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.

Disease dynamics of honeybees with Varroa destructor as parasite and virus vector

“…The exact causes and triggering factors for CCD have not been completely understood yet. Researchers have proposed several possible causes of CCD including stress on nutritional diet, harsh winter conditions, lack of genetic diversity, exposure to certain pesticides, diseases, and parasitic mites Varroa destructor which are also vectors of viral diseases of honeybees [22,42]. Even before CCD was detected in honeybee colonies, studies showed that most of the loses could be generally attributed to two main causes: the vampire mite, Varroa destructor, which feeds on host haemolymph, weakens host immunity and exposes the bees to a variety of viruses, and the tracheal mite, which infests the breathing tubes of the bee, punctures the tracheal wall and sucks the bee's blood and also exposes the bee to a variety of viruses [45,51,32].…”

“…The goal of our work is to develop a useful honeybee-mitevirus system to obtain better understanding on the synergistic effects of honeybee-mite interactions and honeybee-virus interactions on the honeybee populations dynamics, thus develop good practices to control these parasites to maintain or increase honeybee population. The most relevant modeling papers for our study purposes are by Sumpter and Martin [54], and Ratti et al [42] whose work examined the transmission of viruses via Varroa mites, using the susceptible-infectious (SI) disease modeling framework with mites as vectors for transmission. However, Sumpter and Martin assumed that the mites' population is constant while Ratti et al took no account of the fact that virus transmissions occur at different biological stages of Varroa mites and honeybees.…”

Age structure is critical to the population dynamics and survival of honeybee colonies

“…Such hazards may cause injury or death to foraging bees, forcing surviving bees to begin foraging prematurely which will then disrupt the dynamics of the colony, ultimately leading to colony collapse [10–12]. Further research has focused on the effects of parasitism and disease [13–18], for example, the effects of Varroa destructor on honeybee colony dynamics [15–18], the effects of the microsporidian parasite Nosema ceranae [19] and the effects of communicable infections more generally [13]. …”

Bee++: An Object-Oriented, Agent-Based Simulator for Honey Bee Colonies

“…Previous models have simulated the effects of pesticides only by increasing the natural death rate of the foragers [10,11,13,15,18,20,21,52]. Bee++ allows us, in addition, to track the effects of pesticides on, for example, a bee’s ability to navigate its environment or potentially the effects on recruitment by modifying Equations (1), (2), or (5), or parameter α .…”

“…Due to the importance of honey bees, both ecologically and agriculturally [1,2,3,4], and because of their decreasing populations on a global scale, honey bees have been the focus of a large body of research [5,6,7,8,9,10,11,12,13]. The recent problem of colony collapse has led to a surge in research efforts into honey bee colony dynamics and the stresses they face.…”