@Article{Rasmussen_JMathBiol_20161201,
 author		= {Martin Rasmussen and Alan Hastings and Matthew J. Smith and Folashade B. Agusto and Benito M. Chen-Charpentier and Forrest M. Hoffman and Jiang Jiang and Katherine E. O. Todd-Brown and Ying Wang and Ying-Ping Wang and Yiqi Luo},
 title		= {Transit Times and Mean Ages for Nonautonomous and Autonomous Compartmental Systems},
 journal	= JMathBiol,
 volume		= 73,
 number		= 6,
 pages		= {1379--1398},
 doi		= {10.1007/s00285-016-0990-8},
 day		= 1,
 month		= dec,
 year		= 2016,
 abstract	= {We develop a theory for transit times and mean ages for nonautonomous compartmental systems. Using the McKendrick--von F{\"o}rster 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.}
}