期刊
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
卷 462, 期 -, 页码 684-704出版社
ELSEVIER
DOI: 10.1016/j.physa.2016.06.125
关键词
Markov Chain; SIRS epidemic model; Extinction; Persistence; Environmental noise; Lyapunov stability
资金
- EPSRC (EPSRC DTP Grant) [EP/K503174/1]
- Leverhulme Trust [RF-2015-88, RF-2015-385]
- Royal Society of London [IE131408]
- Engineering and Physical Sciences Research Council [1277911] Funding Source: researchfish
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. (C) 2016 The Author(s). Published by Elsevier B.V.
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