Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan.
Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia.
Math Biosci Eng. 2022 Jan;19(2):1944-1969. doi: 10.3934/mbe.2022092. Epub 2021 Dec 22.
The local dynamics with different topological classifications, bifurcation analysis and chaos control in a discrete-time COVID-19 epidemic model are investigated in the interior of $ \mathbb{R}_+^3 $. It is proved that discrete-time COVID-19 epidemic model has boundary equilibrium solution for all involved parameters, but it has an interior equilibrium solution under definite parametric condition. Then by linear stability theory, local dynamics with different topological classifications are investigated about boundary and interior equilibrium solutions of the discrete-time COVID-19 epidemic model. Further for the discrete-time COVID-19 epidemic model, existence of periodic points and convergence rate are also investigated. It is also investigated 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 exists hopf and flip bifurcations, and we have studied these bifurcations by utilizing explicit criterion. Next by feedback control strategy, chaos in the discrete COVID-19 epidemic model is also explored. Finally numerically verified theoretical results.
研究了不同拓扑分类、分岔分析和混沌控制在 $\mathbb{R}_+^3$ 内部离散时间 COVID-19 传染病模型中的局部动力学。证明了对于所有涉及的参数，离散时间 COVID-19 传染病模型具有边界平衡点，但在确定的参数条件下具有内部平衡点。然后，通过线性稳定性理论，研究了离散时间 COVID-19 传染病模型的边界和内部平衡点的不同拓扑分类的局部动力学。进一步，对于离散时间 COVID-19 传染病模型，还研究了周期点的存在性和收敛速度。还研究了边界和内部平衡点可能发生分岔的存在性，并证明了边界平衡点不存在翻转分岔。此外，证明了关于内部平衡点存在 Hopf 和翻转分岔，并且我们已经利用显式准则研究了这些分岔。接下来，通过反馈控制策略，还探索了离散 COVID-19 传染病模型中的混沌。最后通过数值验证了理论结果。
