Title: Enhancement and Numerical Assessment of Novel SARS-CoV-2 Virus Transmission Model. Abstract: Recent pandemic of the coronavirus started in December 2019, which has affected almost all groups of humankind. In this regard, accurate epidemic models are not only crucial for demonstrating the mitigation of the current pandemic but also helpful for forecasting their future dynamics. In this work, we propose a model for SARS-CoV-2 virus transmission to forecast the temporal dynamics of the novel coronavirus disease by considering the characteristics of the disease and the recent literature. Due to the nondeterministic and stochastic nature of the novel-coronavirus disease, we present the model with the aid of stochastic differential equations by considering two infectious phases: pre-symptomatic and symptomatic, because both are significant in the spread of SARS-CoV-2 virus transmission. We ensure that the model is well-posed and identify the necessary conditions for disease eradication by proving the existence, uniqueness, and extinction analysis. The efficacy of the model and the importance of the current study are demonstrated using the actual data. Finally, the model will be simulated using Euler-Maruyama and Milstein’s numerical schemes to support the theoretical findings and show the significance of the results obtained.