Within-host models have been used to successfully describe the dynamics of multiple viral infections, however, the dynamics of SARS-CoV-2 virus infection remain poorly understood. A greater understanding of how the virus interacts with the host can contribute to more realistic epidemiological models and help evaluate the effect of antiviral therapies and vaccines. Here, we present a within-host model to describe SARS-CoV-2 viral dynamics in the upper respiratory tract of individuals enrolled in the UK COVID-19 Human Challenge Study. Using this model, we investigate the viral dynamics and provide timescales of infection that independently verify key epidemiological parameters important in the management of an epidemic. In particular, we estimate that an infected individual is first capable of transmitting the virus after approximately 2.1 days, remains infectious for a further 8.3 days, but can continue to test positive using a PCR test for up to 27 days.