Modeling the dynamics of COVID-19 pandemic with implementation of intervention strategies

The ongoing COVID-19 epidemic spread rapidly throughout India, with 34,587,822 confirmed cases and 468,980 deaths as of November 30, 2021. Major behavioral, clinical, and state interventions have implemented to mitigate the outbreak and prevent the persistence of the COVID-19 in human-to-human transmission in India and worldwide. Hence, the mathematical study of the disease transmission becomes essential to illuminate the real nature of the transmission behavior and control of the diseases. We proposed a compartmental model that stratify into nine stages of infection. The incidence data of the SRAS-CoV-2 outbreak in India was analyzed for the best fit to the epidemic curve and we estimated the parameters from the best fitted curve. Based on the estimated model parameters, we performed a short-term prediction of our model. We performed sensitivity analysis with respect to $$ and obtained that the disease transmission rate has an impact in reducing the spread of diseases. Furthermore, considering the non-pharmaceutical and pharmaceutical intervention policies as control functions, an optimal control problem is implemented to reduce the disease fatality. To mitigate the infected individuals and to minimize the cost of the controls, an objective functional has been formulated and solved with the aid of Pontryagin's maximum principle. This study suggest that the implementation of optimal control strategy at the start of a pandemic tends to decrease the intensity of epidemic peaks, spreading the maximal impact of an epidemic over an extended time period. Our numerical simulations exhibit that the combination of two controls is more effective when compared with the combination of single control as well as no control.