where β(t) is the transmission parameter at time t and D is the average duration of infection. Thus, R 0 can be interpreted as the average number of secondary cases arising from the introduction of a single infective into a wholly susceptible population at a random time of the year. They noted that the condition R 0 < 1 is not sufficient to prevent an outbreak, since chains of transmission can be established during high-infectious seasons if Dβ(t) > 1. However, R 0 < 1 is both necessary and sufficient for longterm disease extinction.