Demographic stochasticity in the SDE SIS epidemic model

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In this paper we discuss the stochastic differential equation (SDE) susceptible- infected-susceptible (SIS) epidemic model with demographic stochasticity. First we prove that the SDE has a unique nonnegative solution which is bounded above. Then we give conditions needed for the solution to become extinct. Next we use the Feller test to calculate the respective probabilities of the solution first hitting zero or the upper limit. We confirm our theoretical results with numerical simulations and then give simulations with realistic parameter values for two example diseases: gonorrhea and pneumococcus.
Original languageEnglish
Pages (from-to)2859-2884
Number of pages26
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number9
Publication statusPublished - 30 Sept 2015


  • SIS epidemic model
  • Brownian motion
  • stochastic differential equations
  • feller test
  • extinction
  • demographic stochasticity


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