To affect the COVID-19 pandemic, lifesaving antiviral therapies must be identified. The number of clinical trials that can be performed is limited. We developed mathematical models to project multiple therapeutic approaches. Our models recapitulate off-treatment viral dynamics and predict a three-phase immune response. Simulated treatment with remdesivir, selinexor, neutralizing antibodies, or cellular immunotherapy demonstrates that rapid viral elimination is possible if in vivo potency is sufficiently high. Therapies dosed soon after peak viral load when symptoms develop may decrease shedding duration and immune response intensity but have little effect on viral area under the curve (AUC), which is driven by high early viral loads. Potent therapy dosed before viral peak during presymptomatic infection could lower AUC. Drug resistance may emerge with a moderately potent agent dosed before viral peak. Our results support early treatment for COVID-19 if shedding duration, not AUC, is most predictive of clinical severity.