Qadeer Khan Abdul, Tasneem Muhammad, Younis Bakri Adam Ibrahim, Ibrahim Tarek Fawzi
Department of Mathematics University of Azad Jammu and Kashmir Muzaffarabad Pakistan.
Department of Mathematics, Faculty of Sciences and Arts in Zahran Alganoob King Khalid University Abha Saudi Arabia.
Math Methods Appl Sci. 2022 Oct 23. doi: 10.1002/mma.8806.
In this paper, we explore local dynamics with topological classifications, bifurcation analysis, and chaos control in a discrete-time COVID-19 epidemic model in the interior of . It is explored that for all involved parametric values, discrete-time COVID-19 epidemic model has boundary equilibrium solution and also it has an interior equilibrium solution under definite parametric condition. We have explored the local dynamics with topological classifications about boundary and interior equilibrium solutions of the discrete-time COVID-19 epidemic model by linear stability theory. Further, for the discrete-time COVID-19 epidemic model, existence of periodic points and convergence rate are also investigated. It is also studied the existence of possible bifurcations about boundary and interior equilibrium solutions and proved that there exists no flip bifurcation about boundary equilibrium solution. Moreover, it is proved that about interior equilibrium solution, there exist Hopf and flip bifurcations, and we have studied these bifurcations by utilizing explicit criterion. Moreover, by feedback control strategy, chaos in the discrete COVID-19 epidemic model is also explored. Finally, theoretical results are verified numerically.
在本文中，我们在离散时间的COVID - 19疫情模型内部，通过拓扑分类、分岔分析和混沌控制来探索局部动力学。研究发现，对于所有涉及的参数值，离散时间的COVID - 19疫情模型具有边界平衡解，并且在一定参数条件下还具有内部平衡解。我们通过线性稳定性理论，对离散时间的COVID - 19疫情模型的边界和内部平衡解进行了拓扑分类的局部动力学研究。此外，对于离散时间的COVID - 19疫情模型，还研究了周期点的存在性和收敛速度。同时，研究了边界和内部平衡解可能的分岔情况，并证明了边界平衡解不存在翻转分岔。而且，证明了关于内部平衡解，存在霍普夫分岔和翻转分岔，我们利用显式准则对这些分岔进行了研究。此外，通过反馈控制策略，还探索了离散COVID - 19疫情模型中的混沌现象。最后，对理论结果进行了数值验证。
