Discrete-time COVID-19 epidemic model with bifurcation and control

A. Q. Khan; M. Tasneem; M. B. Almatrafi; A. Q. Khan; M. Tasneem; M. B. Almatrafi

doi:10.3934/mbe.2022092

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 2: 1944-1969. doi: 10.3934/mbe.2022092

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Discrete-time COVID-19 epidemic model with bifurcation and control

1.
Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan
2.
Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia

Received: 22 September 2021 Accepted: 15 December 2021 Published: 22 December 2021

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.
- COVID-19 epidemic model,
- numerical simulation,
- explicit criterion,
- bifurcation,
- feedback control strategy
Citation: A. Q. Khan, M. Tasneem, M. B. Almatrafi. Discrete-time COVID-19 epidemic model with bifurcation and control[J]. Mathematical Biosciences and Engineering, 2022, 19(2): 1944-1969. doi: 10.3934/mbe.2022092

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Abstract

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.

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