If I had to pick someone, I would probably go with the guy who's already done this exact job less than two years ago and has experience with both global health and government service: https://en.wikipedia.org/wiki/R._Timothy_Ziemer
To expand on this, those problems take a lot of money to deal with, more than his foundation has, so in a lot of cases, the foundation effectively acts as force multiplier to get even more money on the problems.
https://www.vox.com/future-perfect/2020/2/11/21133298/bill-g...
Except Gates is rich precisely because of expertise and talent. Without a doubt he's one of the best managers alive. Doubly so when those organizations are operating in complex, technically challenging, domains like software or epidemology.
2. Bill Gates looks at problems logically, finds missing links, and solves those links. Whether that is refrigeration for vaccines, getting useful data for diseases, etc.
3. Bill Gates knows a ton about diseases, epidemics, etc. He's super curious and doesn't stop learning.
Who could be more qualified for the job?
Gates can certainly bring some unique skills to the table if he was invited, but it seems like we should have an actual doctor leading the charge.
Gates has done more to battle malaria and other diseases than anyone currently alive. His track record is second to none, in terms of building a huge strategy, managing complex systems, and executing a pragmatic plan. And I suspect he has many MDs in his close circle of advisers who he relies on. A leader doesn't need to be a specialist -- they need to be a leader, a generalist, and rely on a team for specialist knowledge.
Good leaders know how to draw on the expertise of others to organize a coordinated response... which the Gates Foundation has proved themselves very capable of doing, particularly with public health issues. The Gates Foundation employs lots of healthcare professionals.
I'd highly suggest looking up some of the talks Gates has done about his work with his foundation. He definitely has his shit together.
The person in charge of the epidemic will not be doing patient diagnosis and care. The person will be doing some aspects of: Logistics, managing a ton of people, political wrangling, PR/media relations, setting and achieving organizational goals.
Of course some disease and medical knowledge will be required, but not being an MD doesn't seem relevant.