ANALYSIS OF A POPULATION BIOLOGY
MODEL DESCRIBING THE INTERACTION
BETWEEN THE PARASITIC MITE,
VARROA JACOBSONI OUDEMANS
AND THE HONEY BEE,
APIS MELLIFERA L., USING
NONLINEAR DIFFERENCE EQUATIONS

W.A. MANGUM

Abstract:

A summary of the derivation of two coupled nonlinear difference equations describing varroa mite parasitism of honey bees is presented. Assuming constant parameters, four cases are constructed by letting reproduction be present or absent and by letting worker bees with the ability to remove their parasites be present or absent. The linear stability analysis of these cases is presented, and, where possible, the biological interpretation of the mathematics is also included. For each case, the effect of varroa mite immigration on the population dynamics is also investigated.