Mathematical approaches to controlling COVID-19: optimal control and financial benefits

Abstract

The global population has suffered extensively as an effect of the coronavirus infection, with the loss of many lives, adverse financial consequences, and increased impoverishment. In this paper, we propose an example of the non-linear mathematical modeling of the COVID-19 phenomenon. Using the fixed point theorem, we established the solution's existence and unicity. We demonstrate how, under the framework, the basic reproduction number can be redefined. The different equilibria of the model are identified, and their stability analyses are carefully examined. According to our argument, it is illustrated that there is a single optimal control that can be used to reduce the expense of the illness load and applied processes. The determination of optimal strategies is examined with the aid of Pontryagin's maximum principle. To support the analytical results, we perform comprehensive digital simulations using the Runge-Kutta 4th-order. The data simulated suggest that the effects of the recommended controls significantly impact the incidence of the disease, in contrast to the absence of control cases. Further, we calculate the incremental cost-effectiveness ratio to assess the cost and benefits of each potential combination of the two control measures. The findings indicate that public attention, personal hygiene practices, and isolating oneself will all contribute to slowing the spread of COVID-19. Furthermore, those who are infected can readily decrease their virus to become virtually non-detectable with treatment consent.