Journal of Mathematical Biology

, Volume 60, Issue 5, pp 687–710

Relating recent infection prevalence to incidence with a sub-population of assay non-progressors


DOI: 10.1007/s00285-009-0282-7

Cite this article as:
McWalter, T.A. & Welte, A. J. Math. Biol. (2010) 60: 687. doi:10.1007/s00285-009-0282-7


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. The analysis is, however, applicable to any assay that forms the basis of a test for recent infection. Analysis of relative contributions of error arising variously from statistical considerations and simplifications of general expressions indicate that statistical error dominates heavily over methodological bias for realistic epidemiological and biological scenarios.


EpidemiologyIncidencePrevalenceCross-sectional survey

Mathematics Subject Classification (2000)

Primary 62MxxSecondary 92C6092D3092D25

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.School of Computational and Applied MathematicsUniversity of the WitwatersrandJohannesburgSouth Africa
  2. 2.DST/NRF Centre of Excellence in Epidemiological Modelling and Analysis (SACEMA)StellenboschSouth Africa