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A Mathematical Model of Forager Loss in Honeybee Colonies Infested with Varroa destructor and the Acute Bee Paralysis Virus

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Abstract

We incorporate a mathematical model of Varroa destructor and the Acute Bee Paralysis Virus with an existing model for a honeybee colony, in which the bee population is divided into hive bees and forager bees based on tasks performed in the colony. The model is a system of five ordinary differential equations with dependent variables: uninfected hive bees, uninfected forager bees, infected hive bees, virus-free mites and virus-carrying mites. The interplay between forager loss and disease infestation is studied. We study the stability of the disease-free equilibrium of the bee-mite-virus model and observe that the disease cannot be fought off in the absence of varroacide treatment. However, the disease-free equilibrium can be stable if the treatment is strong enough and also if the virus-carrying mites become virus-free at a rate faster than the mite birth rate. The critical forager loss due to homing failure, above which the colony fails, is calculated using simulation experiments for disease-free, treated and untreated mite-infested, and treated virus-infested colonies. A virus-infested colony without varroacide treatment fails regardless of the forager mortality rate.

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Acknowledgements

This work was supported in parts by the Natural Science and Engineering Research Council of Canada (NSERC) with an NSERC Engage Grant (EGP 490903-15), and by the Ontario Ministry for Agriculture, Food and Rural Affairs (OMAFRA) with a New Directions Grant (SR9279).

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Authors and Affiliations

  1. Department of Mathematics, Dartmouth College, Hanover, NH, 03755-3551, USA

    Vardayani Ratti

  2. School of Environmental Sciences, University of Guelph, Guelph, ON, N1G 2W1, Canada

    Peter G. Kevan

  3. Department of Mathematics and Statistics, University of Guelph, Guelph, ON, N1G 2W1, Canada

    Hermann J. Eberl

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  1. Vardayani Ratti
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  2. Peter G. Kevan
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  3. Hermann J. Eberl
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Correspondence to Vardayani Ratti.

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Ratti, V., Kevan, P.G. & Eberl, H.J. A Mathematical Model of Forager Loss in Honeybee Colonies Infested with Varroa destructor and the Acute Bee Paralysis Virus. Bull Math Biol 79, 1218–1253 (2017). https://doi.org/10.1007/s11538-017-0281-6

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  • DOI: https://doi.org/10.1007/s11538-017-0281-6

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