The global pandemic of coronavirus disease 2019 (COVID-19) has challenged healthcare systems worldwide. Lockdown, social distancing, and screening are thought to be the best means of stopping the virus from spreading and thus of preventing hospital capacity from being overloaded. However, it has also been suggested that effective outpatient treatment can control pandemics. We adapted a mathematical model of the beneficial effect of lockdown on viral transmission and used it to determine which characteristics of outpatient treatment would stop an epidemic. The data on confirmed cases, recovered cases, and deaths were collected from Sante Publique France. After defining components of the epidemic flow, we used a Morris global sensitivity analysis with a 10-level grid and 1000 trajectories to determine which of the treatment parameters had the largest effect. Treatment effectiveness was defined as a reduction in the patients' contagiousness. Early treatment initiation was associated with better disease control-as long as the treatment was highly effective. However, initiation of a treatment with a moderate effectiveness rate (5%) after the peak of the epidemic was still better than poor distancing (i.e. when compliance with social distancing rules was below 60%). Even though most of today's COVID-19 research is focused on inpatient treatment and vaccines, our results emphasize the potentially beneficial impact of even a moderately effective outpatient treatment on the current pandemic.