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

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Greenhalgh, D. and Liang, Y. and Mao, X. (2016) Modelling the effect of telegraph noise in the SIRS epidemic model using Markovian switching. Physica A: Statistical Mechanics and its Applications, 462. pp. 684-704. ISSN 0378-4371 (https://doi.org/10.1016/j.physa.2016.06.125)

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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.

ORCID iDs

Greenhalgh, D. ORCID logoORCID: https://orcid.org/0000-0001-5380-3307, Liang, Y. ORCID logoORCID: https://orcid.org/0000-0002-0592-876X and Mao, X. ORCID logoORCID: https://orcid.org/0000-0002-6768-9864;
CORE (COnnecting REpositories)