Abstract
In this work, we investigate a mathematical model that depicts the dynamics of COVID-19, with an emphasis on the effectiveness of detection and diagnosis procedures as well as the impact of quarantine measures. Using data from May 1 to May 31, 2020, the current study compares three states: Tamil Nadu, Maharashtra, and Andhra Pradesh. A compartmental model has been developed in order to forecast the pandemic's trajectory and devise an effective control strategy. The study then examines the dynamic progression of the pandemic by including important epidemiological factors into a modified SEIR (Susceptible, Exposed, Infectious, Recovered) model. Our method is a thorough analysis of the equilibria of the deterministic mathematical model in question. We use rigorous techniques to find these equilibrium points and then conduct a comprehensive investigation of their stability. Furthermore, an optimum control problem is applied to reduce the illness fatality, taking into account both pharmaceutical and nonpharmaceutical intervention options as control functions. With the aid of Pontryagin's maximal principle, an objective functional has been created and solved in order to minimize the number of infected people and lower the cost of the controls. In terms of the basic reproduction number, the stability of biologically plausible equilibrium points and the qualitative behavior of the model are examined. We found that the disease transmission rate has an effect on reducing the spread of diseases after conducting sensitivity analysis with regard to the basic reproduction number. According to the findings, Tamil Nadu had the lowest reproduction number ([Formula: see text]) and Maharashtra the highest ([Formula: see text]), indicating regional differences in the efficacy of public health initiatives. Furthermore, it has been demonstrated that appropriate control strategies, such as vaccination (Μ), can successfully reduce infection levels and improve recovery rates. In our study compared to the other two states, Tamil Nadu is notable for its quick recovery and decrease in infection rates. In our findings are more dependable and applicable when mathematical analysis and numerical simulations are combined, which also helps to provide a more thorough understanding of the dynamics at work in the COVID-19 environment. This research also offers suggestions for how government agencies, health groups, and legislators can lessen the effects of COVID-19 and distribute resources as efficiently as possible . Finally, we conclude by discussing the optimal control strategy to contain the epidemic.