The threshold of a stochastic SIRS epidemic model in a population with varying size

Yanan Zhao, Daqing Jiang, Xuerong Mao, Alison Gray

Research output: Contribution to journalArticle

10 Citations (Scopus)
168 Downloads (Pure)

Abstract

In this paper, a stochastic susceptible-infected-removed-susceptible (SIRS) epidemic model in a population with varying size is discussed. A new threshold ~R0 is identified which determines the outcome of the disease. When the noise is small, if ~R0 < 1, the infected proportion of the population disappears, so the disease dies out, whereas if ~R0 > 1, the infected proportion persists in the mean and we derive that the disease is endemic. Furthermore, when R0 > 1 and subject to a condition on some of the model parameters, we show that the solution of the stochastic model oscillates around the endemic equilibrium of the corresponding deterministic system with threshold R0, and the intensity of fluctuation is proportional to that of the white noise. On the other hand, when the noise is large, we find that a large noise intensity has the effect of suppressing the epidemic, so that it dies out. These results are illustrated by computer simulations.
Original languageEnglish
Pages (from-to)1277-1295
Number of pages19
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume20
Issue number4
Early online date28 Feb 2015
DOIs
Publication statusPublished - 2015

Keywords

  • SIRS epidemic model
  • SIRS
  • Lyapunov function

Fingerprint Dive into the research topics of 'The threshold of a stochastic SIRS epidemic model in a population with varying size'. Together they form a unique fingerprint.

  • Profiles

    Cite this