In clinical trials, remdesivir decreased recovery time in hospitalized patients with SARS- CoV-2 and prevented hospitalization when given early during infection, despite not reducing nasal viral loads. In rhesus macaques, early remdesivir prevented pneumonia and lowered lung viral loads, but viral loads increased in nasal passages after five days. We developed mathematical models to explain these results. Our model raises the following hypotheses: 1) in contrast to nasal passages, viral load monotonically decreases in lungs during therapy because of infection-dependent generation of refractory cells, 2) slight reduction in lung viral loads with an imperfect agent may result in a substantial decrease in lung damage, and 3) increases in nasal viral load may occur because of a blunting of peak viral load that decreases the intensity of the innate immune response. We demonstrate that a higher potency drug could lower viral loads in nasal passages and lungs.