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.
Original languageEnglish
Pages (from-to)684-704
Number of pages21
JournalPhysica A: Statistical Mechanics and its Applications
Volume462
Early online date25 Jun 2016
DOIs
Publication statusPublished - 15 Nov 2016

Keywords

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

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