A critical review on applications of the Avrami equation beyond materials science

The Johnson-Mehl-Avrami-Kolmogorov (JMAK) formalization, often referred to as the Avrami equation, was originally developed to describe the progress of phase transformations in material systems. Many other transformations in the life, physical and social sciences follow a similar pattern of nucleati...

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Bibliographic Details
Published in:Journal of the Royal Society interface Vol. 20; no. 203; p. 20230242
Main Authors: Shirzad, Kiana, Viney, Christopher
Format: Journal Article
Language:English
Published: England 21.06.2023
Subjects:
COVID-19 - epidemiology
Humans
Materials Science
Thermodynamics
COVID-19
epidemiology
phase transformations
SIR (susceptible-infected-removed) model
Avrami equation
nucleation and growth
ISSN:1742-5662, 1742-5662
Online Access:Get more information
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Summary:The Johnson-Mehl-Avrami-Kolmogorov (JMAK) formalization, often referred to as the Avrami equation, was originally developed to describe the progress of phase transformations in material systems. Many other transformations in the life, physical and social sciences follow a similar pattern of nucleation and growth. The Avrami equation has been applied widely to modelling such phenomena, including COVID-19, regardless of whether they have a formal thermodynamic basis. We present here an analytical overview of such applications of the Avrami equation outside its conventional use, emphasizing examples from the life sciences. We discuss the similarities that at least partially justify the extended application of the model to such cases. We point out the limitations of such adoption; some are inherent to the model itself, and some are associated with the extended contexts. We also propose a reasoned justification for why the model performs well in many of these non-thermodynamic applications, even when some of its fundamental assumptions are not satisfied. In particular, we explore connections between the relatively accessible verbal and mathematical language of everyday nucleation- and growth-based phase transformations, represented by the Avrami equation, and the more challenging language of the classic SIR (susceptible-infected-removed) model in epidemiology.
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ISSN:1742-5662
1742-5662
DOI:10.1098/rsif.2023.0242