In this research work, we present a mathematical model for novel coronavirus -19 (NCOVID-19) which is consisted on three different compartments susceptible, infected and recovered classes abbreviated as under convex incident rate involving and emigration rate. We first derive the formulation of the model. Also, we give some qualitative aspects for the model including existence of equilibriums and its stability results by using various tools of nonlinear analysis. Then by mean of nonstandard finite difference scheme (NSFD), we simulate the results against the data of Wuhan city for the sixty days. By means of simulation, we show how protection, exposure, emigration, death and cure rates affect the susceptible, infected and recovered population with the passage of time involving emigration. On the basis of simulation, we observe the dynamical behavior due to emigration of susceptible and infected classes or one of these two.