Host–pathogen time series data in wildlife support a transmission function between density and frequency dependence

doi:10.1073/pnas.0809145106

Host–pathogen time series data in wildlife support a transmission function between density and frequency dependence

^aComputational Ecology and Environmental Science Group, Microsoft Research, 7 J J Thompson Avenue, Cambridge CB3 0FB, United Kingdom;
^bSchool of Biological Sciences, University of Liverpool, Crown Street, Liverpool L69 7ZB, United Kingdom;
^cCentre for Ecology and Hydrology, Bush Estate, Edinburgh EH26 0QB, United Kingdom;
^dDepartment of Statistics and Applied Probability, Faculty of Science, National University of Singapore, Singapore 117546; and
^eInstitute of Biological and Environmental Sciences, University of Aberdeen, Tillydrone Avenue, Aberdeen AB24 2TZ, United Kingdom

Edited by Bryan Grenfell, Penn State University, Erie, PA, and accepted by the Editorial Board March 25, 2009
↵¹M.J.S. and S.T. contributed equally to this work. (received for review September 12, 2008)

Abstract

A key aim in epidemiology is to understand how pathogens spread within their host populations. Central to this is an elucidation of a pathogen's transmission dynamics. Mathematical models have generally assumed that either contact rate between hosts is linearly related to host density (density-dependent) or that contact rate is independent of density (frequency-dependent), but attempts to confirm either these or alternative transmission functions have been rare. Here, we fit infection equations to 6 years of data on cowpox virus infection (a zoonotic pathogen) for 4 natural populations to investigate which of these transmission functions is best supported by the data. We utilize a simple reformulation of the traditional transmission equations that greatly aids the estimation of the relationship between density and host contact rate. Our results provide support for an infection rate that is a saturating function of host density. Moreover, we find strong support for seasonality in both the transmission coefficient and the relationship between host contact rate and host density, probably reflecting seasonal variations in social behavior and/or host susceptibility to infection. We find, too, that the identification of an appropriate loss term is a key component in inferring the transmission mechanism. Our study illustrates how time series data of the host–pathogen dynamics, especially of the number of susceptible individuals, can greatly facilitate the fitting of mechanistic disease models.

Footnotes

²To whom correspondence should be addressed. E-mail: matthew.smith{at}microsoft.com
Author contributions: M.J.S., S.T., E.R.K., S.B., A.R.C., X.L., and M.B. designed research; M.J.S., S.T., E.R.K., and S.B. performed research; M.J.S., S.T., E.R.K., and S.B. analyzed data; and M.J.S., S.T., E.R.K., S.B., A.R.C., X.L., and M.B. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission. B.G. is a guest editor invited by the Editorial Board.
This article contains supporting information online at www.pnas.org/cgi/content/full/0809145106/DCSupplemental.
Freely available online through the PNAS open access option.