The smallpox antiviral tecovirimat has recently been purchased by the U.S. Strategic National Stockpile. Given significant uncertainty regarding both the contagiousness of smallpox in a contemporary outbreak and the efficiency of a mass vaccination campaign, vaccine prophylaxis alone may be unable to control a smallpox outbreak following a bioterror attack. Here, we present the results of a compartmental epidemiological model that identifies conditions under which tecovirimat is required to curtail the epidemic by exploring how the interaction between contagiousness and prophylaxis coverage of the affected population affects the ability of the public health response to control a large-scale smallpox outbreak. Each parameter value in the model is based on published empirical data. We describe contagiousness parametrically using a novel method of distributing an assumed R-value over the disease course based on the relative rates of daily viral shedding from human and animal studies of cognate orthopoxvirus infections. Our results suggest that vaccination prophylaxis is sufficient to control the outbreak when caused either by a minimally contagious virus or when a very high percentage of the population receives prophylaxis. As vaccination coverage of the affected population decreases below 70%, vaccine prophylaxis alone is progressively less capable of controlling outbreaks, even those caused by a less contagious virus (R0 less than 4). In these scenarios, tecovirimat treatment is required to control the outbreak (total number of cases under an order of magnitude more than the number of initial infections). The first study to determine the relative importance of smallpox prophylaxis and treatment under a range of highly uncertain epidemiological parameters, this work provides public health decision-makers with an evidence-based guide for responding to a large-scale smallpox outbreak.