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Hyperbolic Representation of the Richards Growth Model

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  • Marcin Molski

    (Quantum Chemistry Department, Adam Mickiewicz University of Poznań, Uniwersytetu Poznańskiego 8, 61-614 Poznań, Poland)

Abstract

The phenomenological universalities (PU) approach is employed to derive the Richards growth function in the unknown hyperbolic representation. The formula derived can be applied in theoretical modeling of sigmoid and involuted growth of biological systems. In the model proposed, the exponent in the Richards function has the following clear biological meaning: it describes the number of cells doubling, leading to an increase in a biomass of the system from m 0 (birth or hatching mass) to the limiting value m ∞ (mass at maturity). The generalized form of the universal growth function is derived. It can be employed in fitting the weight–age data for a variety of biological systems, including copepods, tumors, fish, birds, mammals and dinosaurs. Both the PU methodology and the Richards model can be effectively applied in the theoretical modeling of infectious disease outbreaks. To substantiate this assertion, the simplest PU-SIR (Susceptible–Infective–Removed) epidemiological model is considered. In this approach, it is assumed that the number of births is approximately equal to the number of deaths, while the impact of recovered (quarantined) individuals on the dynamics of the infection is negligible.

Suggested Citation

  • Marcin Molski, 2025. "Hyperbolic Representation of the Richards Growth Model," Mathematics, MDPI, vol. 13(8), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:8:p:1316-:d:1636628
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    References listed on IDEAS

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    1. Yoshinobu Tamura & Shigeru Yamada, 2009. "Flexible Stochastic Differential Equation Modeling For Open-Source-Software Reliability Assessment," World Scientific Book Chapters, in: Tadashi Dohi & Shunji Osaki & Katsushige Sawaki (ed.), Recent Advances In Stochastic Operations Research II, chapter 20, pages 285-300, World Scientific Publishing Co. Pte. Ltd..
    2. P. K. Kapur & Sameer Anand & Shigeru Yamada & Venkata S. S. Yadavalli, 2009. "Stochastic Differential Equation-Based Flexible Software Reliability Growth Model," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-15, July.
    3. Geoffrey B. West & James H. Brown & Brian J. Enquist, 2001. "A general model for ontogenetic growth," Nature, Nature, vol. 413(6856), pages 628-631, October.
    4. Barberis, L. & Condat, C.A., 2012. "Describing interactive growth using vector universalities," Ecological Modelling, Elsevier, vol. 227(C), pages 56-63.
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