When estimating the incidence of acquired immune deficiency syndrome (AIDS), reporting delays can result in serious underestimation of recent diagnoses. Various bivariate intensity functions for non-homogeneous Poisson processes in the plane can be fitted as log-linear models. This is illustrated by application to such reporting delay data. It is shown that (quasi-)stationary models seriously overestimate recent AIDS diagnoses for England and Wales, and that a non-stationary model is more appropriate.