If you see Flaviviridae for examples, then you will see that lethality rate of Flaviviridae family members is slowly decreasing in case of consequent infection. First transmission of "wild" strain from animal to human results with almost 100% deaths, but next transmissions (from one human to another and so on) produce strains with lower lethality rate. And after 10-20 consequent transmissions we're getting a strain with "only" 60% lethality rate, for example. It seems that virus adaptation process went similar in the wild nature. A sequence of transmissions from one monkey to another eventually created an adapted strain, which is harmless for them. The purpose of natural selection is a survival and continued reproduction in the future. For this reason, any "new" virus is always has a high virulence, but as a result of adaptation to unknown host species it becomes less dangerous for them. Because it is more beneficial way for the virus, which leads to greater amounts of copies of viral genome.
This may be true for Ebola since its been around for a few decades.
What if in the future there is that initial animal to human transmission but it happens in a highly populated area and spreads to other locations before it could be contained?
Should I be scared then?
If human-to-human transmission is a predominant way, then we'll see some kind of explosion process which will fade away a bit later due to development of collective immunity. Collective immunity will be maintained by:
1) people who have survived infection;
2) people who were infected with attenuated strains and came through a moderate or asymptomatic form of disease.
We even able to estimate possible death count and predict required amount of time to develop a suitable level of collective immunity, which will be able to stop the epidemic process and prevent it from returning. However, it's required to know an exact speed of virus adaptation, otherwise an inaccuracy will be too high. I'll try to make some calculations a bit later.
P.S. It's interesting that this process slowly goes even in endemic regions with animal-to-human as predominant way of transmission. According to research results, about 7% of local population have strong level of antibodies against Ebolaviridae in their blood, despite the fact that many of them have never suffered any symptoms of the disease. But 7% isn't enough, it's required to have 40-50% of people with antibodies to stop current breakout and 70+% to prevent it from happening again.