Bulletin of Mathematical Biology

, Volume 81, Issue 6, pp 1867–1884 | Cite as

An Improved Version of the Classical Banister Model to Predict Changes in Physical Condition

  • Marcos MatabuenaEmail author
  • Rosana Rodríguez-López


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.


Mathematical models Functional differential equations Difference equations 

Mathematics Subject Classification

34K06 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.


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Copyright information

© Society for Mathematical Biology 2019

Authors and Affiliations

  1. 1.Centro de Investigación en Tecnoloxías da Información (CiTIUS)Universidade de Santiago de CompostelaSantiago de CompostelaSpain
  2. 2.Departamento de Estatística, Análise Matemática e Optimización, Facultade de MatemáticasUniversidade de Santiago de CompostelaSantiago de CompostelaSpain

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