Journal of Mathematical Biology

, Volume 60, Issue 5, pp 687-710

First online:

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

  • Thomas Andrew McWalterAffiliated withSchool of Computational and Applied Mathematics, University of the Witwatersrand
  • , Alex WelteAffiliated withSchool of Computational and Applied Mathematics, University of the WitwatersrandDST/NRF Centre of Excellence in Epidemiological Modelling and Analysis (SACEMA) Email author 

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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.


Epidemiology Incidence Prevalence Cross-sectional survey

Mathematics Subject Classification (2000)

Primary 62Mxx Secondary 92C60 92D30 92D25