Tara C. Smith in Quanta:
This varies by pathogen and is known as a microbe’s “infectious dose.” Usually it takes quite a few, but some microbes require an incredibly small number of organisms to start an infection. Take norovirus for example, the stomach bug notorious for spreading whenever people are in close contact and touch the same surfaces, such as on cruise ships. Its infectious dose can be as small as 18 individual viruses, making it incredibly easy to transmit. It is also very hardy even outside the body, so an infected person who’s oozing the virus may leave a large amount of it behind — enough to easily infect others, even several days later.
More here.