Abstract. Experimental measurements often can only provide limited data from an animal's sensory system. In addition, they exhibit large trial-to-trial and animal-to-animal variability. These limitations pose challenges to building mathematical models intended to make biologically relevant predictions. Here, we present a mathematical model of the early olfactory system of honeybees aiming to overcome these limitations. The model generates olfactory response patterns which conform to the statistics derived from experimental data for a variety of their properties. This allows considering the full dimensionality of the sensory input space as well as avoiding overfitting the underlying data sets. Several known biological mechanisms, including processes of chemical binding and activation of receptors, and spike generation and transmission in the antennal lobe network, are incorporated in the model at a minimal level. It can therefore be used to study how experimentally observed phenomena are shaped by these underlying biophysical processes. We verified that our model can replicate some key experimental findings that were not used when building it. Given appropriate data, our model can be generalized to the early olfactory systems of other insects. It hence provides a possible framework for future numerical and analytical studies of olfactory processing in insects.