I already know the problems presented: The infected area is usually in some third-world shithole with little-to-no infrastructure, much of the equipment is big, heavy, and expensive, etc... but much of it can be made portable with sufficient engineering, and a good chunk of it doesn't even have to be brought along, or can be minimized (e.g. the ventilation/filtering systems that the centers here have to keep quarantine)
If Bill Gates wants to do something with all that cash, maybe he can hire a few engineers an medical types to build a deployable care center that can be flown out to $3rdWorldShitHole in less than 24 hours, and be put to use immediately when an epidemic strikes.
Let's see... the existing system uses minimal investment (mainly in transportable isolation units) to transport a small number of exposed or critically ill people to locations where an existing army of people and mountain of equipment already exists and has supporting infrastructure in place. Your proposed system has us spending tens of millions of dollars (if not more) to transport a (currently non existent) army of people and (currently non existent) mountain of equipment to a place without supporting infrastructure and requiring massive (and currently non existent) logistics pipeline to maintain to support a small number of exposed or critically ill people.
Other than the clueless paranoia displayed in this sub-thread, why on earth would you propose such a back-asswards system?
You, and the OP, are confusing two different problems. The first, moving the most critically ill people to treatment and isolating exposed individuals, is largely a solved problem. The second, quarantine and minimizing the spread of disease among the local population is a very different problem... and even so, it can be largely handled with existing systems. The problem with the Ebola outbreak in Africa was failure to recognize the problem followed up by a "too little, too late" response from the West, combined with cultural issues and behaviors which facilitated the spread of disease. You can't fix either by simply throwing money at them.