I think a lot of people misunderstand what "burn out" actually means when it comes to virulent incurable diseases. The previous Ebola outbreaks have all been in rural African communities and have typically been snuffed out in weeks or months. But one main difference this time is that it has hit densely packed cities in West Africa, making the current outbreak an international threat. "Burn out" is not some biological process than makes the virus die out or something similar. "Burn out" means that the host population have developed enough individuals with effective immunity to curtail and eventually stop the spreading of the virus... Or... The host population has been so decimated that they've effectively become several separate populations and thus the spread of the virus is stopped through social distancing; simple lack of contact between groups of survivors.
Or to quote Dr. Bruce Aylward, WHO assistant director-general in charge of emergencies: "If control measures don't work, at some point, Ebola will have infected everyone who hasn't already been killed or recovered from the virus and there won't be enough people to maintain the virus' spread."
"Burn out" is by far the worst case scenario.
In the previous outbreaks in Africa the affected areas were effectively quarantined by the militant authoritative governments typical of those countries. After the virus had killed off most of the people in the affected villages and "burned itself out", the military moved in and cleaned up the mess. Typically using fire.
If Ebola becomes a global pandemic and we cannot stop it through vaccines it means that we would have to develop a natural group-immunity to to stop it. That means that about one in ten needs to get the virus and survive it. Now, if we use a very conservative estimate of the mortality of this virus that means that one in five of the world's population will be killed.
This is how the Ebola virus usually "burns out"...