The ongoing coronavirus disease 2019 (COVID-19) pandemic is of global concern and has recently emerged in the US. In this paper, we construct a stochastic variant of the SEIR model to estimate a quasi-worst-case scenario prediction of the COVID-19 outbreak in the US West and East Coast population regions by considering the different phases of response implemented by the US as well as transmission dynamics of COVID-19 in countries that were most affected. The model is then fitted to current data and implemented using Runge-Kutta methods. Our computation results predict that the number of new cases would peak around mid-April 2020 and begin to abate by July provided that appropriate COVID-19 measures are promptly implemented and followed, and that the number of cases of COVID-19 might be significantly mitigated by having greater numbers of functional testing kits available for screening. The model is also sensitive to assigned parameter values and reflects the importance of healthcare preparedness during pandemics.