Stochastic dynamical behavior of SIRS epidemic models with random perturbation

Qingshan Yang, Xuerong Mao

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

In this paper, we consider a stochastic SIRS model with parameter perturbation, which is a standard technique in modeling population dynamics. In our model, the disease transmission coefficient and the removal rates are all affected by noise. We show that the stochastic model has a unique positive solution as it is essential in any population model. Then we establish conditions for extinction
or persistence of the infectious disease. When the infective part is forced to expire, the susceptible part converges weakly to an inverse-gamma distribution with explicit shape and scale parameters. In case of persistence, by new stochastic Lyapunov functions, we show the ergodic property and positive
recurrence of the stochastic model. We also derive an estimate for the mean of the stationary distribution. The analytical results are all verified by computer simulations, including examples based on experiments in laboratory populations of mice.
LanguageEnglish
Pages1003-1025
Number of pages23
JournalMathematical Biosciences and Engineering
Volume11
Issue number4
DOIs
Publication statusPublished - Mar 2014

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Random Perturbation
Epidemic Model
Stochastic models
Dynamical Behavior
Stochastic Model
Persistence
Population Dynamics
Computer Simulation
Population
Communicable Diseases
Noise
Population dynamics
Transmission Coefficient
Parameter Perturbation
Infectious Diseases
Gamma distribution
Shape Parameter
Scale Parameter
Lyapunov functions
Population Model

Keywords

  • ergodic property
  • positive recurrence
  • stochastic Lyapunov functions
  • stochastic SIRS models
  • infectious diseases
  • extinction

Cite this

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Stochastic dynamical behavior of SIRS epidemic models with random perturbation. / Yang, Qingshan; Mao, Xuerong.

In: Mathematical Biosciences and Engineering, Vol. 11, No. 4, 03.2014, p. 1003-1025.

Research output: Contribution to journalArticle

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