Transit times and mean ages for nonautonomous and autonomous compartmental systems

Rasmussen, Martin; Hastings, Alan; Smith, Matthew J.; Agusto, Folashade B.; Chen-Charpentier, Benito M.; Hoffman, Forrest M.; Jiang, Jiang; Todd-Brown, Katherine E.  O.; Wang, Ying; Wang, Ying-Ping; Luo, Yiqi

doi:10.1007/s00285-016-0990-8

Title: Transit times and mean ages for nonautonomous and autonomous compartmental systems

Journal Article · Fri Apr 01 00:00:00 EDT 2016 · Journal of Mathematical Biology

DOI:https://doi.org/10.1007/s00285-016-0990-8· OSTI ID:1333444

Rasmussen, Martin; Hastings, Alan; Smith, Matthew J.; Agusto, Folashade B.; Chen-Charpentier, Benito M.; Hoffman, Forrest M.; Jiang, Jiang; Todd-Brown, Katherine E. O.; Wang, Ying; Wang, Ying-Ping; Luo, Yiqi

We develop a theory for residence times and mean ages for nonautonomous compartmental systems. Using the McKendrick–von Forster 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 residence time as the mean age of mass leaving the compartmental system at a particular time and show that our nonautonomous theory is consistent with the autonomous case. We apply these results to study a nine-dimensional nonautonomous compartmental system modeling the carbon cycle, which is a simplified version of the Carnegie–Ames–Stanford approach (CASA) model.

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Research Organization:: Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

Sponsoring Organization:: USDOE

DOE Contract Number:: AC05-76RL01830

OSTI ID:: 1333444

Report Number(s):: PNNL-SA-114617

Journal Information:: Journal of Mathematical Biology, Vol. 73, Issue 6-7; ISSN 0303-6812

Publisher:: Springer

Country of Publication:: United States

Language:: English

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