SDE SIS epidemic models

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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.
Original languageEnglish
Publication statusUnpublished - 2012
EventWorkshop on Stochastic Modelling in Ecosystems - Glasgow, United Kingdom
Duration: 11 Jun 201212 Jun 2012


ConferenceWorkshop on Stochastic Modelling in Ecosystems
Country/TerritoryUnited Kingdom


  • Susceptible-infected-susceptible model
  • pneumococcus
  • gonorrhea
  • stationary distribution
  • basic reproduction number
  • persistence
  • extinction
  • stochastic differential equations
  • Brownian motion


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