Well, there are obviously a couple of solutions.
If you're still all-in for the free market, then just mandate that all hospitals conduct training/drills/etc for particular epidemics (including ones like Ebola that end to result in fluids all over the place, and other epidemics that are perhaps a bit more tidy but airborne), Mandate that hospitals also stock a certain list of materials in some ratio to the number of beds they have. Then audit for compliance, and fine anybody who doesn't comply sufficiently that they aren't saving money via non-compliance. Since every hospital is affected, they all have to raise their prices, and nobody who complies gets priced out of the market.
However, I think that problems like Ebola point to the need for true universal coverage. For an epidemic like Ebola the chain is as strong as the weakest link. It doesn't help if half the population has the world's most comprehensive insurance policies if the other half of the population tries to hide their illness because they're uninsured. I can have the world's greatest insurance plan, but if some minimum wage worker who doesn't get sick days and has no insurance has a drop of swat land on my hamburger because they went to work instead of the hospital despite feeling lousy and being friends with a guy who just got back from West Africa, then I'm probably going to die and my insurer can't do anything about it.
Sure, eventually we'll probably have treatments, but right now we don't, and plasma donations from Ebola survivors only work when you have only a few sick people in the entire country to deal with.
The cheapest way to deal with Ebola is to have people who are sick go to the hospital, and they aren't going to do that if they're stuck with a $20k bill even if it turns out they don't have the disease, and they lose a day of work besides. For the want of $25k, we get an extra $1M worth of epidemic spreading.