The basic reproduction number, R0, is often defined as the average
number of infections generated by a newly infected individual in a fully susceptible
population. The interpretation, meaning, and derivation of R0 are
controversial. However, in the context of mean field models, R0 demarcates
the epidemic threshold below which the infected population approaches zero in the limit of
time. In this manner, R0 has been proposed as a method for
understanding the relative impact of public health interventions with respect to disease
eliminations from a theoretical perspective. The use of R0 is made more
complex by both the strong dependency of R0 on the model form and the stochastic
nature of transmission. A common assumption in models of HIV transmission that have closed
form expressions for R0 is that a single individual’s
behavior is constant over time. In this paper we derive expressions for both
R0 and probability of an epidemic in a
finite population under the assumption that people periodically change their sexual
behavior over time. We illustrate the use of generating functions as a general framework
to model the effects of potentially complex assumptions on the number of transmissions
generated by a newly infected person in a susceptible population. We find that the
relationship between the probability of an epidemic and R0 is not
straightforward, but, that as the rate of change in sexual behavior increases both
R0 and the probability of an epidemic also
decrease.