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In recent years the spread of the ectoparasitic mite Varroa destructor has become the most serious threat to worldwide apiculture. In the model presented here we extend the bee population dynamics with mite viral epidemiology examined in an earlier paper by allowing a bee-dependent mite population size. The results of the analysis match field observations well and give a clear explanation of how Varroa affects the epidemiology of certain naturally occurring bee viruses, causing considerable damages to colonies. The model allows only four possible stable equilibria, using known field parameters. The first one contains only the thriving healthy bees. Here the disease is eradicated and also the mites are wiped out. Alternatively, we find the equilibrium still with no mite population, but with endemic disease among the thriving bee population. Thirdly, infected bees coexist with the mites in the Varroa invasion scenario; in this situation the disease invades the hive, driving the healthy bees to extinction and therefore affecting all the bees. Coexistence is also possible, with both populations of bees and mites thriving and with the disease endemically affecting both species. The analysis is in line with field observations in natural honey bee colonies. Namely, these diseases are endemic and if the mite population is present, necessarily the viral infection occurs. Further, in agreement with the fact that the presence of Varroa increments the viral transmission, the whole bee population may become infected when the disease vector is present in the beehive. Also, a low horizontal transmission rate of the virus among the honey bees will help in protecting the bee colonies from Varroa infestation and viral epidemics.

AN EPIDEMIOLOGICAL MODEL OF VIRAL INFECTIONS IN A VARROA-INFESTED BEE COLONY: THE CASE OF A BEE-DEPENDENT MITE POPULATION SIZE