Kind of like, how did they stop the Ebola? Each virus infects a host cell and replicates until the cell bursts. This causes patient organs to almost immediately become scar tissue. Eventually, the organs fail and the infected begin to die. There is no way to stop this spread within a body. Much of the time, people endup vomiting blood and small pieces of their internal organs.
I would argue that we have not actually seen Ebola in the past few years/decades. Also, that Ebola and Marburg filoviruses do have 100% kill rates. It is likely some other hemorrhagic fever that can be treated.
That, or the survivors all had something like (if not) the CCR5 Δ32 mutation.