AIDS in Ireland: the reporting delay distribution and the implementation of integral equation models

This paper deals with two basic aspects concerning the modelling of AIDS incidence in the context of Irish data. We describe initially the adjustment of the number of AIDS cases (Xij) to allow for reporting delays, where a simple form of the likelihood function for the Xij is supported by GLIM. Subsequently, we consider the accessibility of numerical solution (through a NAG routine) of the integral equation models generated by the back-projection method for the adjusted AIDS cases. Results for the Irish data are summarized for various choices of the incidence distribution.