The basic reproduction number, R<
sub>
0<
/sub>
, 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 R<
sub>
0<
/sub>
are controversial. However, in the context of mean field models, R<
sub>
0<
/sub>
demarcates the epidemic threshold below which the infected population approaches zero in the limit of time. In this manner, R<
sub>
0<
/sub>
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 R<
sub>
0<
/sub>
is made more complex by both the strong dependency of R<
sub>
0<
/sub>
on the model form and the stochastic nature of transmission. A common assumption in models of HIV transmission that have closed form expressions for R<
sub>
0<
/sub>
is that a single individual?s behavior is constant over time. For this research, we derive expressions for both R<
sub>
0<
/sub>
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. In conclusion, we find that the relationship between the probability of an epidemic and R<
sub>
0<
/sub>
is not straightforward, but, that as the rate of change in sexual behavior increases both R<
sub>
0<
/sub>
and the probability of an epidemic also decrease.