Modeling colony collapse disorder in honeybees as a contagion

Christopher M. Kribs-Zaleta; Christopher Mitchell

doi:10.3934/mbe.2014.11.1275

Article Contents

2014, Volume 11, Issue 6: 1275-1294. Doi: 10.3934/mbe.2014.11.1275

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Modeling colony collapse disorder in honeybees as a contagion

Christopher M. Kribs-Zaleta^1, and
Christopher Mitchell^2,

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

Received: March 2014

Revised: July 2014

Published: September 2014

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Abstract

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.

Keywords:

Mathematics Subject Classification: Primary: 92D30, 92D40; Secondary: 37F99.

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