A stochastic differential equation SIS epidemic model

Gray, Alison and Greenhalgh, David and Hu, L. and Mao, Xuerong and Pan, Jiafeng (2011) A stochastic differential equation SIS epidemic model. SIAM Journal on Applied Mathematics, 71 (3). pp. 876-902. (https://doi.org/10.1137/10081856X)

[thumbnail of SDE_SIS_SIAP_Revision.pdf] PDF. Filename: SDE_SIS_SIAP_Revision.pdf
Preprint
Download (5MB)

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 logoORCID: https://orcid.org/0000-0002-6273-0637, Greenhalgh, David ORCID logoORCID: https://orcid.org/0000-0001-5380-3307, Hu, L., Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864 and Pan, Jiafeng ORCID logoORCID: https://orcid.org/0000-0001-5993-3209;
  • Item type:Article
    ID code:29592
    Dates:
    Date
    Event
    2011
    Published
    2 June 2011
    Published Online
    Notes:Changed last author
    Keywords:susceptible-infected-susceptible model, pneumococcus , gonorrhea, stationary distribution, basic reproduction number, persistence, extinction, stochastic differential equations, Brownian motion, Probabilities. Mathematical statistics, Applied Mathematics
    Subjects:Science > Mathematics > Probabilities. Mathematical statistics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:11 Aug 2011 13:57
    Last modified:27 May 2022 00:53
    URI:https://strathprints.strath.ac.uk/id/eprint/29592
CORE (COnnecting REpositories)