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A general theory for target reproduction numbers with applications to ecology and epidemiology

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Abstract

A general framework for threshold parameters in population dynamics is developed using the concept of target reproduction numbers. This framework identifies reproduction numbers and other threshold parameters in the literature in terms of their roles in population control. The framework is applied to the analysis of single and multiple control strategies in ecology and epidemiology, and this provides new biological insights.

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Acknowledgements

The authors would like to thank the Mathematical Biosciences Institute (MBI) at The Ohio State University, which receives its funding through the NSF Grant DMS 1440386, for providing support via two MBI workshops in which this research was initiated and improved. We thank two anonymous reviewers for helpful comments.

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Authors and Affiliations

  1. Departments of Mathematical and Statistical Sciences and of Biological Sciences, University of Alberta, Edmonton, AB, T6G 2E9, Canada

    Mark A. Lewis

  2. Department of Mathematics, University of Central Florida, Orlando, FL, 32816, USA

    Zhisheng Shuai

  3. Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 2Y2, Canada

    P. van den Driessche

Authors
  1. Mark A. Lewis
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  2. Zhisheng Shuai
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  3. P. van den Driessche
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Correspondence to Mark A. Lewis.

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This research was partially supported by the Natural Science and Engineering Research Council of Canada (NSERC) through Discovery Grants (MAL and PvdD), by the Canada Research Chair program (MAL), and by the National Science Foundation (NSF) through the Grant DMS 1716445 (ZS).

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Lewis, M.A., Shuai, Z. & van den Driessche, P. A general theory for target reproduction numbers with applications to ecology and epidemiology. J. Math. Biol. 78, 2317–2339 (2019). https://doi.org/10.1007/s00285-019-01345-4

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  • DOI: https://doi.org/10.1007/s00285-019-01345-4

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