The researchers noted that levels of so-called neutralizing antibodies -- the immune system's first line of defense against infection -- correlate with protection against infection, but for this study they studied only antibody levels. "Published work about many vaccines, such as those against measles, mumps, and rubella, has shown a small decrease each year of 5 to 10% in the neutralizing antibody levels," they wrote. "We found that a significant and rapid decrease in humoral response to the BNT162b2 vaccine was observed within months after vaccination." The study also indicated that immunity for people who get vaccinated after natural Covid-19 infection lasts longer. It's especially strong for people who recovered from infection and then got vaccinated, also. "Overall, the accumulating evidence from our study and others shows that long-term humoral response and vaccine effectiveness in previously infected persons were superior to that in recipients of two doses of vaccine," they wrote. 5 things to know about coronavirus booster shots 5 things to know about coronavirus booster shots A second study from Qatar looked at actual infections among the highly vaccinated population of that small Gulf nation. People there mostly got Pfizer/BioNTech's vaccine, also known as BNT162b2. "BNT162b2-induced protection against infection builds rapidly after the first dose, peaks in the first month after the second dose, and then gradually wanes in subsequent months," Laith Abu-Raddad of Weill Cornell Medicine-Qatar and colleagues wrote. "The waning appears to accelerate after the fourth month, to reach a low level of approximately 20% in subsequent months," they added. Nonetheless, protection against hospitalization and death stayed at above 90%, they said. The waning protection may involve behavior, they noted. "Vaccinated persons presumably have a higher rate of social contact than unvaccinated persons and may also have lower adherence to safety measures," they wrote. "This behavior could reduce real-world effectiveness of the vaccine as compared with its biologic effectiveness, possibly explaining the waning of protection." But it's a signal that countries should prepare for fresh surges of Covid-19. "These findings suggest that a large proportion of the vaccinated population could lose its protection against infection in the coming months, perhaps increasing the potential for new epidemic waves," they wrote. Pfizer has been arguing that immunity from the first two doses of its vaccine begins to wear off after a few months. Last month, Pfizer won authorization from the US Food and Drug Administration for booster doses of its vaccine for some six months after people finish their first two doses. The US Centers for Disease Control and Prevention recommended that people older than 65, people with conditions making them more susceptible to getting seriously ill with breakthrough infections, and people at high risk of infection such as health care workers and prison inmates get boosters. Get CNN Health's weekly newsletter Sign up here to get The Results Are In with Dr. Sanjay Gupta every Tuesday from the CNN Health team. Israel has been boosting its entire population and now says it will require people to have had a third shot to be considered fully vaccinated. In the United States, more than 6 million people have received a third dose of vaccine and average the pace of booster shots is higher than the rate of people getting vaccinated for the first time, according to CDC data.