  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.
