Rasmussen, MartinHastings, AlanSmith, Matthew J.Agusto, Folashade B.Chen-Charpentier, Benito M.Hoffman, Forrest M.Jiang, JiangTodd-Brown, Katherine E. O.Wang, YingWang, Ying-PingLuo, Yiqi2016-12-012016-12-012016-04-01Transit times and mean ages for nonautonomous and autonomous compartmental systems Martin Rasmussen, Alan Hastings, Matthew J. Smith, Folashade B. Agusto, Benito M. Chen-Charpentier, Forrest M. Hoffman, Jiang Jiang, Katherine E. O. Todd-Brown, Ying Wang, Ying-Ping Wang, Yiqi Luo J Math Biol. 2016; 73(6): 1379–1398. Published online 2016 Apr 1. doi: 10.1007/s00285-016-0990-8https://hdl.handle.net/1808/22113We develop a theory for transit times and mean ages for nonautonomous compartmental systems. Using the McKendrick–von Förster equation, we show that the mean ages of mass in a compartmental system satisfy a linear nonautonomous ordinary differential equation that is exponentially stable. We then define a nonautonomous version of transit time as the mean age of mass leaving the compartmental system at a particular time and show that our nonautonomous theory generalises the autonomous case. We apply these results to study a nine-dimensional nonautonomous compartmental system modeling the terrestrial carbon cycle, which is a modification of the Carnegie–Ames–Stanford approach model, and we demonstrate that the nonautonomous versions of transit time and mean age differ significantly from the autonomous quantities when calculated for that model.Copyright © The Author(s) 2016 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.http://creativecommons.org/licenses/by/4.0/Carbon cycleCASA modelCompartmental systemExponential stabilityLinear systemMcKendrick-von Forster equationMean ageNonautonomous dynamical systemTransit timeArticle10.1007/s00285-016-0990-8openAccess