title: A Mathematical Model of Forager Loss in Honeybee Colonies Infested with Varroa destructor and the Acute Bee Paralysis Virus.
abstract: We incorporate a mathematical model of Varroa destructor and the Acute Bee Paralysis Virus with an existing model for a honeybee colony, in which the bee population is divided into hive bees and forager bees based on tasks performed in the colony. The model is a system of five ordinary differential equations with dependent variables: uninfected hive bees, uninfected forager bees, infected hive bees, virus-free mites and virus-carrying mites. The interplay between forager loss and disease infestation is studied. We study the stability of the disease-free equilibrium of the bee-mite-virus model and observe that the disease cannot be fought off in the absence of varroacide treatment. However, the disease-free equilibrium can be stable if the treatment is strong enough and also if the virus-carrying mites become virus-free at a rate faster than the mite birth rate. The critical forager loss due to homing failure, above which the colony fails, is calculated using simulation experiments for disease-free, treated and untreated mite-infested, and treated virus-infested colonies. A virus-infested colony without varroacide treatment fails regardless of the forager mortality rate.
authors.affiliation: Department of Mathematics, Dartmouth College, Hanover, NH, 03755-3551, USA. vardayani.ratti@dartmouth.edu.
authors.forename: Vardayani
authors.initials: V
authors.lastname: Ratti
authors.affiliation: School of Environmental Sciences, University of Guelph, Guelph, ON, N1G 2W1, Canada.
authors.forename: Peter G
authors.initials: PG
authors.lastname: Kevan
authors.affiliation: Department of Mathematics and Statistics, University of Guelph, Guelph, ON, N1G 2W1, Canada.
authors.forename: Hermann J
authors.initials: HJ
authors.lastname: Eberl
mesh_terms: D000818:Animals; D001516:Bees; D056629:Dicistroviridae / Q000472:pathogenicity*; D005247:Feeding Behavior; D008962:Models, Theoretical; D011157:Population Dynamics; D057077:Varroidae
keywords: Acute Bee Paralysis Virus; Forager loss; Homing failure; Honeybees; Mathematical model; Varroa destructor