一类具有水平和垂直传播的连续SIR传染病模型的分岔性质
Bifurcation Property of a Class Continuous SIR Model with Vertical and Horizontal Transmission
DOI: 10.12677/AAM.2017.62025, PDF, HTML, XML, 下载: 1,903  浏览: 2,531  国家自然科学基金支持
作者: 李明山, 张渝曼, 黄晓玉, 李晓培：岭南师范学院数学与统计学院，广东 湛江；冷薇：广州大学经济与统计学院，广东 广州
关键词: SIR模型；垂直传染；中心流形；跨临界分岔；正规形；SIR Model； Vertical Transmission； Center Manifold； Transcritical Bifurcation； Normal Form
摘要: 研究一类具有水平和垂直传播的连续SIR传染病模型分岔性质。首先我们讨论了平衡点类型与参数的关系，从而确定平衡点的双曲性和非双曲性，然后通过中心流形研究了模型在无病平衡点的跨临界分岔和正规形，最后给出了模型跨临界分岔的生物学解释。
Abstract: Bifurcation property of a class SIR model with horizontal and vertical transmission is investigated. Firstly, the type of equilibrium points is determined by discussing its coefficient parameters. Then the transcritical bifurcation and normal form of the model is explored by center manifold theorem. Finally, biological mean of the model is also given.
文章引用：李明山, 张渝曼, 黄晓玉, 冷薇, 李晓培. 一类具有水平和垂直传播的连续SIR传染病模型的分岔性质[J]. 应用数学进展, 2017, 6(2): 218-224. https://doi.org/10.12677/AAM.2017.62025

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