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

The ectoparasitic mite Varroa destructor has become one of the major threats for apiculture worldwide. Varroa destructor attacks the honey bee Apis mellifera weakening its host by sucking hemolymph. However, the damage to bee colonies is not strictly related to parasitic action of the mite but it derives, above all, from the increased transmission of many viral diseases vectored by it. These diseases, such as acute paralysis (ABPV) and deformed wing viruses (DWV), are considered among the main causes of CCD (Colony Collapse Disorder). In this work we discuss an SI model that describes how the presence of the mite affects the epidemiology of these viruses on adult bees. 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 alternative is the Varroa invasion scenario with the extinction of sound bees. Finally, we study the coexistence equilibrium in which honey bees have to share their infected hive with mites. The analysis is in line with some facts observed in natural honey bee colonies. Namely, these diseases are endemic. Further, if the mite population is present, necessarily the viral infection occurs. The findings of this study indicate that a low horizontal transmission rate of the virus among honey bees in beehives will help in protecting bee colonies from Varroa infestation and viral epidemics.