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Springer, Journal of Mathematical Biology, 6-7(73), p. 1379-1398, 2016

DOI: 10.1007/s00285-016-0990-8

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Transit times and mean ages for nonautonomous and autonomous compartmental systems

Journal article published in 2016 by Martin Rasmussen, Alan Hastings, Matthew J. Smith, Folashade B. Agusto, Benito M. Chen Charpentier, Forrest M. Hoffman ORCID, Jiang Jiang ORCID, Katherine E. O. Todd Brown ORCID, Ying Wang, Ying-Ping Wang, Yiqi Luo
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

We develop a theory for transit times and mean ages for nonautonomous compartmental systems. Using the McKendrick???von F??orster 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 (CASA) 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.