  The generation interval is the time between the infection time of an infected
person and the infection time of his or her infector. Probability density
functions for generation intervals have been an important input for epidemic
models and epidemic data analysis. In this paper, we specify a general
stochastic SIR epidemic model and prove that the mean generation interval
decreases when susceptible persons are at risk of infectious contact from
multiple sources. The intuition behind this is that when a susceptible person
has multiple potential infectors, there is a ``race'' to infect him or her in
which only the first infectious contact leads to infection. In an epidemic, the
mean generation interval contracts as the prevalence of infection increases. We
call this global competition among potential infectors. When there is rapid
transmission within clusters of contacts, generation interval contraction can
be caused by a high local prevalence of infection even when the global
prevalence is low. We call this local competition among potential infectors.
Using simulations, we illustrate both types of competition.
  Finally, we show that hazards of infectious contact can be used instead of
generation intervals to estimate the time course of the effective reproductive
number in an epidemic. This approach leads naturally to partial likelihoods for
epidemic data that are very similar to those that arise in survival analysis,
opening a promising avenue of methodological research in infectious disease
epidemiology.
