Stationary distribution of stochastic SIRS epidemic model with standard incidence

Yanan Zhao; Yuguo Lin; Daqing Jiang; Xuerong Mao; Yong Li

doi:10.3934/dcdsb.2016051

Stationary distribution of stochastic SIRS epidemic model with standard incidence

Yanan Zhao, Yuguo Lin, Daqing Jiang, Xuerong Mao, Yong Li

Mathematics And Statistics

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Abstract

We study stochastic versions of a deterministic SIRS (Susceptible, Infective, Recovered, Susceptible) epidemic model with standard incidence. We study the existence of a stationary distribution of stochastic system by the theory of integral Markov semigroup. We prove the distribution densities of the solutions can converge to an invariant density in L¹. This shows the system is ergodic. The presented results are demonstrated by numerical simulations.

Original language	English
Pages (from-to)	2363-2378
Number of pages	16
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	21
Issue number	7
Early online date	31 Aug 2016
DOIs	https://doi.org/10.3934/dcdsb.2016051
Publication status	Published - 30 Sept 2016

Keywords

stationary distribution
diffusion process
Markov semigroups
asymptotic stability
epidemic model
SIRS

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Zhao-etal-DCDSSB-2016-Stationary-distribution-of-stochastic-SIRS-epidemic-modelAccepted author manuscript, 286 KB

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abstract = "We study stochastic versions of a deterministic SIRS (Susceptible, Infective, Recovered, Susceptible) epidemic model with standard incidence. We study the existence of a stationary distribution of stochastic system by the theory of integral Markov semigroup. We prove the distribution densities of the solutions can converge to an invariant density in L1. This shows the system is ergodic. The presented results are demonstrated by numerical simulations.",

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AU - Lin, Yuguo

AU - Jiang, Daqing

AU - Mao, Xuerong

AU - Li, Yong

N1 - 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 Zhao, Y., Lin, Y., Jiang, D., Mao, X., & Li, Y. (2016). Stationary distribution of stochastic SIRS epidemic model with standard incidence. Discrete and Continuous Dynamical Systems - Series B, 21(7). is available online at: http://dx.doi.org/10.3934/dcdsb.2016051

PY - 2016/9/30

Y1 - 2016/9/30

N2 - We study stochastic versions of a deterministic SIRS (Susceptible, Infective, Recovered, Susceptible) epidemic model with standard incidence. We study the existence of a stationary distribution of stochastic system by the theory of integral Markov semigroup. We prove the distribution densities of the solutions can converge to an invariant density in L1. This shows the system is ergodic. The presented results are demonstrated by numerical simulations.

AB - We study stochastic versions of a deterministic SIRS (Susceptible, Infective, Recovered, Susceptible) epidemic model with standard incidence. We study the existence of a stationary distribution of stochastic system by the theory of integral Markov semigroup. We prove the distribution densities of the solutions can converge to an invariant density in L1. This shows the system is ergodic. The presented results are demonstrated by numerical simulations.

KW - stationary distribution

KW - diffusion process

KW - Markov semigroups

KW - asymptotic stability

KW - epidemic model

KW - SIRS

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DO - 10.3934/dcdsb.2016051

M3 - Article

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JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

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ER -

Stationary distribution of stochastic SIRS epidemic model with standard incidence

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