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Journal of Mathematical Biology

, Volume 66, Issue 4–5, pp 1045–1064 | Cite as

Characterizing the next-generation matrix and basic reproduction number in ecological epidemiology

  • M. G. RobertsEmail author
  • J. A. P. Heesterbeek
Article

Abstract

We address the interaction of ecological processes, such as consumer-resource relationships and competition, and the epidemiology of infectious diseases spreading in ecosystems. Modelling such interactions seems essential to understand the dynamics of infectious agents in communities consisting of interacting host and non-host species. We show how the usual epidemiological next-generation matrix approach to characterize invasion into multi-host communities can be extended to calculate \(\mathcal{R _{0}}\), and how this relates to the ecological community matrix. We then present two simple examples to illustrate this approach. The first of these is a model of the rinderpest, wildebeest, grass interaction, where our inferred dynamics qualitatively matches the observed phenomena that occurred after the eradication of rinderpest from the Serengeti ecosystem in the 1980s. The second example is a prey-predator system, where both species are hosts of the same pathogen. It is shown that regions for the parameter values exist where the two host species are only able to coexist when the pathogen is present to mediate the ecological interaction.

Keywords

Epidemiological stability Ecological stability Infectious diseases 

Mathematics Subject Classification (2000)

92D30 92D40 

Notes

Acknowledgments

The authors thank two anonymous referees whose suggestions led to improvements in the manuscript. The first author received financial support from the Marsden Fund under contract MAU1106.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institute of Information and Mathematical Sciences, New Zealand Institute for Advanced Study, and Infectious Disease Research CentreMassey UniversityAucklandNew Zealand
  2. 2.Department of Farm Animal Health, Faculty of Veterinary MedicineUniversity of Utrecht UtrechtThe Netherlands

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