Reproduction Number and Asymptotic Stability for the Dynamics of a Honey Bee Colony with Continuous Age Structure

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 equilib...
Ausführliche Beschreibung

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. Ausführliche Beschreibung