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

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Abstract

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.

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Acknowledgements

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).

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Authors and Affiliations

  1. Centro de Investigación en Tecnoloxías da Información (CiTIUS), Universidade de Santiago de Compostela, Santiago de Compostela, Spain

    Marcos Matabuena

  2. Departamento de Estatística, Análise Matemática e Optimización, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, Spain

    Rosana Rodríguez-López

Authors
  1. Marcos Matabuena
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  2. Rosana Rodríguez-López
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Correspondence to Marcos Matabuena.

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A Appendix

A Appendix

In this appendix, we recall the different approximations obtained through the new models with delay formulated (see Table 1). These approximations are computationally appropriate to estimate the parameters of the models in a practical situation.

Table 1 Positive and negative effects g(t) and h(t), and physical condition p(t)
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Matabuena, M., Rodríguez-López, R. An Improved Version of the Classical Banister Model to Predict Changes in Physical Condition. Bull Math Biol 81, 1867–1884 (2019). https://doi.org/10.1007/s11538-019-00588-y

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