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 (Unpublished)

Abstract

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 ORCID: https://orcid.org/0000-0002-6273-0637

Greenhalgh, David ORCID: https://orcid.org/0000-0001-5380-3307

Mao, Xuerong ORCID: https://orcid.org/0000-0002-6768-9864

Pan, Jiafeng ORCID: https://orcid.org/0000-0001-5993-3209

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• Item metadata

  Item type:	Conference or Workshop Item(Speech)
  ID code:	41322
  Dates:	Date Event 2012 Published
  Subjects:	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