  We present a new analysis of relationships between disease incidence and the
prevalence of an experimentally defined state of `recent infection'. This leads
to a clean separation between biological parameters (properties of disease
progression as reflected in a test for recent infection), which need to be
calibrated, and epidemiological state variables, which are estimated in a
cross-sectional survey. The framework takes into account the possibility that
details of the assay and host/pathogen chemistry leave a (knowable) fraction of
the population in the recent category for all times. This systematically
addresses an issue which is the source of some controversy about the
appropriate use of the BED assay for defining recent HIV infection. Analysis of
relative contributions of error arising variously from statistical
considerations and simplifications of general expressions indicate that
statistical error dominates heavily over all sources of bias for realistic
epidemiological and biological scenarios. Numerical calculations validate the
approximations made in analytical relations.
