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Quantitative Biology > Populations and Evolution

arXiv:2008.01318 (q-bio)
[Submitted on 4 Aug 2020]

Title:Time Is Of The Essence: Incorporating Phase-Type Distributed Delays And Dwell Times Into ODE Models

Authors:Paul J. Hurtado, Cameron Richards
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Abstract:Ordinary differential equations (ODE) models have a wide variety of applications in the fields of mathematics, statistics, and the sciences. Though they are widely used, these models are sometimes viewed as inflexible with respect to the incorporation of time delays. The Generalized Linear Chain Trick (GLCT) serves as a way for modelers to incorporate much more flexible delay or dwell time distribution assumptions than the usual exponential and Erlang distributions. In this paper we demonstrate how the GLCT can be used to generate new ODE models by generalizing or approximating existing models to yield much more general ODEs with phase-type distributed delays or dwell times.
Comments: 16 pages, 1 figure
Subjects: Populations and Evolution (q-bio.PE); Dynamical Systems (math.DS)
MSC classes: 92B99, 37N25, 37M05
Cite as: arXiv:2008.01318 [q-bio.PE]
  (or arXiv:2008.01318v1 [q-bio.PE] for this version)
  https://doi.org/10.48550/arXiv.2008.01318
Journal reference: Mathematics in Applied Sciences and Engineering, 1(4):274-438 (2020)
Related DOI: https://doi.org/10.5206/mase/10857

Submission history

From: Paul Hurtado [view email]
[v1] Tue, 4 Aug 2020 04:09:56 UTC (129 KB)
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