Title: Epidemiology of viruses in adult Apis Mellifera infested by Varroa destructor mite                                        

Abstract: The ectoparasitic mite Varroa destructor has become one of the major world-wide threats for apiculture. Varroa destructor attacks the honey bee Apis mellifera weakening its host by sucking hemolymph. The damage to bee colonies is just not strictly related to the parasitic action of the mite. Above all it is due to the increased trasmission rate of many viral diseases, for which it constitutes a vector. Examples of such diseases are acute paralysis (ABPV) and deformed wing viruses (DWV). They represent the major causes of colony collapse disorder (CCD). 

In this talk we present an SI model for the description of the epidemi-ological effects of these viruses on adult bees, fostered by the presence of the mite. We characterize the system behavior, establishing that ultimately either only sound bees survive, or the disease becomes endemic and mites are wiped out. Another dangerous possible alternative is the Varroa inva- sion scenario with the extinction of the healthy bees. Finally, we study the coexistence equilibrium in which honey bees share their infected hive with mites. The analysis reflects actual facts observed in natural honey bee colonies. Namely, these diseases are endemic. Further, if the mite population is present, necessarily the viral infection occurs. Our findings indicate that a lower horizontal transmission rate of the virus among honey bees in beehives helps in protecting the bee colonies from Varroa infestation and viral epidemics.