Understanding Ebola Virus (EBOV) virulence evolution is not only timely but also raises specific questions because it causes on the most virulent human infections and it is capable of transmission after the death of its host. Using a compartmental epidemiological model that captures all of the virus' transmission routes, we infer the evolutionary dynamics of case fatality ratio (CFR) on the scale of an outbreak and on the long term. Our major finding is that the virus's specific life cycle imposes selection for high levels of virulence and that this pattern is robust to parameter variations in biological ranges. In addition to shedding a new light on the adaptive reasons of EBOV's high virulence, these results generate testable predictions and contribute to informing public health policies. In particular, burial management stands out as the most appropriate intervention since it decreases the R0 of the epidemics, while imposing selection for less virulent strains.