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Approximating Quasi-Stationary Behaviour in Network-Based SIS Dynamics

Overton, CE, Wilkinson, RR, Loyinmi, A, Miller, JC and Sharkey, KJ (2021) Approximating Quasi-Stationary Behaviour in Network-Based SIS Dynamics. Bulletin of Mathematical Biology, 84 (1). ISSN 0092-8240

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Abstract

Deterministic approximations to stochastic Susceptible–Infectious–Susceptible models typically predict a stable endemic steady-state when above threshold. This can be hard to relate to the underlying stochastic dynamics, which has no endemic steady-state but can exhibit approximately stable behaviour. Here, we relate the approximate models to the stochastic dynamics via the definition of the quasi-stationary distribution (QSD), which captures this approximately stable behaviour. We develop a system of ordinary differential equations that approximate the number of infected individuals in the QSD for arbitrary contact networks and parameter values. When the epidemic level is high, these QSD approximations coincide with the existing approximation methods. However, as we approach the epidemic threshold, the models deviate, with these models following the QSD and the existing methods approaching the all susceptible state. Through consistently approximating the QSD, the proposed methods provide a more robust link to the stochastic models.

Item Type: Article
Uncontrolled Keywords: Science & Technology; Life Sciences & Biomedicine; Biology; Mathematical & Computational Biology; Life Sciences & Biomedicine - Other Topics; Moment-closure; Graph; Epidemic model; Stochastic; Pair approximation; STOCHASTIC-THEORY; EPIDEMIC MODELS; DISTRIBUTIONS; TIME; POPULATIONS; EXTINCTION; REINDEER; SPREAD; Humans; Communicable Diseases; Stochastic Processes; Models, Biological; Mathematical Concepts; Epidemics; Epidemic model; Graph; Moment-closure; Pair approximation; Stochastic; Communicable Diseases; Epidemics; Humans; Mathematical Concepts; Models, Biological; Stochastic Processes; 01 Mathematical Sciences; 06 Biological Sciences; Bioinformatics
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions: Computer Science & Mathematics
Publisher: Springer Nature
SWORD Depositor: A Symplectic
Date Deposited: 29 Jun 2022 10:42
Last Modified: 29 Jun 2022 10:45
DOI or Identification number: 10.1007/s11538-021-00964-7
URI: https://researchonline.ljmu.ac.uk/id/eprint/17176

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