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First passage events in biological systems with non-exponential inter-event times

It is often possible to model the dynamics of biological systems as a series of discrete transitions between a finite set of observable states (or compartments). When the residence times in each state, or inter-event times more generally, are exponentially distributed, then one can write a set of or...

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Autores principales: Castro, Mario, López-García, Martín, Lythe, Grant, Molina-París, Carmen
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2018
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6180141/
https://www.ncbi.nlm.nih.gov/pubmed/30305644
http://dx.doi.org/10.1038/s41598-018-32961-7
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author Castro, Mario
López-García, Martín
Lythe, Grant
Molina-París, Carmen
author_facet Castro, Mario
López-García, Martín
Lythe, Grant
Molina-París, Carmen
author_sort Castro, Mario
collection PubMed
description It is often possible to model the dynamics of biological systems as a series of discrete transitions between a finite set of observable states (or compartments). When the residence times in each state, or inter-event times more generally, are exponentially distributed, then one can write a set of ordinary differential equations, which accurately describe the evolution of mean quantities. Non-exponential inter-event times can also be experimentally observed, but are more difficult to analyse mathematically. In this paper, we focus on the computation of first passage events and their probabilities in biological systems with non-exponential inter-event times. We show, with three case studies from Molecular Immunology, Virology and Epidemiology, that significant errors are introduced when drawing conclusions based on the assumption that inter-event times are exponentially distributed. Our approach allows these errors to be avoided with the use of phase-type distributions that approximate arbitrarily distributed inter-event times.
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spelling pubmed-61801412018-10-15 First passage events in biological systems with non-exponential inter-event times Castro, Mario López-García, Martín Lythe, Grant Molina-París, Carmen Sci Rep Article It is often possible to model the dynamics of biological systems as a series of discrete transitions between a finite set of observable states (or compartments). When the residence times in each state, or inter-event times more generally, are exponentially distributed, then one can write a set of ordinary differential equations, which accurately describe the evolution of mean quantities. Non-exponential inter-event times can also be experimentally observed, but are more difficult to analyse mathematically. In this paper, we focus on the computation of first passage events and their probabilities in biological systems with non-exponential inter-event times. We show, with three case studies from Molecular Immunology, Virology and Epidemiology, that significant errors are introduced when drawing conclusions based on the assumption that inter-event times are exponentially distributed. Our approach allows these errors to be avoided with the use of phase-type distributions that approximate arbitrarily distributed inter-event times. Nature Publishing Group UK 2018-10-10 /pmc/articles/PMC6180141/ /pubmed/30305644 http://dx.doi.org/10.1038/s41598-018-32961-7 Text en © The Author(s) 2018 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Article
Castro, Mario
López-García, Martín
Lythe, Grant
Molina-París, Carmen
First passage events in biological systems with non-exponential inter-event times
title First passage events in biological systems with non-exponential inter-event times
title_full First passage events in biological systems with non-exponential inter-event times
title_fullStr First passage events in biological systems with non-exponential inter-event times
title_full_unstemmed First passage events in biological systems with non-exponential inter-event times
title_short First passage events in biological systems with non-exponential inter-event times
title_sort first passage events in biological systems with non-exponential inter-event times
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6180141/
https://www.ncbi.nlm.nih.gov/pubmed/30305644
http://dx.doi.org/10.1038/s41598-018-32961-7
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