Global Analysis and Optimal Control Model of COVID-19

Abstract

COVID-19 remains the concern of the globe as governments struggle to defeat the pandemic. Understanding the dynamics of the epidemic is as important as detecting and treatment of infected individuals. Mathematical models play a crucial role in exploring the dynamics of the outbreak by deducing strategies paramount for curtailing the disease. The research extensively studies the SEQIAHR compartmental model of COVID-19 to provide insight into the dynamics of the disease by underlying tailored strategies designed to minimize the pandemic. We first studied the noncontrol model’s dynamic behaviour by calculating the reproduction number and examining the two nonnegative equilibria’ existence. The model utilizes the Castillo-Chavez method and Lyapunov function to investigate the global stability of the disease at the disease-free and endemic equilibrium. Sensitivity analysis was carried on to determine the impact of some parameters on $R_0$ . We further examined the COVID model to determine the type of bifurcation that it exhibits. To help contain the spread of the disease, we formulated a new SEQIAHR compartmental optimal control model with time-dependent controls: personal protection and vaccination of the susceptible individuals. We solved it by utilizing Pontryagin’s maximum principle after studying the dynamical behaviour of the noncontrol model. We solved the model numerically by considering different simulation controls’ pairing and examined their effectiveness.