The SIS epidemic model with Markovian switching

Population systems are often subject to environmental noise. Motivated by Takeuchi et al. [7], we will discuss in this paper the effect of telegraph noise on the well-known SIS epidemic model. We establish the explicit solution of the stochastic SIS epidemic model, which is useful in performing comp...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 394; no. 2; pp. 496 - 516
Main Authors Gray, Alison, Greenhalgh, David, Mao, Xuerong, Pan, Jiafeng
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.10.2012
Subjects
[formula omitted] [formula omitted]
Extinction
Markov chain
Persistence
SIS epidemic model
Markov chain
Persistence
Streptococcus pneumoniae
Extinction
SIS epidemic model
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Summary:Population systems are often subject to environmental noise. Motivated by Takeuchi et al. [7], we will discuss in this paper the effect of telegraph noise on the well-known SIS epidemic model. We establish the explicit solution of the stochastic SIS epidemic model, which is useful in performing computer simulations. We also establish the conditions for extinction and persistence for the stochastic SIS epidemic model and compare these with the corresponding conditions for the deterministic SIS epidemic model. We first prove these results for a two-state Markov chain and then generalise them to a finite state space Markov chain. Computer simulations based on the explicit solution and the Euler–Maruyama scheme are performed to illustrate our theory. We include a more realistic example using appropriate parameter values for the spread of Streptococcuspneumoniae in children.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2012.05.029