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"People" meet "Markovians" - Individual-based modelling with hybrid stochastic systems

Hawker, M and Siekmann, I (2024) "People" meet "Markovians" - Individual-based modelling with hybrid stochastic systems. Journal of Biological Systems. ISSN 0218-3390

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Individual-based models (IBM) enable modellers to avoid far-reaching abstractions and strong simplifications by allowing for a state-based representation of individuals.The fact that IBMs are not represented using a standardised mathematical framework such as differential equations makes it harder to reproduce IBMs and introduces difficulties in the analysis of IBMs. We propose a model architecture based on representing individuals via Markov models. Individuals are coupled to populations—for which ndividuals are not explicitly represented—that are modelled by differential equations. The resulting models consisting of continuous-time finite-state Markov models coupled to systems of differential equations are examples of piecewise-deterministic Markov processes(PDMP). We will demonstrate that PDMPs, also known as hybrid stochastic systems ,allow us to design detailed state-based representations of individuals which at the same time can be systematically analysed by taking advantage of the theory of PDMPs.We will illustrate design and analysis of IBMs using PDMPs via the example of a predator that intermittently feeds on a logistically-growing prey by stochastically switching between a resting and a feeding state.This simple model shows a surprisingly rich dynamics which, nevertheless, can be comprehensively analysed using the theory of PDMPs.

Item Type: Article
Additional Information: Electronic version of an article published in Journal of Biological System, 2024, 10.1142/S0218339023400028 © 2024 World Scientific Publishing Company, https://doi.org/10.1142/S0218339023400028
Uncontrolled Keywords: 06 Biological Sciences; 08 Information and Computing Sciences; 09 Engineering; Bioinformatics
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Q Science > QH Natural history > QH301 Biology
Divisions: Computer Science & Mathematics
Publisher: World Scientific Publishing
SWORD Depositor: A Symplectic
Date Deposited: 12 Jan 2024 15:34
Last Modified: 28 Apr 2024 14:45
DOI or ID number: 10.1142/s0218339023400028
URI: https://researchonline.ljmu.ac.uk/id/eprint/22260
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