This paper is concerned with the numerical methods of susceptible exposed infectious recovered (SEIR) epidemic model of coronavirus disease 2019 (COVID-19). The model is explicated numerically with three numerical schemes, forward Euler, Runge-Kutta of order 4 (RK-4), and the proposed non-standard finite difference (NSFD) technique, respectively. In the epidemic model of infectious diseases, positivity is the main property of a consistent framework, since the negative value of a subpopulation is useless. The NSFD technique ends up being a more important and trustable numerical system than forward Euler and RK-4 techniques since it preserves positivity, stability, and convergence. On the contrary, forward Euler and RK-4 schemes do not hold these characteristics for some choices of step sizes. Numerical simulations confirmed the findings.