Hermann J. Eberl, Mallory R. Frederick, Peter G. Kevan
Abstract:
We present a simple mathematical model of the infestation of
a honeybee colony by the Acute Paralysis Virus, which is
carried by parasitic varroa mites (Varroa destructor).
This is a system of nonlinear ordinary differential equations
for the dependent variables: number of mites that carry the virus,
number of healthy bees and number of sick bees.
We study this model with a mix of analytical and computational
techniques. Our results indicate that, depending on model parameters
and initial data, bee colonies in which the virus is present can,
over years, function seemingly like healthy colonies before they
decline and disappear rapidly (e.g. Colony Collapse Disorder,
wintering losses). This is a consequence of the fact that a
certain number of worker bees is required in a colony to maintain
and care for the brood, in order to ensure continued production
of new bees.
Published September 25, 2010.
Math Subject Classifications: 92D25, 92D30.
Key Words: Honeybees; varroa destructor; acute bee paralysis virus;
colony collapse disorder; wintering losses; mathematical model.
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Hermann J. Eberl Department of Mathematics and Statistics University of Guelph, Guelph, ON, N1G 2W1, Canada email: heberl@uoguelph.ca |
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Mallory R. Frederick Department of Mathematics and Statistics University of Guelph, Guelph, ON, N1G 2W1, Canada email: mfrederi@uoguelph.ca |
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Peter G. Kevan School of Environmental Sciences University of Guelph, Guelph, ON, N1G 2W1, Canada email: pkevan@uoguelph.ca |
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