The Western honeybee (Apis mellifera) is in trouble: For years, beekeepers in North America and Europe have reported drastic numbers of incidents of colony failure. In Canada and other regions with colder climates these manifest themselves primarily as overwintering losses. The exact reasons are not understood yet, but several potential culprits have been suggested. The consensus seems to be emerging that colony failure is mostly a multi-factorial phenomenon whereby the effects of several stressors, each of which might be tolerable, amplify each other when they interact. To explore this, we develop a mathematical model for honeybee colonies infested with the ectoparasitic mite Varroa destructor, which is a vector for several known viral honeybee diseases. Among those, we focus on the Acute Bee Paralysis Virus (ABPV) that has been frequently implicated in Colony Collapse Disorder. We also include exposure of foraging honeybees to neonicotinoids in the field. This results in a system of 4-5 ordinary differential equations with periodic coefficients which we study with a blend of analytical and numerical techniques. This is joint work with Vardayani Ratti (Dartmouth College) and Peter G Kevan FRSC (School of Environmental Science, U Guelph).