Actually, it is even more dramatic. Infection rate is essentially binary: either the disease spreads (which means the number of sick people goes up until pretty much everyone in the community who is not immune gets it - this is called epidemic) or the number of sick people decreases and the disease dies off. There is a tipping point depending on the percentage of people who is immune. For common flu you need to have 50-70% vaccinated to prevent epidemic (its basic reproduction number, R0 per wiki article, is between 2 and 3).

http://en.wikipedia.org/wiki/Mathematical_modelling_of_infec...