Chen, Guoting; Li, Tiecheng Stability of stochastic delayed SIR model. (English) Zbl 1176.93079 Stoch. Dyn. 9, No. 2, 231-252 (2009). Summary: A stochastic version of the SIR model is investigated in this paper. The stability in probability of the steady state of the system is proved under suitable conditions on the white noise perturbations. Linearizations of the systems both with and without delay are given and their exponentially mean square stabilities are studied. Cited in 29 Documents MSC: 93E15 Stochastic stability in control theory 93E03 Stochastic systems in control theory (general) Keywords:stability; SIR (susceptible, infective and removed) model; stochastic differential system; time delay; global solution PDF BibTeX XML Cite \textit{G. Chen} and \textit{T. Li}, Stoch. Dyn. 9, No. 2, 231--252 (2009; Zbl 1176.93079) Full Text: DOI References: [1] DOI: 10.1016/j.sysconle.2005.03.003 · Zbl 1129.34330 [2] Arnold L., Lecture Notes Math 1486, in: Lyapunov Exponent (1990) [3] DOI: 10.1016/S0022-460X(03)00211-6 · Zbl 1236.70044 [4] DOI: 10.1016/j.jmaa.2003.12.004 · Zbl 1043.92034 [5] DOI: 10.1016/S0362-546X(99)00285-0 · Zbl 1015.92049 [6] Beretta E., J. Math. Biol. 33 pp 250– [7] Cooke K. L., Rocky Mount. J. Math. 9 pp 253– [8] Friedman A., Stochastic Differential Equations and Applications 1 (1975) · Zbl 0323.60056 [9] DOI: 10.1090/S0002-9947-1973-0319268-3 [10] DOI: 10.1007/978-1-4615-8065-2 [11] Halanay A., Differential Equations: Stability, Oscillations, Time Lags (1966) · Zbl 0144.08701 [12] Ito K., J. Math. Kyoto Univ. 4 pp 1– · Zbl 0131.16402 [13] Katafigiotis L. S., Random Oper. Stoch. Eqns. 3 pp 333– [14] DOI: 10.1137/1112019 [15] DOI: 10.1016/j.nonrwa.2004.10.001 · Zbl 1144.34374 [16] DOI: 10.1016/S0304-4149(97)00062-8 · Zbl 0911.60049 [17] DOI: 10.1137/060650234 · Zbl 1167.34036 [18] Mao X., Exponential Stability of Stochastic Differential Equations (1994) · Zbl 0806.60044 [19] Mao X., Stochastic Differential Equations and Applications (1997) · Zbl 0892.60057 [20] DOI: 10.1016/S0304-4149(01)00126-0 · Zbl 1058.60046 [21] DOI: 10.1007/BF02218856 · Zbl 0807.34092 [22] DOI: 10.1016/j.jmaa.2004.09.027 · Zbl 1062.92055 [23] DOI: 10.1016/j.physa.2005.02.057 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.