Stability and Hopf Bifurcation Analysis of an Epidemic Model with Time Delay | Zendy

Yue Zhang | Zendy; Xue Li | Zendy; Xianghua Zhang | Zendy; Guisheng Yin | Zendy

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Stability and Hopf Bifurcation Analysis of an Epidemic Model with Time Delay

Author(s) -

Yue Zhang,

Xue Li,

Xianghua Zhang,

Guisheng Yin

Publication year - 2021

Publication title -

computational and mathematical methods in medicine

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.462

H-Index - 48

eISSN - 1748-6718

pISSN - 1748-670X

DOI - 10.1155/2021/1895764

Subject(s) - hopf bifurcation , center manifold , mathematics , saddle node bifurcation , stability (learning theory) , transcritical bifurcation , epidemic model , biological applications of bifurcation theory , bifurcation , bifurcation theory , pitchfork bifurcation , period doubling bifurcation , bifurcation diagram , manifold (fluid mechanics) , mathematical analysis , fixed point , control theory (sociology) , computer science , nonlinear system , physics , population , artificial intelligence , medicine , control (management) , quantum mechanics , machine learning , mechanical engineering , environmental health , engineering

Epidemic models are normally used to describe the spread of infectious diseases. In this paper, we will discuss an epidemic model with time delay. Firstly, the existence of the positive fixed point is proven; and then, the stability and Hopf bifurcation are investigated by analyzing the distribution of the roots of the associated characteristic equations. Thirdly, the theory of normal form and manifold is used to drive an explicit algorithm for determining the direction of Hopf bifurcation and the stability of the bifurcation periodic solutions. Finally, some simulation results are carried out to validate our theoretic analysis.

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