Transit 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

arXiv · 1603.02497

Transit 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

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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.

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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. 2016-03-08. Transit times and mean ages for nonautonomous and autonomous compartmental systems. https://arxiv.org/abs/1603.02497

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