Abstract
In this article, a non-linear mathematical model has been proposed by incorporating the influential non-medicinal prevention measures together with an optimal control strategy to minimize the intervention cost of COVID-19 outbreak in India. During the unavailability of prescribed vaccines or antivirals, the transmission of COVID-19 infection has triggered the human health catastrophe. In the model, the disease-free equilibrium point is globally asymptotically stable if R-0 < 1, whereas due to inefficacy of prevention measures the endemic equilibrium point becomes locally asymptotically stable for R-0 > 1. The sensitivity analysis has shown the impact of various parameters on the reproduction number. The numerical simulations indicate that if R-0 becomes greater than unity then the pandemic will be disastrous later. Adequate implementation of prevention measures, detection at its full intensity and timely hospitalization facilities can lead to the elimination of the COVID-19 pandemic from India.