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Budwick There are two classes of vaccine: sterilising and non-sterilising. Sometimes there simply isn't a sterilising vaccine available, such as for influenza and COVID and many other viral diseases.
The memory response elicited by most human viral vaccines does not protect against reinfection, but rather against the development of disease. An individual may be exposed repeatedly to viruses and never be aware of it, because the memory response eliminates the virus before signs and symptoms develop. After vaccination with inactivated poliovirus vaccine, virus replication may take place in the intestine, but effectively blocks the development of poliomyelitis. On the other hand, the human papillomavirus vaccine is over 90% effective at blocking infection. Consequently the HPV vaccine induces sterilizing immunity.
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No vaccine is 100% effective at inducing immunity in a population. Consequently, the level of immunity is not equal to the number of people immunized. For example, when 80% of a population is immunized with measles vaccine, about 76% of the population is actually immune, well below the 93 to 95% required for herd immunity.
https://www.virology.ws/2021/03/11/how-vaccines-work/