The ongoing Ebola outbreak poses an alarming risk to the countries of West Africa and beyond. To assess the effectiveness of containment strategies, we developed a stochastic model of Ebola transmission between and within the general community, hospitals, and funerals, calibrated to incidence data from Liberia. We find that a combined approach of case isolation, contact-tracing with quarantine, and sanitary funeral practices must be implemented with utmost urgency in order to reverse the growth of the outbreak. As of 19 September, under status quo, our model predicts that the epidemic will continue to spread, generating a predicted 224 (134 to 358) daily cases by 1 December, 280 (184 to 441) by 15 December, and 348 (249 to 545) by 30 December.