Connections between compartmental systems with pipes and integro-differential equations

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Compartmental models are a frequently used tool for the mathematical description of physiologic processes. In the classical models the mass transport between compartments is assumed instant (requiring no time). In that case the model equations are ordinary differential equations. In this paper we give the mathematical description of models in which the mass transport between compartments requires a given definite time or transit times are distributed according to given probability distribution functions. We call such models compartmental systems with pipes and show that their mathematical description can be given by delay differential equations as well as by certain integro-differential equations. In addition to the qualitative analysis of the solutions of the equations describing the pipe-compartmental models, we also investigate the behavior of the equilibrium state as well as the existence of limits of the solutions.

Original languageEnglish
Pages (from-to)1215-1238
Number of pages24
JournalMathematical Modelling
Issue number9-12
Publication statusPublished - 1986


ASJC Scopus subject areas

  • Engineering(all)

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