How anti-vaccination is like a nuclear bomb
How quickly the disease spreads, if it spreads at all, depends on the number of people vaccinated. Again, we find very simple math: if, on average, an infected person encounters less than one unvaccinated person while he/she is contagious, the disease will die out. If, however, an infected person encounters more than one unvaccinated person while he/she is contagious, the disease will multiply: each new infected person infects new ones.
A fairly decent analogy (even if I have a terminology nit: induced reactions are not decays)