Mathematical model of COVID-19 dynamics in the presence of multiple controls

The coronavirus disease 19 (COVID-19), caused by the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-COV-2), is an infectious disease constituting the most significant challenge to human and socio-economic development across the globe. Many studies have been conducted to gain more knowledge on the dynamic spread of SARS-COV-2 in the community of people. In this study, a new mathematical model made up of a system of non-linear ODEs is designed and meticulously analyzed to understand the dynamics of transmission of COVID-19. Specific necessary properties exhibited by the COVID-19 model are examined through the theory of non-negativity and boundedness of solutions. The threshold parameter measuring the invasion potential of COVID-19 in the population is worked out by employing the Next Generation Matrix approach. The model is shown to have two endemic equilibria whenever basic reproduction number \(\mathcal {R}_{0}<1\) ${\mathcal{R}}_0<1$ . The analysis of the endemic equilibrium stability is explored using a suitably constructed Lyapunov function. It is shown that the COVID-19 model is globally asymptotically stable whenever the associated basic reproduction number is beyond unity. The Latin Hypercube Sampling or Partial Rank Correlation Coefficient is utilized to examine how parameter changes affect the COVID-19 spread in the population. Furthermore, the study considers six optimal control interventions to flatten the curve of the coronavirus pandemic in society. Numerical experiments of the COVID-19 model are executed in MatLab to corroborate the qualitative analysis of the model.