# On discretely structured growth models and their moments

Source: [On discretely structured growth models and their moments](<https://www.sota2.com/research/paper/68fa5f731e209131ce9e9ff9>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T19:17:45.746Z

Authors: Benjamin J. Walker, Helen M. Byrne

Published: 2024-10-02T09:44:53.000Z

## Abstract

The logistic equation is ubiquitous in applied mathematics as a minimal model of saturating growth. Here, we examine a broad generalisation of the logistic growth model to discretely structured populations, motivated by examples that range from the ageing of individuals in a species to immune cell exhaustion by cancerous tissue. Through exploration of a range of concrete examples and a general analysis of polynomial kinetics, we derive necessary and sufficient conditions for the dependence of the kinetics on structure to result in closed, low-dimensional moment equations that are exact. Further, we showcase how coarse-grained moment information can be used to elucidate the details of structured dynamics, with immediate potential for model selection and hypothesis testing. This paper belongs to the special collection: Problems, Progress and Perspectives in Mathematical and Computational Biology.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2410.01862>)

[PDF](<https://arxiv.org/pdf/2410.01862.pdf>)