A Mathematical Model of the Honeybee–Varroa destructor–Acute Bee Paralysis Virus System with Seasonal Effects

Ratti, Vardayani; Kevan, Peter G.; Eberl, Hermann J.

doi:10.1007/s11538-015-0093-5

Cited by 37 publications

(46 citation statements)

References 30 publications

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“…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 .…”

Section: Modelmentioning

confidence: 99%

“…Several mathematical studies have addressed the compounding effects of pesticides and parasites on a honey bee colony [15,20,21,22,23]. In [15,20], the effects of acute bee paralysis (vectored by the Varroa destructor) are studied in combination with pesticides and seasonality respectively. Pettis et al predicted that an exposure to pesticides will increase the susceptibility of Nosema ceranae [23], which was shown experimentally by [22].…”

Section: Introductionmentioning

confidence: 99%

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

Betti

LeClair

Wahl

et al. 2017

Insects

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We present a model and associated simulation package () to capture the natural dynamics of a honey bee colony in a spatially-explicit landscape, with temporally-variable, weather-dependent parameters. The simulation tracks bees of different ages and castes, food stores within the colony, pollen and nectar sources and the spatial position of individual foragers outside the hive. We track explicitly the intake of pesticides in individual bees and their ability to metabolize these toxins, such that the impact of sub-lethal doses of pesticides can be explored. Moreover, pathogen populations (in particular, Nosema apis, Nosema cerenae and Varroa mites) have been included in the model and may be introduced at any time or location. The ability to study interactions among pesticides, climate, biodiversity and pathogens in this predictive framework should prove useful to a wide range of researchers studying honey bee populations. To this end, the simulation package is written in open source, object-oriented code (C++) and can be easily modified by the user. Here, we demonstrate the use of the model by exploring the effects of sub-lethal pesticide exposure on the flight behaviour of foragers.

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Section: Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Betti

LeClair

Wahl

et al. 2017

Insects

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“…it is easy to see that the total mite population becomes extinct. The effect of intraspecific competition among mites is described by the Leslie Gower term at rate p. It accounts for the mite population dependence on the total number of adult bees, the "resource for which they compete" in the colony, 8 . The parameter h expresses the average number of mites per bee.…”

Section: The Modelmentioning

confidence: 99%

AN EPIDEMIOLOGICAL MODEL OF VIRAL INFECTIONS IN A VARROA-INFESTED BEE COLONY: THE CASE OF A BEE-DEPENDENT MITE POPULATION SIZE

Bernardi¹,

Venturino²

2017

Mathematical Biology and Biological Physics

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In recent years the spread of the ectoparasitic mite Varroa destructor has become the most serious threat to worldwide apiculture. In the model presented here we extend the bee population dynamics with mite viral epidemiology examined in an earlier paper by allowing a bee-dependent mite population size. The results of the analysis match field observations well and give a clear explanation of how Varroa affects the epidemiology of certain naturally occurring bee viruses, causing considerable damages to colonies. The model allows only four possible stable equilibria, using known field parameters. The first one contains only the thriving healthy bees. Here the disease is eradicated and also the mites are wiped out. Alternatively, we find the equilibrium still with no mite population, but with endemic disease among the thriving bee population. Thirdly, infected bees coexist with the mites in the Varroa invasion scenario; in this situation the disease invades the hive, driving the healthy bees to extinction and therefore affecting all the bees. Coexistence is also possible, with both populations of bees and mites thriving and with the disease endemically affecting both species. The analysis is in line with field observations in natural honey bee colonies. Namely, these diseases are endemic and if the mite population is present, necessarily the viral infection occurs. Further, in agreement with the fact that the presence of Varroa increments the viral transmission, the whole bee population may become infected when the disease vector is present in the beehive. Also, a low horizontal transmission rate of the virus among the honey bees will help in protecting the bee colonies from Varroa infestation and viral epidemics.

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“…There is a work [39] that investigated seasonal food availability and transition of hive to foragers. The most recent recent works [29,36] consider the seasonality in the queen egg-laying rate. Messan et al [29] applied seasonality effects into the pollen collection rate that has annual periodicity by the first order harmonic.…”

Section: Introductionmentioning

confidence: 99%

“…Motivated by the previous work on honeybee population models with age structure [22][23][24] and seasonality [29,36,39], we propose and study honeybee population models with different delay terms to include age structure. We use data to validate our models and explore which model would be more appreciated and the importance of incorporating seasonality in the honeybee population model.…”

Section: Introductionmentioning

confidence: 99%

How to model honeybee population dynamics: stage structure and seasonality

Messan¹,

Messan²,

DeGrandi-Hoffman³

et al. 2020

Math Appl Sci Eng

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Western honeybees (Apis Mellifera) serve extremely important roles in our ecosystem and economics as they are responsible for pollinating $ 215 billion dollars annually over the world. Unfortunately, honeybee population and their colonies have been declined dramatically. The purpose of this article is to explore how we should model honeybee population with age structure and validate the model using empirical data so that we can identify different factors that lead to the survival and healthy of the honeybee colony. Our theoretical study combined with simulations and data validation suggests that the proper age structure incorporated in the model and seasonality are important for modeling honeybee population. Specifically, our work implies that the model assuming that (1) the adult bees are survived from the egg population rather than the brood population; and (2) seasonality in the queen egg laying rate, give the better fit than other honeybee models. The related theoretical and numerical analysis of the most fit model indicate that (a) the survival of honeybee colonies requires a large queen egg-laying rate and smaller values of the other life history parameter values in addition to proper initial condition; (b) both brood and adult bee populations are increasing with respect to the increase in the egg-laying rate and the decreasing in other parameter values; and (c) seasonality may promote/suppress the survival of the honeybee colony.

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A Mathematical Model of the Honeybee–Varroa destructor–Acute Bee Paralysis Virus System with Seasonal Effects

Cited by 37 publications

References 30 publications

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

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

AN EPIDEMIOLOGICAL MODEL OF VIRAL INFECTIONS IN A VARROA-INFESTED BEE COLONY: THE CASE OF A BEE-DEPENDENT MITE POPULATION SIZE

How to model honeybee population dynamics: stage structure and seasonality

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