Exploring bifurcation and chaos control in a discrete-time Lotka–Volterra model framework for COVID-19 modeling

This study investigates the dynamics of a discrete-time epidemic model of COVID-19 formulated on the basis of the Lotka–Volterra framework. The positivity and boundedness of solutions are established to ensure biological feasibility. A stability analysis identifies equilibrium points and reveals critical bifurcations that influence disease transmission. Numerical simulations confirm the occurrence of flip and Neimark–Sacker bifurcations, leading to complex periodic and quasi-periodic oscillations. The analysis of Lyapunov exponents further highlights the transition from stable dynamics to chaotic behavior as key parameters vary. In addition, effective chaos-control strategies are explored to stabilize the system, thereby mitigating unpredictable epidemic oscillations and promoting reliable long-term disease dynamics. These findings underscore the importance of controlling epidemiological factors to prevent irregular epidemic waves and to maintain long-term stability in disease transmission.