Like many Black and rural Americans, Denese Rankin, a 55-year-old retired bookkeeper and receptionist in Castleberry, Ala., did not want the Covid-19 vaccine.

Ms. Rankin worried about side effects — she had seen stories on social media about people developing Bell’s palsy, for example, after they were vaccinated. She thought the vaccines had come about too quickly to be safe. And she worried that the vaccinations might turn out to be another example in the government’s long history of medical experimentation on Black people.

In Florida, less than one-quarter of delivered coronavirus vaccines have been used, even as older people sat in lawn chairs all night waiting for their shots. In Puerto Rico, last week’s vaccine shipments did not arrive until the workers who would have administered them had left for the Christmas holiday. In California, doctors are worried about whether there will be enough hospital staff members to both administer vaccines and tend to the swelling number of Covid-19 patients.

CAPE TOWN — A few months from now, a factory in South Africa is expected to begin churning out a million doses of Covid-19 vaccine each day in the African country hardest-hit by the pandemic.

But those vials will probably be shipped to a distribution center in Europe and then rushed to Western countries that have pre-ordered them by the hundreds of millions. None have been set aside for South Africa.

The country, which will help manufacture the vaccine and whose citizens have enrolled in clinical trials, does not expect to see the first trickle of doses until around the middle of next year. By then, the United States, Britain and Canada may already have vaccinated more than 100 million people.