Título: A Model in Differential Equations to Describe the Mite Varroa Destructor Population Dynamic in Apis Mellifera Colonies.
Autores: Norberto Aníbal Maidana, Miguel Alberto Benavente y Martin Eguaras


Varroa destructor, previously known as Varroa jacobsoni, is an ectoparasite of honeybee brood and adult bee. With the introduction of beekeepers of the European bee A. mellifera into indonesia, the area where A. cereana was endemic, the V. destructor, adapted to the new host, was propagated by contact to anothers countries [1]. In A. cerana, mite reproduction only occurs in the small number of drone brood cell. Consequently, mite population remain low (< 800) and no adverse effects are seen [2]. Another reason for this is the A. cerana bee's behavioural, which groom the worker cells [3]. In A. mellifera colonies, V. destructor reproduce also worker cells causing a non limited population increase contributing to hive collapse in some years. Different models describing the Varroa population growth have been created previously [3], [4], [5], [6]. In [3] a model which consist in a Ordinary Differential Equation with two lags has been study. In [4], [5], [6] a difference equation model has been presented. In this new model, that consist in a System of Ordinary Differential Equations, we considerate two phases of the population mite. The phoretic phase, and the mite in worker and drone brood reproductive phase. Therefore, we no need to considerate an emergent or a rate entry as a function of time like in the continuos model [3], being this facts a consequence of the model dynamic.

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