(CNN) After overcoming a bout with Covid-19, President Donald Trump said he was immune to the virus.
Experts say it's possible to get reinfected. But it's rare.
"So 38 million cases worldwide. A couple of dozen cases of reinfection reported so far," Dr. Soumya Swaminathan, a chief scientist at the World Health Organization, told CNN earlier this week.
Dr. Anthony Fauci, the director of the National Institute of Allergy and Infectious Diseases said this week health officials are beginning to see "a number of cases" reported as reinfections.
"Well-documented cases," he said, '"of people who were infected, after a relatively brief period of time measured anywhere from weeks to several months come back, get exposed and get infected again."
"So you really have to be careful that you're not completely 'immune,'" Fauci said.
In August, doctors reported a 25-year-old Nevada man appeared to be the first documented case of Covid-19 reinfection in the US. The man was first diagnosed with Covid-19 in April and after getting better -- and testing negative twice -- he tested positive for the virus a little more than a month later.
A separate team of researchers reported in August a 33-year-old man living in Hong Kong had Covid-19 twice this year: in March and August.
And earlier this year, an 89-year-old Dutch woman -- who also had a rare white blood cell cancer -- died after catching Covid-19 twice, experts said. She became the first and only known person to die after getting reinfected.
While it is possible to get infected again with the virus, there are still questions scientists are working to answer, including who is more likely to get reinfected and how long antibodies protect people from another infection.
Several new reports published recently show Covid-19 immunity can last for months.
Researchers from the University of Arizona found antibodies that protect against infection can last for at least five to seven months after a Covid-19 infection.
With the pandemic under a year old, it will likely take time before scientists can get a clear picture of immunity.
"That said, we know that people who were infected with the first SARS coronavirus, which is the most similar virus to SARS-CoV-2, are still seeing immunity 17 years after infection. If SARS-CoV-2 is anything like the first one, we expect antibodies to last at least two years, and it would be unlikely for anything much shorter," Deepta Bhattacharya, an immunobiologist at the University of Arizona College of Medicine, previously told CNN.
Other studies, one out of Massachusetts and the other out of Canada, supported the idea of long-lasting immunity.
That suggests "that if a vaccine is properly designed, it has the potential to induce a durable antibody response that can help protect the vaccinated person against the virus that causes COVID-19," Jennifer Gommerman, professor of immunology at the University of Toronto, said in a statement.
What's unclear is how second infections could impact any Covid-19 vaccine. The Nevada man experienced more critical symptoms during his second infection while the Hong Kong man did not have any obvious symptoms during his reinfection.
"The implications of reinfections could be relevant for vaccine development and application," according to the authors of a recent study in The Lancet.
There's something else researchers have begun to notice: People who have a tougher bout with the illness tend to have a stronger immune response.
"There is a difference between people who are asymptomatic, who had a very mild infection, there seem to be a slightly larger number of those who don't have detectable antibodies," Swaminathan, with WHO, says. "But almost everyone who has moderate to severe disease has antibodies."
Bhattacharya, from Arizona, echoed that finding.
"The people sampled from the ICU had higher levels of antibodies than people who had milder disease," he said, adding that he doesn't yet know what that will mean for long-term immunity.