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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/79494 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/79494 http://eprints.org/relation/isIndexCodesVersionOf https://pure.iiasa.ac.at/id/document/79494 archive 5 disk0/00/01/48/04 2017-09-06 07:55:40 2021-08-27 17:29:19 2017-09-06 07:55:40 article show Diekmann O. Gyllenberg M. Metz J.A.J. 7506 pub prog_eep Linear chain trick; Delay-differential equation; Renewal equation; Markov chain; Physiologically structured populations; Epidemic models We consider the question of when delay systems, which are intrinsically infinite dimensional, can be represented by finite dimensional systems. Specifically, we give conditions for when all the information about the solutions of the delay system can be obtained from the solutions of a finite system of ordinary differential equations. For linear autonomous systems and linear systems with time-dependent input we give necessary and sufficient conditions and in the nonlinear case we give sufficient conditions. Most of our results for linear renewal and delay differential equations are known in different guises. The novelty lies in the approach which is tailored for applications to models of physiologically structured populations. Our results on linear systems with input and nonlinear systems are new. 2018-12 published Springer US 10.1007/s10884-017-9611-5 206 public Journal of Dynamics and Differential Equations 30 4 1439-1467 TRUE 1040-7294 FALSE info:eu-repo/semantics/article