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.
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
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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