Already, there have already been several dozen documented reinfections around the world, though current numbers are almost certainly an undercount. If subsequent infections are indeed mild or asymptomatic, many of them will go undetected. It can also be difficult to establish two separate infections in the same person.
But so far, the available research suggests just a tiny subset of the more than 30 million people in the United States — and 132 million globally — who’ve had a confirmed Covid-19 case have become infected again. Studies indicate that the vast majority of people mount a robust and long-lasting immune response after being infected for the first time with SARS-CoV-2, the virus that causes Covid-19. A study that followed health care workers in U.K. for six months, for example, found that those who had an initial Covid-19 infection carried protective antibodies for the length of the study period; the few who tested positive again generally had no symptoms (it’s unclear, though, if they could still transmit the virus). A study out of Denmark also found reinfections were rare, though they were more common in people 65 and up.
UPDATE April 10: An April 9 Lancet study of UK health workers found good immunity after having had Covid:
A previous history of SARS-CoV-2 infection was associated with an 84% lower risk of infection, with median protective effect observed 7 months following primary infection. This time period is the minimum probable effect because seroconversions were not included. This study shows that previous infection with SARS-CoV-2 induces effective immunity to future infections in most individuals.
Even CDC now says, “Confirmed and suspected cases of reinfection have been reported, but remain rare.”