Delay Induced Hopf Bifurcation of an Epidemic Model with Graded Infection Rates for Internet Worms

Zhao Tao; Bi Dianjie

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Delay Induced Hopf Bifurcation of an Epidemic Model with Graded Infection Rates for Internet Worms

机译：具有网络蠕虫感染率分级的流行病模型的延迟诱导霍普夫分叉

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A delayed SEIQRS worm propagation model with different infection rates for the exposed computers and the infectious computers is investigated in this paper. The results are given in terms of the local stability and Hopf bifurcation. Sufficient conditions for the local stability and the existence of Hopf bifurcation are obtained by using eigenvalue method and choosing the delay as the bifurcation parameter. In particular, the direction and the stability of the Hopf bifurcation are investigated by means of the normal form theory and center manifold theorem. Finally, a numerical example is also presented to support the obtained theoretical results.

机译：研究了暴露计算机和感染计算机具有不同感染率的SEIQRS延迟蠕虫传播模型。结果是根据局部稳定性和Hopf分叉给出的。通过特征值方法，选择时延作为分岔参数，得到了局部稳定的充分条件和Hopf分岔的存在。特别地，利用范式理论和中心流形定理研究了霍普夫分支的方向和稳定性。最后，还给出了一个数值例子来支持所获得的理论结果。

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《Mathematical Problems in Engineering》 |2017年第12期|9563862.1-9563862.10|共10页
作者
Zhao Tao; Bi Dianjie;
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Anhui Univ Finance & Econ, Sch Management Sci & Engn, Bengbu 233030, Peoples R China;

Anhui Univ Finance & Econ, Sch Management Sci & Engn, Bengbu 233030, Peoples R China;

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1. Hopf bifurcation analysis for an epidemic model over the Internet with two delays [J] . Tao Zhao, Dianjie Bi Advances in Difference Equations . 2018,第1期

机译：具有两个延迟的Internet上的流行模型的Hopf分叉分析
2. Hopf bifurcation of a delayed SIQR epidemic model with constant input and nonlinear incidence rate [J] . Juan Liu, Kai Wang Advances in Difference Equations . 2016,第1期

机译：具有固定输入和非线性发生率的时滞SIQR流行病模型的Hopf分支。
3. Stability and Hopf Bifurcation in a Delayed SIS Epidemic Model with Double Epidemic Hypothesis [J] . JiangangZhang, YandongChu, WenjuDu, International journal of nonlinear sciences and numerical simulation . 2018,第6期

机译：双疫情假设延迟SIS流行病模型中的稳定性和Hopf分叉
4. Analysis of an internet worm propagation model with graded infection rates [C] . Fangwei Wang, Yunkai Zhang, Honggang Guo, International Conference on Future Computer and Information Technology . 2014

机译：评分感染率互联网蠕虫传播模型分析
5. A numerical study of the effects of multiplicative noise on a supercritical delay induced Hopf bifurcation in a gene expression model. [D] . Mondragon Palomino, Octavio. 2007

机译：在基因表达模型中，乘性噪声对超临界延迟诱导的Hopf分叉的影响的数值研究。
6. Stability and Hopf Bifurcation in a Delayed HIV Infection Model with General Incidence Rate and Immune Impairment [O] . Fuxiang Li, Wanbiao Ma, Zhichao Jiang, 2015

机译：具有一般发生率和免疫功能障碍的延迟HIV感染模型中的稳定性和Hopf分叉
7. Delay Induced Hopf Bifurcation of an Epidemic Model with Graded Infection Rates for Internet Worms [O] . Tao Zhao, Dianjie Bi 2017

机译：延迟互联网蠕虫分级感染率的疫情诱导跳跃分岔
8. Prelude to Hopf Bifurcation in an Epidemic Model: Analysis of a Characteristic Equation Associated with a Nonlinear Volterra Integral Equation [R] . Diekmann, O., Montijn, R. 1981

机译：流行病模型中Hopf分岔的前奏：与非线性Volterra积分方程相关的特征方程的分析

Delay Induced Hopf Bifurcation of an Epidemic Model with Graded Infection Rates for Internet Worms

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