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A non-linear SEIR mathematical model for coronavirus disease in India has been proposed, by incorporating the saturated incidence rate on the occurrence of new infections. In the model, the threshold quantity known as the reproduction number is evaluated which determines the stability of disease-free equilibrium and the endemic equilibrium points. The disease-free equilibrium point becomes globally asymptotically stable when the corresponding reproduction number is less than unity, whereas, if it is greater than unity then the endemic equilibrium point comes into existence, which is locally asymptotically stable under certain restrictions on the parameters value in the model. The impact of various parameters on the threshold quantity is signified by the sensitivity analysis. Numerical results imply that by implementing and strictly following the prevention measures a rapid reduction in the reproduction number for COVID-19 can be observed, through which the coronavirus disease can be controlled. [ABSTRACT FROM AUTHOR]