Eighth Mississippi State - UAB Conference on Differential Equations and Computational Simulations. Electron. J. Diff. Eqns., Conference 19 (2010), pp. 85-98.

Importance of brood maintenance terms in simple models of the honeybee - Varroa destructor - acute bee paralysis virus complex

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
Mallory R. Frederick
Department of Mathematics and Statistics
University of Guelph, Guelph, ON, N1G 2W1, Canada
email: mfrederi@uoguelph.ca
Peter G. Kevan
School of Environmental Sciences
University of Guelph, Guelph, ON, N1G 2W1, Canada
email: pkevan@uoguelph.ca

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