An Environmental Model of Honey Bee Colony Collapse Due to Pesticide Contamination

  • P. Magal
  • G. F. WebbEmail author
  • Yixiang Wu
Original Paper


We develop a model of honey bee colony collapse based on the contamination of forager bees in environmental regions contaminated with pesticides. An important feature of the model is the daily homing capacity each day of foragers bees. The model consists of difference equations describing the daily homing of uncontaminated and contaminated forager bees, with an increased homing failure of contaminated bees. The model quantifies colony collapse in terms of the fraction of contaminated bees subject to this increased homing failure. If the fraction is sufficiently high, then the hive falls below a viability threshold population size that leads to rapid disintegration. If the fraction is sufficiently low, then the hive can rise above the viability threshold and attain a stable population level.


Colony collapse Pesticide contamination Difference equation 

Mathematics Subject Classification

92D25 92D40 



The authors express thanks to Dr. Frederic Barraquand, CNRS, IMB Bordeaux, France, for helpful assistance in the biological background of this work.

Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Society for Mathematical Biology 2019

Authors and Affiliations

  1. 1.Université de BordeauxBordeauxFrance
  2. 2.Vanderbilt UniversityNashvilleUSA

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