Home > Publications . Search All . Browse All . Country . Browse PSC Pubs . PSC Report Series

PSC In The News

RSS Feed icon

Lam discusses shifts in global population, past and future

Thompson says LGBT social movement will bring new strength in push for tighter gun control

Yang says devalued pound will decrease resources for the families of migrant workers in Britain

Highlights

Frey's new report explores how the changing US electorate could shape the next 5 presidential elections, 2016 to 2032

U-M's Data Science Initiative offers expanded consulting services via CSCAR

Elizabeth Bruch promoted to Associate Professor

Susan Murphy elected to the National Academy of Sciences

Next Brown Bag

PSC Brown Bags
will resume fall 2016

Qualitative Theory of Compartmental Systems With Lags

Archived Abstract of Former PSC Researcher

Jacquez, J.A., and Carl P. Simon. 2002. "Qualitative Theory of Compartmental Systems With Lags." Mathematical Biosciences, 180(specialissue): 329-362.

Dynamic models of many processes in the biological and physical sciences give systems of ordinary differential equations called compartmental systems. Often, these systems include time lags; in this context, continuous probability density functions (pdfs) of lags are far more important than discrete lags. There is a relatively complete theory of compartmental systems without lags, both linear and non-linear [SIAM Rev. 35 (1993) 43]. The authors extend their previous work on compartmental systems without lags to show that, for discrete lags and for a very large class of pdfs of continuous lags, compartmental systems with lags are equivalent to larger compartmental systems without lags. Consequently, the properties of compartmental systems with lags are the same as those of compartmental systems without lags. For a very large class of compartmental systems with time lags, one can show that the time lags themselves can be generated by compartmental systems without lags. Thus, such systems can be partitioned into a main system, which is the original system without the lags, plus compartmental subsystems without lags that generate the lags. The latter may be linear or non-linear and may be. inserted into main systems that are linear or non-linear. The state variables of the compartmental lag subsystems are hidden variables in the formulation with explicit lags. (C) 2002 Elsevier Science Inc. All rights reserved.

Browse | Search : All Pubs | Next