In this paper, we develop an extension of compartmental epidemiological models which is suitable for COVID-19. The model presented in this paper comprises seven compartments in the progression of the disease. This model, named as the SINTRUE (Susceptible, Infected and pre-symptomatic, Infected and Symptomatic but Not Tested, Tested Positive, Recorded Recovered, Unrecorded Recovered, and Expired) model. The proposed model incorporates transmission due to asymptomatic carriers and captures the spread of the disease due to the movement of people to/from different administrative boundaries within a country. In addition, the model allows estimating the number of undocumented infections in the population and the number of unrecorded recoveries. The associated parameters in the model can help architect the public health policy and operational management of the pandemic. The results show that the testing rate of the asymptomatic patients is a crucial parameter to fight against the pandemic. The model is also shown to have a better predictive capability than the other epidemiological models.