It works for any number of infected monks.
If there is only one infected he will kill himself on day 2 when he realises no-one else has a red spot. If he sees a red spot he does not kill himself.
If two monks are infected they will each see one red spot on day two, and think they are safe. On day 2 they will realise there must be two red spots (and they can only see one) and so top themselves (as no monks commited suicide on day 2).
The logic continues for any number. The will all comit suicide on the day they realise they can see one less spot than the number of days elapsed from the initial statement!

Cheers
Nigel