Resurgence in focus: Covid-19 dynamics and optimal control frameworks

The resurgence of Covid-19, accompanied by various variants of the virus, highlights the fact that Covid-19 is still present within the population. The study proposed a Covid-19 dynamical model for analyzing the effect of vaccination and the continuous use of non-medical interventions for addressing Covid-19 transmission dynamics. The Lyaponov function and Jacobian matrix techniques were used to analyze the stability of the model's equilibria. The model was transformed into a problem of optimal control with time-dependent variables, aimed at managing efforts to prevent the spread of Covid-19. Numerical assessments were deployed to assess the effect of vaccination and the continuous use of non-medical intervention strategies to mitigate the spread of Covid-19. The global sensitivity analysis of the model was used to detect the key parameters influencing the behavior of the model. In addition, numerical results showed a significant decrease in the basic reproduction rate $\left({ℛ}_0\right)$ when implementing $\sigma$ and $\xi$ , either separately or together. The optimal control results suggested that the control measures should be consistently enforced without any relaxation. 2010 Mathematics Subject Classification: 92D30, 93C95, 49 N90, 34H05, 37 N25.