  The ectoparasitic mite Varroa destructor has become one of the major
worldwide threats for apiculture. 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 the parasitic action of the mite but it
derives, above all, from its action as vector increasing the trasmission of
many viral diseases such as acute paralysis (ABPV) and deformed wing viruses
(DWV), that 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
healthy bees survive, or the disease becomes endemic and mites are wiped out.
Another dangerous alternative is the Varroa invasion scenario with the
extinction of healthy bees. The final possible configuration is the coexistence
equilibrium in which honey bees share their infected hive with mites. The
analysis is in line with some observed facts 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.
