On discretely structured growth models and their moments

Journal article

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.

Authors: Walker, B; Byrne, H

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Bulletin of Mathematical Biology More from this journal
• Volume: 87
• Issue: 6
• Article number: 71
• Publication date: 2025-05-12
• Acceptance date: 2025-04-03
• DOI: 10.1007/s11538-025-01446-w
• EISSN: 1522-9602
• ISSN: 0092-8240
• Language: English
• Keywords: logistic growth; structured models; moment equations