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A Discrete-Continuous Modeling Framework to Study the Role of Swarming in a Honeybee-Varroa destrutor-Virus System

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Mathematical and Computational Approaches in Advancing Modern Science and Engineering

Abstract

In this paper, we present a general discrete-continuous modeling framework to study the effect of swarming on the dynamics of a honeybee colony infested with varroa mite and Acute Bee Paralysis Virus (ABPV) . Two scenarios are studied under which swarming takes place i.e., swarming due to overcrowding and swarming at fixed time intervals. For this purpose, we use an existing mathematical model in the literature. The dependent variables in the model are uninfected bees, infected bees, virus carrying mites and total mites that infest the colony. The model is studied in variable coefficients, in particular, step functions with each season as a constant in time. It is observed that the percentage of healthy bees leaving with the swarm has a great impact on the strength and survival of the parent colony. A colony, that otherwise dies off due to virus, survives as a properly working colony if the percentage of the mites leaving the parent colony is above a critical value.

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Correspondence to Vardayani Ratti .

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Ratti, V., Kevan, P.G., Eberl, H.J. (2016). A Discrete-Continuous Modeling Framework to Study the Role of Swarming in a Honeybee-Varroa destrutor-Virus System. In: Bélair, J., Frigaard, I., Kunze, H., Makarov, R., Melnik, R., Spiteri, R. (eds) Mathematical and Computational Approaches in Advancing Modern Science and Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-30379-6_28

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