Abstract
Mathematical models have been successfully used to study the progression of various infectious diseases for many years. In this chapter, we demonstrate how the susceptible-infected-removed (SIR) modeling framework can be applied to study diseases of honey bee colonies. We focus on the acute bee paralysis virus, which is transmitted by the parasitic mite Varroa destructor as a vector. The resulting model consists of four nonautonomous, nonlinear ordinary differential equations, which we study with analytical and computational techniques. Our results indicate that, depending on model parameters, in the absence of the virus, a mite infestation can lead either to extinction of the bee colony or to an endemic infestation that allows the bee colony to survive. However, when the mites also carry the virus, this infection is very difficult to be fought off without remedial intervention and might lead to the extinction of the colony.