Demographic stochasticity in the SDE SIS epidemic model

David Greenhalgh; Yanfeng  Liang; Xuerong  Mao

doi:10.3934/dcdsb.2015.20.2859

Article Contents

2015, Volume 20, Issue 9: 2859-2884. Doi: 10.3934/dcdsb.2015.20.2859

This issue Previous Article Mathematical analysis of population migration and its effects to spread of epidemics Next Article Remarks on the free boundary problem of compressible Euler equations in physical vacuum with general initial densities

Demographic stochasticity in the SDE SIS epidemic model

1.
Department of Mathematics and Statistics, University of Strathclyde, Livingstone Tower, 26, Richmond Street, Gasgow G1 1XH
2.
Department of Mathematics and Statistics, University of Strathclyde, Livingstone Tower, 26, Richmond Street, Glasgow G1 1XH

Received: June 30, 2014

Revised: June 30, 2015

Published: October 2015

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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.

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Mathematics Subject Classification: Primary: 34F05, 60H10, 60H30, 92D30; Secondary: 93E03.

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