Walker Benjamin J, Byrne Helen M
Department of Mathematics, University College London, Gordon Street, London, WC1H 0AY, UK.
Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Woodstock Road, Oxford, OX2 6GG, UK.
Bull Math Biol. 2025 May 12;87(6):71. doi: 10.1007/s11538-025-01446-w.
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.
逻辑斯蒂方程在应用数学中无处不在，是饱和增长的最小模型。在此，我们研究逻辑斯蒂增长模型对离散结构种群的广义推广，其动机源于从物种个体衰老到癌组织导致免疫细胞耗竭等一系列实例。通过对一系列具体例子的探索以及对多项式动力学的一般分析，我们推导出动力学对结构的依赖性导致精确的封闭低维矩方程的充要条件。此外，我们展示了粗粒度矩信息如何用于阐明结构动力学的细节，这在模型选择和假设检验方面具有直接潜力。本文属于特刊：数学与计算生物学中的问题、进展与展望。
