute to organ damage and mortality. In this paper, we present the bifurcation analysis of a dynamical model for the initial innate system response to pulmonary infection. The model describes the interaction between a pathogen and neutrophilis (also known as polymorphonuclear leukocytes). It is shown that the system undergoes a sequence of bifurcations including subcritical and supercritical Bogdanov–Takens bifurcations, Hopf bifurcation, and degenerate Hopf bifurcation as the parameters vary, and the model exhibits rich dynamics such as the existence of multiple coexistent periodic oscillations, homoclinic orbits, bistability and tristability, etc. Numerical simulations are presented to explain the theoretical results.

中文翻译：

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对初始肺部感染的先天免疫反应动力学模型的分岔分析

据报道，COVID-19 患者在重症期中性粒细胞计数增加，淋巴细胞计数减少，中性粒细胞可能导致器官损伤和死亡。在本文中，我们提出了对肺部感染的初始先天系统反应的动力学模型的分岔分析。该模型描述了病原体和中性粒细胞（也称为多形核白细胞）之间的相互作用。结果表明，随着参数的变化，系统经历了一系列的分岔，包括亚临界和超临界 Bogdanov-Takens 分岔、Hopf 分岔和简并 Hopf 分岔，模型表现出丰富的动力学特征，例如存在多个共存周期振荡、同宿轨道、双稳态和三稳态等。