Dynamical analysis of a discrete‐time COVID‐19 epidemic model

• Published in: Mathematical methods in the applied sciences Vol. 46; no. 4; pp. 4789 - 4814
• Main Authors: Qadeer Khan, Abdul, Tasneem, Muhammad, Younis, Bakri Adam Ibrahim, Ibrahim, Tarek Fawzi
• Format: Journal Article
• Language: English
• Published: Germany Wiley Subscription Services, Inc 15.03.2023; John Wiley and Sons Inc
• Subjects: bifurcation; Bifurcations; Classification; COVID-19; COVID‐19 epidemic model; Epidemics; Equilibrium; explicit criterion; Feedback control; feedback control strategy; numerical simulation; Topology; feedback control strategy; bifurcation; COVID‐19 epidemic model; explicit criterion; numerical simulation
• ISSN: 0170-4214; 1099-1476
• 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 ℝ+4$$ {\mathbb{R}}_{+}^4 $$. 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.