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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

Demographic stochasticity in the SDE SIS epidemic model

Pages: 2859 - 2884, Volume 20, Issue 9, November 2015      doi:10.3934/dcdsb.2015.20.2859

 
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David Greenhalgh - Department of Mathematics and Statistics, University of Strathclyde, Livingstone Tower, 26, Richmond Street, Gasgow G1 1XH, United Kingdom (email)
Yanfeng Liang - Department of Mathematics and Statistics, University of Strathclyde, Livingstone Tower, 26, Richmond Street, Glasgow G1 1XH, United Kingdom (email)
Xuerong Mao - Department of Mathematics and Statistics, University of Strathclyde, Livingstone Tower, 26, Richmond Street, Glasgow G1 1XH, United Kingdom (email)

Abstract: In this paper we discuss the stochastic differential equation (SDE) susceptible-infected-susceptible (SIS) epidemic model with demographic stoch-asticity. 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.

Keywords:  SIS epidemic model, demographic stochasticity, extinction, Feller test, stochastic differential equations, Brownian motion.
Mathematics Subject Classification:  Primary: 34F05, 60H10, 60H30, 92D30; Secondary: 93E03.

Received: July 2014;      Revised: July 2015;      Available Online: September 2015.

 References