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Lyapunov exponent and almost sure asymptotic stability of a stochastic SIRS model
Chen, Guoting (Université de Lille 1)
Li, Tiecheng (Tsinghua University. Department of Mathematical Sciences)
Liu, Changjian (Soochow University. School of Mathematics)

Data: 2014
Resum: Epidemiological models with bilinear incidence rate usually have an asymptotically stable trivial equilibrium corresponding to the disease-free state, or an asymptotically stable nontrivial equilibrium (i. e. interior equilibrium) corresponding to the endemic state. In this paper, we consider an epidemiological model, which is a SIRS (susceptible-infected-removed-susceptible) model in uenced by random perturbations. We prove that the solutions of the system are positive for all positive initial conditions and that the solutions are global, that is, there is no finite explosion time. We present necessary and suficient condition for the almost sure asymptotic stability of the steady state of the stochastic system.
Nota: This work was supported in part by the Labex CEMPI (ANR-11-LABX-0007-01). T. Li is supported by the NSFC grant 11072122. C. Liu is supported by NSFC grant 11371269.
Drets: Tots els drets reservats
Llengua: Anglès
Document: article ; recerca ; publishedVersion
Matèria: Stability ; SIRS model ; Stochastic dierential system
Publicat a: Publicacions matemàtiques, Vol. Extra, Núm. (2014) , p. 153-165, ISSN 0214-1493

Adreça original:
DOI: 10.5565/PUBLMAT_Extra14_08
DOI: 10.5565/287207

13 p, 338.9 KB

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