An epidemiological model of viral infections in a Varroa-infested bee colony: the case of a bee-dependent mite population size

摘要

In recent years the spread of the ectoparasitic mite Varroa destructor hasbecome the most serious threat to worldwide apiculture. In the model presentedhere we extend the bee population dynamics with mite viral epidemiologyexamined in an earlier paper by allowing a bee-dependent mite population size.The results of the analysis match field observations well and give a clearexplanation of how Varroa affects the epidemiology of certain naturallyoccurring bee viruses, causing considerable damages to colonies. The modelallows only four possible stable equilibria, using known field parameters. Thefirst one contains only the thriving healthy bees. Here the disease iseradicated and also the mites are wiped out. Alternatively, we find theequilibrium still with no mite population, but with endemic disease among thethriving bee population. Thirdly, infected bees coexist with the mites in theVarroa 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 thrivingand with the disease endemically affecting both species. The analysis is inline with field observations in natural honey bee colonies. Namely, thesediseases are endemic and if the mite population is present, necessarily theviral infection occurs. Further, in agreement with the fact that the presenceof Varroa increments the viral transmission, the whole bee population maybecome infected when the disease vector is present in the beehive. Also, a lowhorizontal transmission rate of the virus among the honey bees will help inprotecting the bee colonies from Varroa infestation and viral epidemics.