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

Matthew J. Smith, Sandra Telfer, Eva R. Kallio, Sarah Burthe, Alex R. Cook, Xavier Lambin, and Michael Begon

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 six years of data on cowpox virus infection (a zoonotic pathogen) for four natural populations to investigate which of these transmission functions are best supported by the data. We utilise 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 behaviour 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.

NOTE: M.J.S. Made a mistake in the Author Contributions section to this paper and the Author Contributions should more appropriately read:

Author contributions

MB and XL jointly run the on-going vole disease dynamics programme at Kielder. Field study designed and carried out by S.T., M.B., S.B. and X.L. Conversion of field data to time series done by S.T., S.B. and M.B. Analysis devised by M.J.S., A.R.C., M.B., X.L. and E.R.K. M.J.S. developed the equations. Model fitting was performed by M.J.S. and E.R.K. The manuscript was written by M.J.S. and M.B. with help from all of the other authors. “

Details

Publication typeArticle
Published inProceedings of the National Academy of Sciences of the United States of America, 106(19), pp. 7905-7909
URLhttp://www.pnas.org/content/106/19/7905.full
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