Location: Carl Hayden Bee Research CenterTitle: Disease dynamics of honeybees with Varroa destructor as parasite and virus vector
|KANG, YUN - ARIZONA STATE UNIVERSITY|
|BLANCO, KRYSTAL - ARIZONA STATE UNIVERSITY|
|DAVIS, TALIA - ARIZONA STATE UNIVERSITY|
|WANG, YING - ARIZONA STATE UNIVERSITY|
Submitted to: Mathematical Biosciences
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 2/26/2016
Publication Date: 3/9/2016
Citation: Kang, Y., Blanco, K., Davis, T., Wang, Y., Hoffman, G.D. 2016. Disease dynamics of honeybees with Varroa destructor as parasite and virus vector. Mathematical Biosciences. 275:71-92.
Interpretive Summary: Honey bee colonies often are lost from a combination of Varroa mites and high virus titers. The combination of a parasite and pathogen and the associated reductions in adult bee lifespan erode population numbers. Colonies die because there are not enough adult workers to rear brood, forage and conduct other duties in the hive. We constructed a mathematical model to describe the growth of Varroa populations and spread of virus in honey bee colonies to better understand the conditions and processes that lead to colony death. The model revealed that colonies can survive if they have virus but are mite-free as long as virus transmission rates are low. This scenario occurred before the introduction of Varroa into the U.S. Virus were commonly detected in colonies, but the bees seemed unaffected. The model also predicted that colonies with Varroa but no virus also can survive, depending on initial mite and colony population sizes. However, the combination of Varroa with virus, led to rapid virus transmission through the mite into the bee population, a persistence of virus infections in the colony population, and inevitable colony death. The ultimate cause of death was an insufficient ratio of adult bees to brood to sustain colony growth. The results of our model analyses indicate that Varroa control strategies need to keep mite levels low throughout the season to insure low virus transmission rates. Colony management strategies that maintain high adult to brood ratios (e.g., high quality queens and good nutrition) in the presence of Varroa and virus also are needed to prevent ratios of adult bees to brood from slipping below critical levels.
Technical 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 article, we propose a honeybee-mite-virus model that incorporates (1) parasitic interactions between honeybees and the Varroa mites; (2) 've virus transmission terms between honeybees and mites at di'erent 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 e'ects 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 e'ects of parasitism and virus infections on honeybee population dynamics and its persistence. Interesting 'ndings from our work include: (a) Due to Allee e'ects experienced by the honeybee population, initial conditions are essential for the survival of the colony. (b) Low adult honeybees to brood ratios have destabilizing e'ects on the system which generate 'uctuating 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 e'ects on the system, and parasitic mites could make disease more persistent. Our model illustrates how the synergy between the parasitic mite and virus infections consequently generates rich dynamics including multiple attractors where all species can coexist or go extinct depending on initial conditions. Our 'ndings may provide important insights on honeybee diseases and parasites and how to best control them.