Demographic stochasticity in the SDE SIS epidemic model

Greenhalgh, David and Liang, Yanfeng and Mao, Xuerong (2015) Demographic stochasticity in the SDE SIS epidemic model. Discrete and Continuous Dynamical Systems - Series B, 20 (9). pp. 2859-2884. ISSN 1531-3492 (https://doi.org/10.3934/dcdsb.2015.20.2859)

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Abstract

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.

ORCID iDs

Greenhalgh, David ORCID logoORCID: https://orcid.org/0000-0001-5380-3307, Liang, Yanfeng ORCID logoORCID: https://orcid.org/0000-0002-0592-876X and Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864;
  • Item type:Article
    ID code:54139
    Dates:
    Date
    Event
    30 September 2015
    Published
    25 July 2015
    Accepted
    Notes:This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and Continuous Dynamical Systems - Series B following peer review. The definitive publisher-authenticated version Greenhalgh, D., Liang, Y., & Mao, X. (2015). Demographic stochasticity in the SDE SIS epidemic model. Discrete and Continuous Dynamical Systems - Series B, 20(9), 2859-2884. 10.3934/dcdsb.2015.20.2859 is available online at: http://dx.doi.org/10.3934/dcdsb.2015.20.2859
    Subjects:Science > Mathematics > Probabilities. Mathematical statistics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:02 Sep 2015 13:44
    Last modified:11 Nov 2024 11:09
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/54139
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