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

D. Greenhalgh, Y. Liang and X. Mao

Physica A: Statistical Mechanics and its Applications, 2016, vol. 462, issue C, 684-704

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; SIRS epidemic model; Extinction; Persistence; Environmental noise; Lyapunov stability (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (9)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437116304009
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:462:y:2016:i:c:p:684-704

DOI: 10.1016/j.physa.2016.06.125

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().