A Matter of Maturity: To Delay or Not to Delay? Continuous-Time Compartmental Models of Structured Populations in the Literature 2000–2016

Document Type

Article

Publication Date

2-1-2018

Keywords

Age structure, Compartmental model, Continuous‐time population model, Delay differential equation, Maturation rate, McKendrick–von Foerster partial differential equation, Ordinary differential equation, Stage structure

Abstract

Structured compartmental models in mathematical biology track age classes, stage classes, or size classes of a population. Structured modeling becomes important when mechanistic formulations or intraspecific interactions are class‐dependent. The classic derivation of such models from partial differential equations produces time delays in the transition rates between classes. In particular, the transition from juvenile to adult has a delay equal to the maturation period of the organism. In the literature, many structured compartmental models, posed as ordinary differential equations, omit this delay. We reviewed occurrences of continuous‐time compartmental models for age‐ and stage‐structured populations in the recent literature (2000–2016) to discover which papers did so. About half of the 249 papers we reviewed used a maturation delay. Papers with ecological models were more likely to have the delay than papers with disease models, and mathematically focused papers were more likely to have the delay than biologically focused papers.

Journal Title

Natural Resource Modeling

Volume

31

Issue

1

DOI

10.1111/nrm.12160

First Department

Mathematics

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@ the James White Library

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