The basic reproduction number R_0 is the number of infections caused
by one infectious case when the population has no immunity to
infection, when infections are growing exponentially. In models of
unstructured populations, R_0 predicts many important epidemic
statistics like the total number of cases over time and the
vaccination coverage needed to achieve herd immunity.
However, in a structured population, where some epidemiological
parameters vary with some population characteristic like age, R_0
provides no information on these important epidemic statistics. I show
by example, using two mathematical models of populations that have 2
epidemiological groups, that if one group is small but has very high
transmission within that group, R_0 is driven by this group and can be
very large, while the total number of people infected by an epidemic
or the critical vaccination coverage can be tiny.