The prevalence of injection drug use has been of especial interest for assessment of the impact of blood-borne viruses. However, the incidence of injection drug use has been underresearched. Our 2-fold aim in this study was to estimate 1) how many other persons, per annum, an injection drug user (IDU) has the equivalent of full responsibility (EFR) for initiating into injection drug use and 2) the consequences for IDUs' replacement rate. EFR initiation rates are strongly associated with incarceration history, so that our analysis of IDUs' replacement rate must incorporate when, in their injecting career, IDUs were first incarcerated. To do so, we have first to estimate piecewise constant incarceration rates in conjunction with EFR initiation rates, which are then combined with rates of cessation from injecting to model IDUs' replacement rate over their injecting career, analogous to the reproduction number of an epidemic model. We apply our approach to Scotland's IDUs, using over 2,500 anonymous injector participants who were interviewed in Scotland's Needle Exchange Surveillance Initiative during 2008-2009. Our approach was made possible by the inclusion of key questions about initiations. Finally, we extend our model to include an immediate quit rate, as a reasoned compensation for higher-than-expected replacement rates, and we estimate how high initiates' quit rate should be for IDUs' replacement rate to be 1.