At first glance, a mathematical model that describes how quickly materials transform from one phase to another might seem to have few other practical applications.
But what if this kind of model could be adapted to predict the spread of the next pandemic?
Two UC Merced researchers have been studying the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation, which helps scientists describe and predict how materials change over time, such as when crystals grow from a liquid, or when a new solid phase with a different composition emerges in an existing solid.
In 2023, chemical and materials engineering Professor Christopher Viney and graduate researcher Kiana Shirzad published a review paper in the Journal of the Royal Society Interface, critically assessing the applicability of the JMAK equation in fields beyond materials science. The Royal Society, based in London, is the world's oldest scientific academy in continuous existence. Shirzad and Viney's 2023 paper was the top-cited work for the journal in 2024.
Now, Shirzad and Viney have published a follow-up paper in another Royal Society journal, Royal Society Open Science. They address some basic limitations of the original JMAK equation that the physical world doesn't always adhere to - that regions of the transformed material appear either all at once or at a steady rate, and that they grow at a constant speed. The physical world is not as predictable.
Shirzad and Viney improved the equation to handle more realistic and complicated changes over time, while maintaining its intuitive roots and keeping the math accessible at a "Calculus I" level. Their version of the equation explains how its parameters can adopt values that extend beyond the classical limits, which can help with modeling phase transformations and their analogs in a wider variety of materials and systems.
In their 2023 work, Shirzad and Viney examined when using the JMAK equation in other fields can be appropriate - and when it isn't. They were particularly interested in using the equation to describe the spread of COVID-19. Typically, that sort of work is done through the much more challenging mathematics of classic epidemiology models.
The 2020 pandemic made it clear that scientists and community leaders need to describe and predict the spread of a virus effectively, using analogies and data-driven models that can help to persuade broad and often skeptical audiences about ways to best "flatten the curve."
"The relative simplicity of the JMAK equation, and the accessible language of everyday transformations such as solidification of liquid water into ice, provide a potentially useful communication framework," the researchers said. "Our enhanced version of the equation is applicable to the quantitative modeling of the rate at which a pandemic can spread through a population."
Viney and Shirzad are now preparing a third paper, in which they will report the details of their work on fitting the enhanced JMAK equation to the spread of COVID-19 in several countries.
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