Mathematical Biosciences and Engineering, 2014, 11(6): 1275-1294. doi: 10.3934/mbe.2014.11.1275.

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Modeling colony collapse disorder in honeybees as a contagion

1. Departments of Mathematics and Curriculum & Instruction, University of Texas at Arlington, Box 19408, Arlington, TX 76019-0408
2. Department of Mathematics, University of Texas at Arlington, Box 19408, Arlington, TX 76019-0408

Honeybee pollination accounts annually for over $14 billion in United States agriculture alone. Within the past decade there has been a mysterious mass die-off of honeybees, an estimated 10 million beehives and sometimes as much as 90% of an apiary. There is still no consensus on what causes this phenomenon, called Colony Collapse Disorder, or CCD. Several mathematical models have studied CCD by only focusing on infection dynamics. We created a model to account for both healthy hive dynamics and hive extinction due to CCD, modeling CCD via a transmissible infection brought to the hive by foragers. The system of three ordinary differential equations accounts for multiple hive population behaviors including Allee effects and colony collapse. Numerical analysis leads to critical hive sizes for multiple scenarios and highlights the role of accelerated forager recruitment in emptying hives during colony collapse.
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Keywords Allee effect; Honey bees; multistability.; extinction; bifurcations

Citation: Christopher M. Kribs-Zaleta, Christopher Mitchell. Modeling colony collapse disorder in honeybees as a contagion. Mathematical Biosciences and Engineering, 2014, 11(6): 1275-1294. doi: 10.3934/mbe.2014.11.1275

References

  • 1. Journal of Theoretical Biology, 223 (2003), 451-464.
  • 2. Quat. Rev. Zool., 12 (1937), 406-425.
  • 3. United States Department of Agriculture, June 2010. Retrieved 2013-08-28 from http://www.ars.usda.gov/is/br/ccd/ccdprogressreport2010.pdf.
  • 4. How To Books, London, 2008.
  • 5. Journal of Apicultural Research, 49 (2010), 124-125.
  • 6. Ecological Modelling, 45 (1989), 133-150.
  • 7. Journal of Mathematical Biology, 28 (1990), 365-382.
  • 8. Technical Report 2012-12, University of Texas at Arlington Mathematics Department, Arlington, TX. Available online at http://www.uta.edu/math/preprint/rep2012_12.pdf.
  • 9. Electronic Journal of Differential Equations (EJDE) [electronic only] Conf. 19 (2010), 85-98. Available from: http://eudml.org/doc/232749.
  • 10. Ecological Economics, 68 (2009), 810-821.
  • 11. Environmental Microbiology, 10 (2008), 2659-2669.
  • 12. Reproduction, Fertility, and Development, 24 (2012), 1079-1083.
  • 13. Unpublished Thesis, School of Mathematics and Statistics, University of Sydney, Sydney, 2009.
  • 14. PLoS ONE, 8 (2013), e59084.
  • 15. PLoS ONE, 6 (2011), e18491.
  • 16. PLoS Biology, 5 (2007), e168.
  • 17. Uludag Bee Journal, 10 (2010), 85-95.
  • 18. Nosema Ceranae, PLoS ONE, 8 (2013), e70182.
  • 19. Ecological Modelling, 265 (2013), 158-169.
  • 20. Ecological Modelling, 204 (2007), 219-245.
  • 21. Journal of Animal Ecology, 73 (2004), 51-63.
  • 22. Social Studies Of Science (Sage Publications, Ltd.), 43 (2013), 215-240.
  • 23. American Bee Journal, 141 (2001), 287-288.
  • 24. USDA, 2010. Available from: http://www.ars.usda.gov/is/br/ccd/ccdprogressreport2010.pdf.
  • 25. Mathematical Biosciences, 180 (2002), 29-48.
  • 26. Journal of Apicultural Research, 49 (2010), 7-14.
  • 27. Science, 302 (2003), 296-299.

 

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Copyright Info: 2014, Christopher M. Kribs-Zaleta, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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