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

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


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

Topics: Zoology, Ecology and Environment
Publisher: PNAS
Year: 2009
DOI identifier: 10.1073/pnas.0809145106
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