A new approach to predict changes in physical condition: A new extension of the classical Banister model

Abstract: In this article, a new model based on techniques of differential equations is introduced to predict the athletic performance based training load and a data sample of the physical form of athletes arises. This model is an extension of the classical model of Banister but, in this case, unlike the classical Banister model, the variation produced in the athletic performance depends, not only on the current training load, but also on the training performed the previous day. The model has been validated with the training data of a cyclist taken from the reference \cite{Clarke}, obtaining an excellent fit of the predicted data with respect to the experimental data.