Ratti Vardayani, Kevan Peter G, Eberl Hermann J
Department of Mathematics, Dartmouth College, Hanover, NH, 03755-3551, USA.
School of Environmental Sciences, University of Guelph, Guelph, ON, N1G 2W1, Canada.
Bull Math Biol. 2017 Jun;79(6):1218-1253. doi: 10.1007/s11538-017-0281-6. Epub 2017 Apr 11.
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.
我们将狄斯瓦螨和急性蜜蜂麻痹病毒的数学模型与现有的蜜蜂蜂群模型相结合，在该模型中，蜜蜂种群根据在蜂群中执行的任务分为蜂巢蜜蜂和觅食蜜蜂。该模型是一个由五个常微分方程组成的系统，其因变量包括：未感染的蜂巢蜜蜂、未感染的觅食蜜蜂、感染的蜂巢蜜蜂、无病毒的螨虫和携带病毒的螨虫。研究了觅食蜜蜂损失与疾病侵染之间的相互作用。我们研究了蜜蜂-螨虫-病毒模型无病平衡点的稳定性，观察到在没有杀螨剂处理的情况下，疾病无法被抵御。然而，如果处理力度足够大，并且携带病毒的螨虫以比螨虫出生率更快的速度变为无病毒状态，无病平衡点可以是稳定的。使用无病、经处理和未经处理的螨虫侵染以及经处理的病毒侵染蜂群的模拟实验，计算了由于归巢失败导致的关键觅食蜜蜂损失，超过这个损失蜂群就会失败。一个未经杀螨剂处理的病毒侵染蜂群，无论觅食蜜蜂死亡率如何都会失败。
