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

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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

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Epidemic Model
Endemic Equilibrium
White noise
Stochastic models
Stochastic Model
Proportion
Computer Simulation
Die
Directly proportional
Fluctuations
Computer simulation
Model

Keywords

  • SIRS epidemic model
  • SIRS
  • Lyapunov function

Cite this

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The threshold of a stochastic SIRS epidemic model in a population with varying size. / Zhao, Yanan; Jiang, Daqing; Mao, Xuerong; Gray, Alison.

In: Discrete and Continuous Dynamical Systems - Series B, Vol. 20, No. 4, 2015, p. 1277-1295.

Research output: Contribution to journalArticle

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