He is also influential among a large group of Americans, as is any president.
He called for Obama to resign after a single case of ebola[1] in the US. Clearly he agrees with me that the president has an effect in fighting infectious disease.
1.https://www.axios.com/trump-obama-resign-787b042d-0361-48f1-...
Yet this has nothing to do with the fact that whether to go into lock-down or not and what kind of measures to take are taken by State actors, not the federal government. We can see that right now with the debate on school opening: the Federal government has no power.
I am not sure where you think that States play almost no role, the USA is one of the countries where the local States have the most power compared to any other Western democracy out there.
Nevermind that in the states the main actors responsible in times of health crises are the local State authorities not the Federal ones. Your 'under his care' is terribly loaded.