Stability and Bogdanov-Takens Bifurcation of an SIS Epidemic Model with Saturated Treatment Function

Xiao Yanju; Zhang Weipeng; Deng Guifeng; Liu Zhehua

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Stability and Bogdanov-Takens Bifurcation of an SIS Epidemic Model with Saturated Treatment Function

机译：具有饱和治疗功能的SIS流行病模型的稳定性和Bogdanov-Takens分叉

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This paper introduces the global dynamics of an SIS model with bilinear incidence rate and saturated treatment function. The treatment function is a continuous and differential function which shows the effect of delayed treatment when the rate of treatment is lower and the number of infected individuals is getting larger. Sufficient conditions for the existence and global asymptotic stability of the disease-free and endemic equilibria are given in this paper. The first Lyapunov coefficient is computed to determine various types of Hopf bifurcation, such as subcritical or supercritical. By some complex algebra, the Bogdanov-Takens normal form and the three types of bifurcation curves are derived. Finally, mathematical analysis and numerical simulations are given to support our theoretical results.

机译：本文介绍了具有双线性入射率和饱和处理函数的SIS模型的全局动力学。治疗功能是一种连续的微分功能，当治疗率较低且感染个体的数量越来越多时，它显示出延迟治疗的效果。给出了无病和地方病平衡的存在和全局渐近稳定性的充分条件。计算第一李雅普诺夫系数以确定各种类型的霍普夫分叉，例如亚临界或超临界。通过一些复杂的代数，可以得出Bogdanov-Takens范式和三种分叉曲线。最后，通过数学分析和数值模拟来支持我们的理论结果。

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来源
《Mathematical Problems in Engineering》 |2015年第1期|745732.1-745732.14|共14页
作者
Xiao Yanju; Zhang Weipeng; Deng Guifeng; Liu Zhehua;
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NE Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China.;

NE Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China.;

Shanghai Lixin Univ Commerce, Sch Math & Informat, Shanghai 201620, Peoples R China.;

NE Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China.;

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1. Stability and Bogdanov-Takens Bifurcation of an SIS Epidemic Model with Saturated Treatment Function [J] . YanjuXiao, WeipengZhang, GuifengDeng, Mathematical Problems in Engineering: Theory, Methods and Applications . 2015,第5期

机译：具有饱和治疗功能的SIS流行病模型的稳定性和Bogdanov-Takens分叉
2. Backward bifurcation and stability analysis of a network-based SIS epidemic model with saturated treatment function [J] . Huang Yi-Jie, Li Chun-Hsien Physica, A. Statistical mechanics and its applications . 2019,第期

机译：饱和治疗功能的基于网络SIS流行病模型的向后分岔和稳定性分析
3. Bifurcation analysis of an SIS epidemic model with saturated incidence rate and saturated treatment function [J] . Tingting Zhou, Weipeng Zhang, Qiuying Lu Applied mathematics and computation . 2014,第Null期

机译：具有饱和发病率和饱和治疗功能的SIS传染病模型的分叉分析
4. Stability and bifurcation of an epidemic model with saturated treatment function [C] . Jin Gao, Min Zhao 2010 International conference on bio-inspired systems and signal processing. . 2010

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5. Vehicle handling, stability, and bifurcation analysis for nonlinear vehicle models. [D] . Nguyen, Vincent. 2005

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6. Bifurcations of an epidemic model with non-monotonic incidence rate of saturated mass action [O] . Yugui Zhou, Dongmei Xiao, Yilong Li -1

机译：具有非单调饱和质量作用发生率的流行病模型的分支
7. Stability and Bogdanov-Takens Bifurcation of an SIS Epidemic Model with Saturated Treatment Function [O] . Yanju Xiao, Weipeng Zhang, Guifeng Deng, 2015

机译：饱和治疗功能的SIS流行病模型的稳定性和Bogdanov-Takens分叉

Stability and Bogdanov-Takens Bifurcation of an SIS Epidemic Model with Saturated Treatment Function

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