ANALYSIS AND OPTIMAL CONTROL OF A VACCINATED PANDEMIC COVID-19 MODEL

In this article, we propose a modified SVIRS model that describes the evolution of the Covid-19 on a human population during a vaccination strategy. After describing our proposed model, we study the local and the global stability analysis of the model using Routh-Hurwitz criteria and by constructing the Lyapunov functions. In order to formulate an optimal control problem, we study the sensitivity analysis of the model parameters to determine the model robustness to parameter values, that is, to help us know the parameters that have a high impact on the reproduction number \(\mathscr {R}_{0}\) ${\mathcal{R}}_0$ and to propose some appropriate control. The existence of the optimal control is investigated, and a characterization of the optimal control is given using the Pontryagin’s maximum principle. By this, we propose three control strategies that help the public health officials to implement programs to achieve collective immunity and thus come closer to reduce the spread of the SARS-CoV-2 virus. These strategies are as follows: awareness and prevention, administrative measures and awareness campaigns about the importance of vaccination and also the prevention measures, and finally, strengthening internal measures by controlling the proportion of immigrants coming to the country. In the end, some numerical simulations are performed to illustrate the theoretical results.