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The antiviral remdesivir has been approved by regulatory bodies such as the European Medicines Agency (EMA) and the US Food and Drug administration (FDA) for the treatment of COVID-19. However, its efficacy is debated and toxicity concerns might limit the therapeutic range of this drug. Computational models that aid in balancing efficacy and toxicity would be of great help. Parametrizing models is difficult because the prodrug remdesivir is metabolized to its active form (RDV-TP) upon cell entry, which complicates dose–activity relationships. Here, we employ a computational model that allows drug efficacy predictions based on the binding affinity of RDV-TP for its target polymerase in SARS-CoV-2. We identify an optimal infusion rate to maximize remdesivir efficacy. We also assess drug efficacy in suppressing both wild-type and resistant strains, and thereby describe a drug regimen that may select for resistance. Our results differ from predictions using prodrug dose–response curves (pseudo-EC50s). We expect that reaching 90% inhibition (EC90) is insufficient to suppress SARS-CoV-2 in the lungs. While standard dosing mildly inhibits viral polymerase and therefore likely reduces morbidity, we also expect selection for resistant mutants for most realistic parameter ranges. To increase efficacy and safeguard against resistance, we recommend more clinical trials with dosing regimens that substantially increase the levels of RDV-TP and/or pair remdesivir with companion antivirals.