Reproduction Number And Asymptotic Stability For The Dynamics of a Honey Bee Colony with Continuous Age Structure

Matthew Betti; Lindi Wahl; Mair Zamir

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arXiv · 1611.00732

Reproduction Number And Asymptotic Stability For The Dynamics of a Honey Bee Colony with Continuous Age Structure

Matthew Betti·Lindi Wahl·Mair Zamir

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Abstract

A system of partial differential equations is derived as a model for the dynamics of a honey bee colony with a continuous age distribution, and the system is then extended to include the effects of a simplified infectious disease. In the disease-free case we analytically derive the equilibrium age distribution within the colony and propose a novel approach for determining the global asymptotic stability of a reduced model. Furthermore, we present a method for determining the basic reproduction number $R_0$ of the infection; the method can be applied to other age-structured disease models with interacting susceptible classes. The results of asymptotic stability indicate that a honey bee colony suffering losses will recover naturally so long as the cause of the losses is removed before the colony collapses. Our expression for $R_0$ has potential uses in the tracking and control of an infectious disease within a bee colony.

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Matthew Betti, Lindi Wahl, Mair Zamir. 2016-11-02. Reproduction Number And Asymptotic Stability For The Dynamics of a Honey Bee Colony with Continuous Age Structure. https://arxiv.org/abs/1611.00732

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