Transmission assumptions generate conflicting predictions in host–vector disease models: a case study in West Nile virus

Authors

  • Marjorie J. Wonham,

    Corresponding author
    1. Department of Biological Sciences and Department of Mathematical and Statistical Sciences, Centre for Mathematical Biology, University of Alberta, CAB 632, Edmonton, AB, Canada T6G 2G1
      * E-mail: mwonham@ualberta.ca
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  • Mark A. Lewis,

    1. Department of Biological Sciences and Department of Mathematical and Statistical Sciences, Centre for Mathematical Biology, University of Alberta, CAB 632, Edmonton, AB, Canada T6G 2G1
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  • Joanna Rencławowicz,

    1. Department of Biological Sciences and Department of Mathematical and Statistical Sciences, Centre for Mathematical Biology, University of Alberta, CAB 632, Edmonton, AB, Canada T6G 2G1
    2. Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8W 3P4
    3. Institute of Mathematics, Polish Academy of Sciences, Sniadeckich 8, 00-956 Warsaw, Poland
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  • P. Van Den Driessche

    1. Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8W 3P4
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* E-mail: mwonham@ualberta.ca

Abstract

This review synthesizes the conflicting outbreak predictions generated by different biological assumptions in host–vector disease models. It is motivated by the North American outbreak of West Nile virus, an emerging infectious disease that has prompted at least five dynamical modelling studies. Mathematical models have long proven successful in investigating the dynamics and control of infectious disease systems. The underlying assumptions in these epidemiological models determine their mathematical structure, and therefore influence their predictions. A crucial assumption is the host–vector interaction encapsulated in the disease-transmission term, and a key prediction is the basic reproduction number, ℛ0. We connect these two model elements by demonstrating how the choice of transmission term qualitatively and quantitatively alters ℛ0 and therefore alters predicted disease dynamics and control implications. Whereas some transmission terms predict that reducing the host population will reduce disease outbreaks, others predict that this will exacerbate infection risk. These conflicting predictions are reconciled by understanding that different transmission terms apply biologically only at certain population densities, outside which they can generate erroneous predictions. For West Nile virus, ℛ0 estimates for six common North American bird species indicate that all would be effective outbreak hosts.

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