  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.
