Optimal control of the coronavirus pandemic with both pharmaceutical and non-pharmaceutical interventions.

Coronaviruses are types of viruses that are widely spread in humans, birds, and other mammals, leading to hepatic, respiratory, neurologic, and enteric diseases. The disease is presently a pandemic with great medical, economical, and political impacts, and it is mostly spread through physical contact. To extinct the virus, keeping physical distance and taking vaccine are key. In this study, a dynamical transmission compartment model for coronavirus (COVID-19) is designed and rigorously analyzed using Routh-Hurwitz condition for the stability analysis. A global dynamics of mathematical formulation was investigated with the help of a constructed Lyapunov function. We further examined parameter sensitivities (local and global) to identify terms with greater impact or influence on the dynamics of the disease. Our approach is data driven to test the efficacy of the proposed model. The formulation was incorporated with available confirmed cases from January 22, 2020, to December 20, 2021, and parameterized using real-time series data that were collected on a daily basis for the first 705 days for fourteen countries, out of which the model was simulated using four selected countries: USA, Italy, South Africa, and Nigeria. A least square technique was adopted for the estimation of parameters. The simulated solutions of the model were analyzed using MAPLE-18 with Runge-Kutta-Felberg method (RKF45 solver). The model entrenched parameters analysis revealed that there are both disease-free and endemic equilibrium points. The solutions depicted that the free equilibrium point for COVID-19 is asymptotic locally stable, when the epidemiological reproduction number condition