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.
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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.
Creators(s): |
Gray, Alison ![]() ![]() ![]() ![]() | Item type: | Article |
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ID code: | 29592 |
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: | 19 Feb 2021 04:31 |
URI: | https://strathprints.strath.ac.uk/id/eprint/29592 |
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