具有Beddington-DeAnglis发生率和饱和治疗率的SEIRS模型的研究
Study on SEIRS Model with Beddington-DeAnglis Incidence and Saturation Treatment Rate
摘要: 本文建立了具有Beddington-DeAnglis发生率和饱和治疗率的SEIRS模型，通过构造Lyapunov函数和Dulac函数，并利用Hurwitz判据来分析无病平衡点和地方性平衡点的稳定性。可以得到，当R0c<1时，无病平衡点是局部渐进稳定和全局渐进稳定的，根据平面定性理论以及Dulac函数，地方性平衡点是局部渐进稳定和全局渐进稳定的。
Abstract: This article establishes a SEIRS model with Beddington-DeAnglis incidence and saturation treat-ment rates. By constructing Lyapunov and Dulac functions, and using the Hurwitz criterion, the sta-bility of disease-free and endemic equilibrium points is analyzed. It can be obtained that when R0c<1, the disease-free equilibrium point is locally asymptotically stable and globally asymp-totically stable. According to plane qualitative theory and Dulac function, the local equilibrium point is locally asymptotically stable and globally asymptotically stable.
文章引用：杨睿文. 具有Beddington-DeAnglis发生率和饱和治疗率的SEIRS模型的研究[J]. 应用数学进展, 2023, 12(12): 5010-5017. https://doi.org/10.12677/AAM.2023.1212492

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