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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.
Original language | English |
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Pages (from-to) | 876-902 |
Number of pages | 27 |
Journal | SIAM Journal on Applied Mathematics |
Volume | 71 |
Issue number | 3 |
Early online date | 2 Jun 2011 |
DOIs | |
Publication status | Published - 2011 |
Keywords
- susceptible-infected-susceptible model
- pneumococcus
- gonorrhea
- stationary distribution
- basic reproduction number
- persistence
- extinction
- stochastic differential equations
- Brownian motion
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PME seminar
Pan, J. (Invited speaker)
10 Dec 2014Activity: Participating in or organising an event types › Participation in workshop, seminar, course