SDE SIS epidemic models
Gray, Alison and Greenhalgh, David and Mao, Xuerong and Pan, Jiafeng (2012) SDE SIS epidemic models. In: Workshop on Stochastic Modelling in Ecosystems, 2012-06-11 - 2012-06-12. (Unpublished)
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In this paper we extend the classical susceptible-infected-susceptible epidemic model from a deterministic framework to a stochastic one and formulate it as a stochastic differential equation (SDE) for the number of infectious individuals $I(t)$. We then prove that this SDE has a unique global positive solution $I(t)$ and establish conditions for extinction and persistence of $I(t)$. We discuss perturbation by stochastic noise. In the case of persistence we show the existence of a stationary distribution and derive expressions for its mean and variance. The results are illustrated by computer simulations, including two examples based on real-life diseases.
ORCID iDs
Gray, Alison
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Item type: Conference or Workshop Item(Speech) ID code: 41322 Dates: DateEvent2012PublishedSubjects: Science > Mathematics > Probabilities. Mathematical statistics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 02 Oct 2012 10:05 Last modified: 11 Nov 2024 16:35 URI: https://strathprints.strath.ac.uk/id/eprint/41322