Modelling the effect of telegraph noise in the SIRS epidemic model using Markovian switching

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Abstract

We discuss the effect of introducing telegraph noise, which is an example of an environmental noise, into the susceptible-infectious-recovered-susceptible (SIRS) model by examining the model using a finite-state Markov Chain (MC). First we start with a two-state MC and show that there exists a unique nonnegative solution and establish the conditions for extinction and persistence. We then explain how the results can be generalised to a finite-state MC. The results for the SIR (Susceptible-Infectious-Removed) model with Markovian Switching (MS) are a special case. Numerical simulations are produced to confirm our theoretical results.
LanguageEnglish
Pages684-704
Number of pages21
JournalPhysica A: Statistical Mechanics and its Applications
Volume462
Early online date25 Jun 2016
DOIs
Publication statusPublished - 15 Nov 2016

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Markovian Switching
Markov chains
Epidemic Model
Markov chain
Modeling
Nonnegative Solution
Extinction
Persistence
extinction
Model
Numerical Simulation
simulation

Keywords

  • Markov Chain
  • Lyapunov stability
  • environmental noise
  • persistence
  • extinction
  • SIRS epidemic model

Cite this

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title = "Modelling the effect of telegraph noise in the SIRS epidemic model using Markovian switching",
abstract = "We discuss the effect of introducing telegraph noise, which is an example of an environmental noise, into the susceptible-infectious-recovered-susceptible (SIRS) model by examining the model using a finite-state Markov Chain (MC). First we start with a two-state MC and show that there exists a unique nonnegative solution and establish the conditions for extinction and persistence. We then explain how the results can be generalised to a finite-state MC. The results for the SIR (Susceptible-Infectious-Removed) model with Markovian Switching (MS) are a special case. Numerical simulations are produced to confirm our theoretical results.",
keywords = "Markov Chain, Lyapunov stability, environmental noise, persistence, extinction, SIRS epidemic model",
author = "D. Greenhalgh and Y. Liang and X. Mao",
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AU - Greenhalgh, D.

AU - Liang, Y.

AU - Mao, X.

PY - 2016/11/15

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N2 - We discuss the effect of introducing telegraph noise, which is an example of an environmental noise, into the susceptible-infectious-recovered-susceptible (SIRS) model by examining the model using a finite-state Markov Chain (MC). First we start with a two-state MC and show that there exists a unique nonnegative solution and establish the conditions for extinction and persistence. We then explain how the results can be generalised to a finite-state MC. The results for the SIR (Susceptible-Infectious-Removed) model with Markovian Switching (MS) are a special case. Numerical simulations are produced to confirm our theoretical results.

AB - We discuss the effect of introducing telegraph noise, which is an example of an environmental noise, into the susceptible-infectious-recovered-susceptible (SIRS) model by examining the model using a finite-state Markov Chain (MC). First we start with a two-state MC and show that there exists a unique nonnegative solution and establish the conditions for extinction and persistence. We then explain how the results can be generalised to a finite-state MC. The results for the SIR (Susceptible-Infectious-Removed) model with Markovian Switching (MS) are a special case. Numerical simulations are produced to confirm our theoretical results.

KW - Markov Chain

KW - Lyapunov stability

KW - environmental noise

KW - persistence

KW - extinction

KW - SIRS epidemic model

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JO - Physica A: Statistical Mechanics and its Applications

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