But public health experts say the pileup of unclaimed appointments in Mississippi exposes something more worrisome: the large number of people who are reluctant to get inoculated. “It’s time to do the heavy lifting needed to overcome the hesitancy we’re encountering,” said Dr. Obie McNair, an internal medicine practitioner in Jackson, the state capital, whose office has a plentiful supply of vaccines but not enough takers. Though access remains a problem in rural Mississippi, experts say that the state — one of the first to open eligibility to all adults three weeks ago — may be a harbinger of what much of the country will confront in the coming weeks, as increasing supplies enable most Americans who want the vaccine to easily make appointments... When it comes to rates of vaccination, Mississippi still has a way to go, with just a quarter of all residents having received at least one dose compared to the nationwide average of 33 percent, according to state data. Other southern states, among them Tennessee, Arkansas, Alabama and Georgia, have similarly low rates of vaccination.