In this paper, a vector-borne disease model with two delays and reinfection is established and considered. First of all, the existence of the equilibrium of the system, under different cases of two delays, is discussed through analyzing the corresponding characteristic equation of the linear system. Some conditions that the system undergoes Hopf bifurcation at the endemic equilibrium are obtained. Furthermore, by employing the normal form method and the center manifold theorem for delay differential equations, some explicit formulas used to describe the properties of bifurcating periodic solutions are derived. Finally, the numerical examples and simulations are presented to verify our theoretical conclusions. Meanwhile, the influences of the degree of partial protection for recovered people acquired by a primary infection on the endemic equilibrium and the critical values of the two delays are analyzed.

中文翻译：

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具有两次延迟和再感染的媒介传播疾病模型的稳定性和 Hopf 分叉分析

本文建立并考虑了具有两次延迟和再感染的病媒传播疾病模型。首先，通过分析线性系统的相应特征方程，讨论了系统在两种时滞不同情况下平衡点的存在性。得到了系统在地方性平衡时发生Hopf分叉的一些条件。此外，利用时滞微分方程的范式方法和中心流形定理，推导出了一些用于描述分岔周期解性质的显式公式。最后，给出了数值例子和模拟来验证我们的理论结论。同时，