具有饱和发生率和饱和治疗函数的离散SIS传染病模型的分岔分析
Bifurcation Analysis of Discrete SIS Model with Saturated Incidence and Saturated Treatment Function
DOI: 10.12677/DSC.2019.84026, PDF,    国家自然科学基金支持
作者: 陈雨青, 梁铭轩, 唐巧媚, 周效良：岭南师范学院数学与统计学院，广东 湛江
关键词: 离散SIS模型；稳定性；跨临界分岔；Flip分岔；Discrete SIS Model； Stability； Transcritical Bifurcation； Flip Bifurcation
摘要: 本文探讨了一类具有饱和发生率和饱和治疗函数的离散SIS模型，得到模型无病平衡点的类型及双曲性利用中心流形定理与分岔理论得到无病平衡点产生跨临界分岔和flip分岔的条件。最后给出分岔的生物学解释。
Abstract: In this paper, we discuss the discrete SIS models with saturation incidence and saturation treat-ment function. We obtain the type and hyperbolicity of the disease-free equilibrium point. We also use the central manifold theorem and the bifurcation theory to obtain the conditions of Tran-scritical bifurcation and flip bifurcation for disease-free equilibrium point. Finally, the biological explanation of bifurcation is given.
文章引用：陈雨青, 梁铭轩, 唐巧媚, 周效良. 具有饱和发生率和饱和治疗函数的离散SIS传染病模型的分岔分析[J]. 动力系统与控制, 2019, 8(4): 242-247. https://doi.org/10.12677/DSC.2019.84026

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