Mathematical Analysis and Optimal Strategy for a COVID-19 Pandemic Model with Intervention

The COVID-19 pandemic has spread to every corner of the globe. The virus was first spotted in Wuhan, China, in December 2019 and has since spread worldwide. It has impacted every one of us in the hardest way possible. In this paper, a mathematical model based on differential equations is proposed. This model depicts the infection patterns of COVID-19 transmission, taking asymptomatic individuals and hospitalization into account. The basic reproduction number is computed using the next-generation matrix method. This is found to be a critical signal describing the dynamics of the COVID-19 transmission. The local stability of the steady states has been investigated. The model's global stability is demonstrated using the second method of Lyapunov and the LaSalle invariance principle. In addition, an optimal control problem is formulated to reduce fatality by considering pharmaceutical intervention options as control functions. COVID-19 transmission dynamics change when an intervention is introduced. In order to limit the number of infected individuals and reduce control costs, an appropriate objective functional has been developed and solved using Pontryagin's maximal principle. Furthermore, extensive simulations have been conducted for various initial conditions and parameter values in order to validate the theoretical aspects.