Bifurcation analysis of a fractional-order SIQR model with double time delays

被引:4
|
作者
Liu, Shouzong [1 ]
Yu, Ling [1 ]
Huang, Mingzhan [1 ]
机构
[1] Xinyang Normal Univ, Coll Math & Stat, Xinyang 464000, Peoples R China
基金
中国国家自然科学基金;
关键词
Fractional order; delay; stability; Hopf bifurcation; STABILITY; DYNAMICS; CHAOS;
D O I
10.1142/S1793524520500679
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
In this paper, a fractional-order delayed SIQR model with nonlinear incidence rate is investigated. Two time delays are incorporated in the model to describe the incubation period and the time caused by the healing cycle. By analyzing the associated characteristic equations, the stability of the endemic equilibrium and the existence of Hopf bifurcation are obtained in three different cases. Besides, the critical values of time delays at which a Hopf bifurcation occurs are obtained, and the influence of the fractional order on the dynamics behavior of the system is also investigated. Numerically, it has been shown that when the endemic equilibrium is locally stable, the convergence rate of the system becomes slower with the increase of the fractional order. Besides, our studies also imply that the decline of the fractional order may convert a oscillatory system into a stable one. Furthermore, we find in all these three cases, the bifurcation values are very sensitive to the change of the fractional order, and they decrease with the increase of the order, which means the Hopf bifurcation gradually occurs in advance.
引用
收藏
页数:31
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