具有混沌、稳定性和分岔的离散时间 COVID-19 流行病模型

Discrete-time COVID-19 epidemic model with chaos, stability and bifurcation.

作者信息

Al-Basyouni K S, Khan A Q

机构信息

Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia.

Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan.

出版信息

Results Phys. 2022 Dec;43:106038. doi: 10.1016/j.rinp.2022.106038. Epub 2022 Oct 13.

DOI:10.1016/j.rinp.2022.106038

PMID:36268519

原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC9556946/

Abstract

In this paper, we explore local behavior at fixed points, chaos and bifurcations of a discrete COVID-19 epidemic model in the interior of . It is explored that for all involved parametric values, COVID-19 model has boundary fixed point and also it has an interior fixed point under certain parametric condition(s). We have investigated local behavior at boundary and interior fixed points of COVID-19 model by linear stability theory. It is also explored the existence of possible bifurcations at respective fixed points, and proved that at boundary fixed point there exists no flip bifurcation but at interior fixed point it undergoes both flip and hopf bifurcations, and we have explored said bifurcations by explicit criterion. Moreover, chaos in COVID-19 model is also investigated by feedback control strategy. Finally, theoretical results are verified numerically.

摘要

在本文中，我们探讨了一个离散的COVID-19疫情模型在内部的不动点处的局部行为、混沌和分岔情况。研究发现，对于所有涉及的参数值，COVID-19模型都有边界不动点，并且在某些参数条件下还有一个内部不动点。我们通过线性稳定性理论研究了COVID-19模型在边界和内部不动点处的局部行为。还探讨了在各个不动点处可能存在的分岔情况，并证明在边界不动点处不存在翻转分岔，但在内部不动点处它会经历翻转分岔和霍普夫分岔，并且我们通过明确的准则研究了上述分岔情况。此外，还通过反馈控制策略研究了COVID-19模型中的混沌现象。最后，对理论结果进行了数值验证。