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

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


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. 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.

Original languageEnglish (US)
Pages (from-to)1379-1398
Number of pages20
JournalJournal of Mathematical Biology
Issue number6-7
StatePublished - Dec 1 2016
Externally publishedYes


  • CASA model
  • Carbon cycle
  • Compartmental system
  • Exponential stability
  • Linear system
  • McKendrick–von Förster equation
  • Mean age
  • Nonautonomous dynamical system
  • Transit time

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics


Dive into the research topics of 'Transit times and mean ages for nonautonomous and autonomous compartmental systems'. Together they form a unique fingerprint.

Cite this