Transit times and mean ages for nonautonomous and autonomous compartmental systems
- Imperial College London, London (United Kingdom)
- Univ. of California, Davis, CA (United States)
- Microsoft Research, Cambridge (United Kingdom)
- Univ. of Kansas, Lawrence, KS (United States)
- Univ. of Texas, Arlington, TX (United States)
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Univ. of Oklahoma, Norman, OK (United States)
- Univ. of Oklahoma, Norman, OK (United States); Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
- CSIRO Oceans and Atmosphere, Aspendale, VIC (Australia)
We 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. Lastly, 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.
- Research Organization:
- Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- Grant/Contract Number:
- EP/I004165/1; W911NF-13-1-0305; AC05-00OR22725
- OSTI ID:
- 1251563
- Alternate ID(s):
- OSTI ID: 1327769
- Journal Information:
- Journal of Mathematical Biology, Vol. 73, Issue 6-7; ISSN 0303-6812
- Publisher:
- SpringerCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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