Perhaps you can't, but who cares? If people (and therefore groups of them as corporations) were left free to innovate and produce, there wouldn't be any practical problem regarding antibiotic resistance that you would likely have become aware of in the first place.
More fundamentally, capitalism needs more than just an economic defense (plenty of people and organizations do that today, and while their arguments are essentially true, they are not going to win that way). Capitalism is the only moral social system because it is by definition the only one that is compatible with individual rights. Individual rights are required because only reason allows mankind to maintain the conditions required for his survival. Any other system or "tweak" necessarily requires the initiation or threat of non-retalliatory force upon innocent men, which necessarily stops their minds in a manner proportional to the degree and scope of the threat.
The next step is pretty simple - what is the good? The altruistic idea of the good is not logically sound; if the good is defined as helping others, how is the good defined for the recipients of that help? To tack on another rule to solve the conundrum isn't sensible - to morally bifurcate humanity a priori (in this case, without looking at the specific actions of a particular person that arise from free will) should give you pause. Rand's answer is that every human being exists for their own sake, and that the good is what is in their own long-term rational self-interest. This is a precondition for proper and healthy human relationships; to the extent that people pursue this, they improve their lot and lives.
So to reiterate: from a scientific perspective, this is not a practical problem that doctors would face under true captialism, and morally speaking (which, in Rand's view, is exactly equivalent to the practical), there is nothing that can exist that is better than capitalism.