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In the absence of effective vaccine/antiviral strategies for reducing the burden of the coronavirus disease 2019 (COVID-19) pandemic in India, the main focus has been on basic non-pharmaceutical interventions (NPIs), such as nationwide lockdown (travel restrictions and the closure of schools, shopping malls, and worshipping and other gathering places), quarantining of exposed individuals, and isolation of infected individuals. In the present study, we propose a compartmental epidemic model incorporating quarantine and isolation compartments to (i) describe the current transmission patterns of COVID-19 in India, (ii) assess the impact of currently implemented NPIs, and (iii) predict the future course of the pandemic with various scenarios of NPIs in India. For R0 < 1, the system has a globally asymptotically stable disease free equilibrium, while for R0 > 1, the system has one unstable disease free equilibrium and a unique locally stable endemic equilibrium. By using the method of least squares and the best fit curve, we estimate the model parameters to calibrate the model with daily new confirmed cases and cumulative confirmed cases in India for the period from May 1, 2020 to June 25, 2020. Our result shows that the implementation of an almost perfect isolation in India and 33.33% increment in contact-tracing on June 26, 2020 may reduce the number of cumulative confirmed cases of COVID-19 in India by around 53.8% at the end of July 2020. Nationwide lockdown with high efficiency can diminish COVID-19 cases drastically, but combined NPIs may accomplish the strongest and most rapid impact on the spreading of COVID-19 in India. [ABSTRACT FROM AUTHOR]