An Improved Version of the Classical Banister Model to Predict Changes in Physical Condition
In this paper, we formulate and provide the solutions to two new models to predict changes in physical condition by using the information of the training load of an individual. The first model is based on a functional differential equation, and the second one on an integral differential equation. Both models are an extension to the classical Banister model and allow to overcome its main drawback: the variations in physical condition are influenced by the training loads of the previous days and not only of the same day. Finally, it is illustrated how the first model works with a real example of the training process of a cyclist.
KeywordsMathematical models Functional differential equations Difference equations
Mathematics Subject Classification34K06 39A06 39A60
The authors are grateful to the editor and anonymous referees for their interesting comments. This work has received financial support from the Consellería de Cultura, Educación e Ordenación Universitaria (accreditation 2016-2019, ED431G/08 and reference competitive group 2014-2017, GRC2014/030) and the European Regional Development Fund (ERDF). The second author is partially supported by AEI of Spain (Under Grant MTM2016-75140-P) and Xunta de Galicia (under Grants GRC2015/004 and R2016-022).
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
- Banister E, Calvert T, Savage M, Bach T (1975) A systems model of training for athletic performance. Aust J Sports Med 7(3):57–61Google Scholar
- Kampakis S (2016) Predictive modelling of football injuries. arXiv preprint arXiv:1609.07480Google Scholar
- Kenney WL, Wilmore J, Costill D (2015) Physiology of sport and exercise 6th edition. Human kineticsGoogle Scholar
- Pfeiffer M (2008) Modeling the relationship between training and performance-a comparison of two antagonistic concepts. Int J Comput Sci Sport 7(2):13–32Google Scholar
- Viru AA, Viru M (2001) Biochemical monitoring of sport training. Human Kinetics, ChampaignGoogle Scholar