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Circadian clocks regulate the immune system, rendering humans more susceptible to infections at certain times of the day. Circadian modulation of SARS-CoV-2 infection has not yet been clearly established, nonetheless the circadian control of other respiratory viruses such as influenza A makes apparent the need to study the interaction between circadian rhythms and COVID-19 disease progression. We incorporated circadian oscillations into a mechanistic model of SARS-CoV-2 dynamics and immune response fit to viral load data from COVID-19 patients. The model predicts that circadian variation of parameters associated with the innate immune response and viral death rate lead to faster clearance of the virus, whereas circadian variation of parameters representing the susceptible cell infection rate, the viral production rate, and the adaptive immune response lead to slower clearance of the virus. We then used a model of remdesivir to simulate antiviral therapy. Our model simulations predict that the effectiveness of the treatment depends on the time of day the drug is administered. This prediction is conditional on the plausible, but entirely hypothetical, circadian interactions added to the model. Based on our proof-of-concept modeling results, we advocate for experimental and clinical studies to assess the impact that dosing time of day may have on the efficacy and toxicity of current COVID-19 antiviral drugs.