The novel coronavirus responsible for COVID-19 was first identified in Hubei Province, China in December, 2019. Within a matter of months the virus had spread and become a global pandemic. In addition to international air travel, local travel (e.g. by passenger car) contributes to the geographic spread of COVID-19. We modify the common susceptible-exposed-infectious-removed (SEIR) virus spread model and investigate the extent to which short-term travel associated with driving influences the spread of the virus. We consider the case study of the US state of Minnesota, and calibrated the proposed model with travel and viral spread data. Using our modified SEIR model that considers local short-term travel, we are able to better explain the virus spread than using the long-term travel SEIR model. Short-term travel associated with driving is predicted to be a significant contributor to the historical and future spread of COVID-19. The calibrated model also predicts the proportion of infections that were detected. We find that if driving trips remain at current levels, a substantial increase in COVID-19 cases may be observed in Minnesota, while decreasing intrastate travel could help contain the virus spread.