A Mathematical Analysis and Evaluation of Varroa mite Control Methods for a Mite-infested Honey bee Colony

TL;DR

This paper develops a mathematical model to analyze honey bee colony dynamics and evaluates control strategies for Varroa mite infestation, highlighting the importance of reproductive regulation and behavioral defenses.

Contribution

It introduces a novel mathematical framework for assessing mite control methods and identifies key biological factors influencing colony survival and mite management.

Findings

Mite-free reproduction number determines colony survival.

Queen egg-laying rate and hygienic behavior are critical in controlling mites.

Strategies limiting mite reproduction are more effective than mite-killing methods.

Abstract

In this paper, we present a mathematical model for the interaction between honey bees and mites. The dynamics of a mite-infested honey bee colony and the evaluation of the commonly used mite-control strategies (traditional, mechanical and chemical) are studied. The mite-free and mite reproduction numbers are derived using the next generation operator approach. The mathematical analysis of the model reveals that in the absence of mites, the colony survives if the mite-free reproduction number is greater than unity otherwise it goes extinct. Stability and sensitivity analyses of the model reveal that the egg laying rate of the queen bee is key in regulating mite reproduction. Adult bee grooming and hygienic behavior of worker bees have also been shown to play a vital role in reducing parasitism. Using the Volterra-Lyapunov stable matrix approach, the mite-infested equilibrium is confirmed to be globally asymptotically stable when the mite-free reproduction number is greater than unity and the mite reproduction number is greater than unity. It is also shown that varroa mite control strategies that focus on limiting mite-reproduction such as caging the queen bee and using a young queen bee quickly reduces the mite reproduction number to a value less than unity compared to those that are intended to kill the mites.