Inoculation prompts the immune system to make antibodies to the virus, but as mutations change its shape, the virus can become more resistant to those antibodies. In the worst case, failing to stop the spread of the virus globally would allow more mutations that could make existing vaccines less effective, leaving even inoculated populations vulnerable.

“This idea that no one is safe until everyone is safe is not just an adage, it is really true,” said Andrea Taylor, the assistant director at Duke Global Health Innovation Center.

Even in the most optimistic scenarios, Ms. Taylor said, at the current pace of production, there will not be enough vaccines for true global coverage until 2023. The current rollout plans across Africa are expected to vaccinate only 20 to 35 percent of the population this year if everything goes right.

And while some wealthy countries have secured enough vaccine to cover their populations multiple times, South Africa has secured just 22.5 million doses for its 60 million people, and many nations lag farther behind.