Approximating Quasi-Stationary Behaviour in Network-Based SIS Dynamics

Overton, Christopher E, Wilkinson, Robert R, Loyinmi, Adedapo, Miller, Joel C and Sharkey, Kieran J ORCID: 0000-0002-7210-9246 (2022) Approximating Quasi-Stationary Behaviour in Network-Based SIS Dynamics. BULLETIN OF MATHEMATICAL BIOLOGY, 84 (1). 4-.

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Official URL: http://dx.doi.org/10.1007/s11538-021-00964-7

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:	Moment-closure, Graph, Epidemic model, Stochastic, Pair approximation
Divisions:	Faculty of Science and Engineering > School of Physical Sciences
Depositing User:	Symplectic Admin
Date Deposited:	16 Aug 2022 15:33
Last Modified:	18 Jan 2023 20:56
DOI:	10.1007/s11538-021-00964-7
Open Access URL:	https://arxiv.org/abs/2208.05901
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3157531