As Florida residents struggle to get appointments for covid-19 vaccines, some are worried the already limited supply may be going to people who don't even live in the state.

"Right now, my husband is over 65 and he called and actually went online and put his name in and after a couple of days got a response, 'we will let you know when it's coming,'" resident Leesa Harding told CBS News' Manuel Bojorquez.

Under Florida's vaccine plan healthcare workers, long-term care workers, and those 65 years and older who are at least part-time residents are eligible to get the vaccine.

Data from the Florida Department of Health revealed more than 1.1 million people have been vaccinated in the state. Out of those 1.1 million people, 39,000 reside outside of Florida.

It's a new trend being called "vaccine tourism," in which people from outside the state travel to Florida to get vaccinated.

The state is cracking down on the problem. Florida Governor Ron DeSantis said people who get the vaccine need to live in the state, despite originally downplaying reports of vaccine tourism.

"We just want to make sure it's for Floridians," DeSantis said Tuesday.

But there's evidence that's not always the case. The Buenos Aires newspaper Clarín reported that a dozen wealthy Argentines have traveled to Miami, Florida to get the shot.

In a recent Instagram video post, Argentinian television TV personality Yanina Latorre's elderly mother was seen getting vaccinated in Miami.

Other outlets reported a celebrity lawyer from Argentina got the vaccine while she was visiting Florida.

CBS News reached out to both women but did not hear back.

Miami Mayor Francis Suarez said the reports of people traveling to places like Miami to get a vaccine impacts city residents.

"It's sort of a slap in the face to this community that is desperately trying to get vaccinated," Suarez said.

Miami is just one of several cities where vaccine supplies are already limited. Suarez said more needs to be done to prevent people from other countries and states from traveling to Miami just to receive the vaccine.

"I think what we need to do is be able to verify people's addresses and make sure they're somebody from the community," Suarez said.

Martin Firestone is a travel insurance broker in Toronto, Canada, where the vaccine isn't expected until the Fall. He said for many of his clients who usually spend their winter months in Florida, the attitude toward receiving the vaccine is almost like winning the lottery.

"They had no intentions of going down this year, only when the vaccine became available or they heard from their friends who are down in those communities now and say, 'I've got my first shot already. Like why don't you come down?' That prompted them to now say, 'Okay, we're ready and we're heading down,'" he said.

Two India travel agencies are reportedly marketing vaccine travel packages. For thousands of dollars, the packages reportedly include roundtrip airfare to the United States and a shot upon arrival.

Neither responded to CBS News' request for comment. But on a social media post, one of the agencies claimed everything will be done with proper permission from the United States.

Harvard law professor Glenn Cohen, a medical tourism expert, said he wasn't shocked when he heard of vaccine tourism and he sees it growing.

"Yeah, I think the best thing we could do would be assisting other countries to meet their rollout and to supply them with vaccines to meet the needs of their population so that we don't create this market where the wealthy and able-bodied can travel," said Cohen. "Unfortunately, we've ended up in a place where every country has its purchase order and every country is doing its own distribution. And that setup is part of what has set the preconditions for this instance of vaccine tourism."

Vaccine tourism isn't just a U.S. phenomenon. A British travel agency is offering a vaccine tourism package for the equivalent of more than $30,000 that includes air travel to Dubai, lodging and both doses of the vaccine. In a statement, the travel agency told CBS News that remaining ethical is paramount to it. 

After CBS News' story aired, Florida's surgeon general signed a public health advisory prioritizing state residents for the vaccine. Under the advisory, those getting the vaccine in Florida will now need a proof-of-residency.