title: Disease dynamics of honeybees with Varroa destructor as parasite and virus vector.
abstract: The worldwide decline in honeybee colonies during the past 50 years has often been linked to the spread of the parasitic mite Varroa destructor and its interaction with certain honeybee viruses carried by Varroa mites. In this paper, we propose a honeybee-mite-virus model that incorporates (1) parasitic interactions between honeybees and the Varroa mites; (2) five virus transmission terms between honeybees and mites at different stages of Varroa mites: from honeybees to honeybees, from adult honeybees to the phoretic mites, from brood to the reproductive mites, from the reproductive mites to brood, and from adult honeybees to the phoretic mites; and (3) Allee effects in the honeybee population generated by its internal organization such as division of labor. We provide completed local and global analysis for the full system and its subsystems. Our analytical and numerical results allow us have a better understanding of the synergistic effects of parasitism and virus infections on honeybee population dynamics and its persistence. Interesting findings from our work include: (a) due to Allee effects experienced by the honeybee population, initial conditions are essential for the survival of the colony. (b) Low adult honeybees to brood ratios have destabilizing effects on the system which generate fluctuating dynamics that lead to a catastrophic event where both honeybees and mites suddenly become extinct. This catastrophic event could be potentially linked to Colony Collapse Disorder (CCD) of honeybee colonies. (c) Virus infections may have stabilizing effects on the system, and parasitic mites could make disease more persistent. Our model illustrates how the synergy between the parasitic mites and virus infections consequently generates rich dynamics including multiple attractors where all species can coexist or go extinct depending on initial conditions. Our findings may provide important insights on honeybee viruses and parasites and how to best control them.
authors.affiliation: Sciences and Mathematics Faculty, College of Letters and Sciences, Arizona State University, Mesa, AZ 85212, USA. Electronic address: yun.kang@asu.edu.
authors.forename: Yun
authors.initials: Y
authors.lastname: Kang
authors.affiliation: Simon A. Levin Mathematical and Computational Modeling Sciences Center, Arizona State University, Tempe, AZ 85281, USA.
authors.forename: Krystal
authors.initials: K
authors.lastname: Blanco
authors.affiliation: School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85281, USA.
authors.forename: Talia
authors.initials: T
authors.lastname: Davis
authors.affiliation: School of Life Sciences, Arizona State University, Tempe, AZ 85281, USA.
authors.forename: Ying
authors.initials: Y
authors.lastname: Wang
authors.affiliation: Carl Hayden Bee Research Center, USDA-ARS, 2000 East Allen Road, Tucson, AZ 85719, USA.
authors.forename: Gloria
authors.initials: G
authors.lastname: DeGrandi-Hoffman
mesh_terms: D000818:Animals; D001096:Arachnid Vectors / Q000821:virology; D001516:Bees / Q000469:parasitology* / Q000821:virology*; D056631:Colony Collapse / Q000469:parasitology / Q000821:virology; D006790:Host-Parasite Interactions; D055641:Mathematical Concepts; D008954:Models, Biological; D057077:Varroidae / Q000472:pathogenicity* / Q000821:virology*; D014777:Virus Diseases / Q000635:transmission
keywords: Allee Effects; Colony Collapse Disorder (CCD); Extinction; Honeybees; Parasite; Virus