Mathematical Models for the Comprehension of Chemical Contamination into the Hive

Honeybees are very sensible organisms and their vulnerability toward chemical pollution is an priority environmental issue. In this chapter the importance and the fundamental of a mathematical model able to predict the fate of chemicals into the hive is described. The ‘Hive model’ presented here is able to consider different contamination pathways: from inside the hive via pesticide treatments against bee pests, or from outside, by means of the eventual contamination present in nectar, pollen, resin, water, air or vegetation. The input parameters of the model are the physical-chemical properties of the compound and the major characteristics of the hive ecosystem, from which it calculates contamination residues in bee products (honey, pollen, royal jelly, wax and propolis) over time. The model can be applied to all non ionic chemicals with a measurable vapour pressure (volatile or semi-volatile compounds). The model was validated with contamination data in bees, wax and honey following tau-fluvalinate application in two experimental hives. The comparison between measured and modelled data over a period of six months was very good. Even if more experimental data should be provided for a better calibration of the model, it seems to correctly quantify the main contamination pathways from outside and within the hive.