We propose a mathematical model to investigate the transmission dynamics of COVID-19. The model incorporates both human-to-human and environment-to-human transmission pathways, and employs different transmission rates to represent the epidemiological characteristics at different time periods. Using this model and publicly reported data, we perform a case study for Hamilton County, the fourth-most populous county in the state of Tennessee and a region that could represent the typical situation of COVID-19 in the United States (US). Our data fitting and simulation results show that the environment may play an important role in the transmission and spread of the coronavirus. In addition, we numerically simulate a range of epidemic scenarios and make near-term forecasts on the development and trend of COVID-19 in Hamilton County.