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The recently observed honey bee colony losses have already raised concerns about the future of the managed honey bees and the bees in general. One of the most powerful approach to simulate and predict the dynamics of a complex system, which a honey bee colony undoubtedly is, is the mathematical modelling. We have adopted a compartment model to study the behaviour in a honey bee colony. A system of three ordinary differential equations with a control on the mites was introduced to model the populations of the hive bees, forager bees and mites. We solve a parameter identification inverse problem to reconstruct the values, which are directly unobservable but vital in honeybee management. We apply an adjoint equation optimization approach to solve the inverse problem. Numerical test examples are discussed and the paper is concluded with important implications about the honey bee management. [ABSTRACT FROM AUTHOR]

The model is a system of two nonlinear ordinary differential equations (ODEs) with dependent variables: the number of bees working in the hive and the number of bees that work outside the hive referred here as foragers. The population dynamics is studied. In this small study we present an effective simple algorithm to solve the parameter identification problem of the model in [10]. The parameters are identified using a least square method combined with backward Euler approximation of the ODE system and a Newton method technique for optimization of the cost functional. Numerical results of the parameters, representing the solution to the inverse problem are provided. [ABSTRACT FROM AUTHOR]

Inverse, or coefficient identification problem for honey bee colony population model is considered. On the base of the numerical solution to a weakly coupled system of ordinary differential equations (ODEs) with initial conditions, specific constant parameters are found by minimization of a quadratic discrete functional, which expresses the difference between the computed and measured numbers of bees working in and outside the hive. The optimization procedure uses quasilinearization which assures second order of convergence. Numerical simulations with synthetic and real data are discussed. [ABSTRACT FROM AUTHOR]