Honeybee (Apis mellifera) colonies continue to experience high annual losses that remain poorly explained. Numerous interacting pressures including pests, pathogens, pesticides and climate change have been linked to the losses.

Western honeybee, Apis mellifera, is in trouble.

Recent years have seen honeybees in distress, with up to 35% of colonies breaking down annually.There is no single cause that is believed to be responsible for the honeybee losses.

In this project, we study a mathematical model for the honeybees-varroa destructor-virus complex in which, based on division of labour, the bee population is divided into two categories: hive bees and foragers. The model is based on our previous work and consists of nonlinear ordinary differential equations for the dependent variables: uninfected hive bees, uninfected foragers, infected hive bees, virus-carrying mites, and virus-free mites. The main objective of the model is to study the interplay between disease and division of labour in a honeybee colony. The model is focused on Acute Bee Paralysis Virus and is studied with a combination of analytical and computational techniques. We use well-established methods for studying autonomous systems qualitatively. Using computer simulations, we investigate whether the results of the autonomous case carry over to the case where the coefficients are functions of time. Further, we study the non-autonomous model to gain deep insight into the interplay of the factors under consideration.

We observe that the disease cannot be fought off in the absence of varroacide treatment. However, if the treatment is strong enough and if the virus-carrying mites become virus-free at a rate faster than the mite birth rate, the disease can be fought off. The critical forager loss due to homing failure, above which the colony fails, is calculated using simulation experiments for disease-free, treated and untreated mite-infested, and treated virus-infested colonies. A virus-infested colony without varroacide treatment fails regardless of the forager mortality rate.

Collaborators: Hermann J Eberl (Department of Mathematics, Guelph, Canada) and Peter G Kevan (School of Environmental Sciences, Guelph, Canada)