The decline of honeybee colonies around the world has been linked to the presence of the Varroa destructor, a mite acting as a virus vector for the Acute Bee Paralysis Virus. We developed a model of the infestation of the Apis melliifera honeybee colony by the Acute Bee Paralysis Virus, which is transmitted by the parasitic Varroa destructor. This is a four dimensional system of nonlinear ODE's for healthy and virus infected bees, total number of mites in the colony and number of mites that carry the virus. The Acute Bee Paralysis Virus can be transmitted between infected and uninfected bees, infected mite to adult bee, infected bee to phoretic mite, and reproductive mites to bee brood. This model is studied with analytical techniques deriving the conditions under which the bee colony can fight off an Acute Bee Paralysis Virus epidemic.
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