Ordinary Differential Equations
Lyapunov exponent of a stochastic SIRS model
Comptes Rendus. Mathématique, Volume 351 (2013) no. 1-2, pp. 33-35.

We consider a SIRS (susceptible–infected–removed–susceptible) model influenced by random perturbations. We prove that the solutions are positive for positive initial conditions and are global, that is, there is no finite explosion time. We present necessary and sufficient conditions for the almost sure asymptotic stability of the steady state of the stochastic system.

Nous considérons un modèle de type SIRS avec perturbation stochastique. Nous démontrons que les solutions sont positives pour des conditions initiales positives et sont définies globalement. Nous présentons des conditions nécessaires et suffisantes pour la stabilité asymptotique presque sûre de la solution triviale du système stochastique.

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DOI: 10.1016/j.crma.2012.11.010
Chen, Guoting 1; Li, Tiecheng 2; Liu, Changjian 3

1 UFR de Mathématiques, UMR CNRS 8524, Université de Lille-1, 59655 Villeneuve dʼAscq cedex, France
2 Department of Mathematical Sciences, Tsinghua University, Beijing 100084, PR China
3 School of Mathematics, Soochow University, Suzhou 215006, PR China
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Chen, Guoting; Li, Tiecheng; Liu, Changjian. Lyapunov exponent of a stochastic SIRS model. Comptes Rendus. Mathématique, Volume 351 (2013) no. 1-2, pp. 33-35. doi : 10.1016/j.crma.2012.11.010. http://www.numdam.org/articles/10.1016/j.crma.2012.11.010/

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