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Volumn 469, Issue , 2017, Pages 510-517

Stationary distribution and extinction of a stochastic SIRS epidemic model with standard incidence

Author keywords

Extinction; Nonlinear incidence; Stationary distribution; Stochastic SIRS epidemic model

Indexed keywords

EPIDEMIOLOGY; LIGHT EXTINCTION; LYAPUNOV FUNCTIONS; STOCHASTIC SYSTEMS;

EID: 84999636213     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2016.11.077     Document Type: Article
Times cited : (57)

References (31)
  • 1
    • 0025985176 scopus 로고
    • Contributions to the mathematical theory of epidemics-I
    • [1] Kermack, W.O., McKendrick, A.G., Contributions to the mathematical theory of epidemics-I. Bull. Math. Biol. 53 (1991), 33–55.
    • (1991) Bull. Math. Biol. , vol.53 , pp. 33-55
    • Kermack, W.O.1    McKendrick, A.G.2
  • 2
    • 85124060458 scopus 로고    scopus 로고
    • Modeling and Dynamics of Infectious Diseases
    • Higher Education Press
    • [2] Ma, Z., Zhou, Y., Wu, J., Modeling and Dynamics of Infectious Diseases. 2009, Higher Education Press.
    • (2009)
    • Ma, Z.1    Zhou, Y.2    Wu, J.3
  • 3
    • 84862833105 scopus 로고    scopus 로고
    • Analysis of rabies in China: transmission dynamics and control
    • [3] Zhang, J., Jin, Z., Sun, G.-Q., Zhou, T., Ruan, S., Analysis of rabies in China: transmission dynamics and control. PLoS One, 6, 2011, e20891.
    • (2011) PLoS One , vol.6 , pp. e20891
    • Zhang, J.1    Jin, Z.2    Sun, G.-Q.3    Zhou, T.4    Ruan, S.5
  • 4
    • 34249301320 scopus 로고    scopus 로고
    • Some properties of a simple stochastic epidemic model of SIR type
    • [4] Tuckwell, H.C., Williams, R.J., Some properties of a simple stochastic epidemic model of SIR type. Math. Biosci. 208 (2007), 76–97.
    • (2007) Math. Biosci. , vol.208 , pp. 76-97
    • Tuckwell, H.C.1    Williams, R.J.2
  • 5
    • 42249098829 scopus 로고    scopus 로고
    • An introduction to stochastic epidemic models
    • Springer
    • [5] Allen, L.J.S., An introduction to stochastic epidemic models. Mathematical Epidemiology, 2008, Springer, 81–130.
    • (2008) Mathematical Epidemiology , pp. 81-130
    • Allen, L.J.S.1
  • 6
    • 84928893084 scopus 로고
    • Introduction to Stochastic Differential Equations
    • Dekker New York
    • [6] Thomas, C.G., Introduction to Stochastic Differential Equations. 1988, Dekker, New York.
    • (1988)
    • Thomas, C.G.1
  • 7
    • 0003722979 scopus 로고    scopus 로고
    • Stochastic Differential Equations: An Introduction with Applications
    • Springer
    • [7] Øksendal, B., Stochastic Differential Equations: An Introduction with Applications. 2010, Springer.
    • (2010)
    • Øksendal, B.1
  • 8
    • 0003561266 scopus 로고    scopus 로고
    • Stochastic Differential Equations and their Applications
    • Horwood Chichester
    • [8] Mao, X., Stochastic Differential Equations and their Applications. 1997, Horwood, Chichester.
    • (1997)
    • Mao, X.1
  • 9
    • 0242563961 scopus 로고    scopus 로고
    • Environmental noise suppresses explosion in population dynamics
    • [9] Mao, X., Marion, G., Renshaw, E., Environmental noise suppresses explosion in population dynamics. Stochastic Process. Appl. 97 (2002), 95–110.
    • (2002) Stochastic Process. Appl. , vol.97 , pp. 95-110
    • Mao, X.1    Marion, G.2    Renshaw, E.3
  • 10
    • 0033314540 scopus 로고    scopus 로고
    • Stochastic spatial models
    • [10] Durrett, R., Stochastic spatial models. SIAM Rev. 41 (1999), 677–718.
    • (1999) SIAM Rev. , vol.41 , pp. 677-718
    • Durrett, R.1
  • 11
    • 84455169402 scopus 로고    scopus 로고
    • The ergodicity and extinction of stochastically perturbed SIR and SEIR epidemic models with saturated incidence
    • [11] Yang, Q., Jiang, D., Shi, N., Ji, C., The ergodicity and extinction of stochastically perturbed SIR and SEIR epidemic models with saturated incidence. J. Math. Anal. Appl. 388 (2012), 248–271.
    • (2012) J. Math. Anal. Appl. , vol.388 , pp. 248-271
    • Yang, Q.1    Jiang, D.2    Shi, N.3    Ji, C.4
  • 12
    • 79960370338 scopus 로고    scopus 로고
    • A stochastic differential equation SIS epidemic model
    • [12] Gray, A., Greenhalgh, D., Hu, L., Mao, X., Pan, J., A stochastic differential equation SIS epidemic model. SIAM J. Appl. Math. 71 (2011), 876–902.
    • (2011) SIAM J. Appl. Math. , vol.71 , pp. 876-902
    • Gray, A.1    Greenhalgh, D.2    Hu, L.3    Mao, X.4    Pan, J.5
  • 13
    • 0035413567 scopus 로고    scopus 로고
    • Long term behavior of solutions of the Lotka–Volterra system under small random perturbations
    • [13] Khasminskii, R.Z., Klebaner, F.C., Long term behavior of solutions of the Lotka–Volterra system under small random perturbations. Ann. Appl. Probab. 11 (2001), 952–963.
    • (2001) Ann. Appl. Probab. , vol.11 , pp. 952-963
    • Khasminskii, R.Z.1    Klebaner, F.C.2
  • 14
    • 84889259690 scopus 로고    scopus 로고
    • Parallel logic gates in synthetic gene networks induced by non-gaussian noise
    • [14] Xu, Y., Jin, X., Zhang, H., Parallel logic gates in synthetic gene networks induced by non-gaussian noise. Phys. Rev. E, 88, 2013, 052721.
    • (2013) Phys. Rev. E , vol.88
    • Xu, Y.1    Jin, X.2    Zhang, H.3
  • 15
    • 84947491559 scopus 로고    scopus 로고
    • The evolutionary dynamics of stochastic epidemic model with nonlinear incidence rate
    • [15] Li, D., Cui, J., Liu, M., Liu, S., The evolutionary dynamics of stochastic epidemic model with nonlinear incidence rate. Bull. Math. Biol. 77 (2015), 1705–1743.
    • (2015) Bull. Math. Biol. , vol.77 , pp. 1705-1743
    • Li, D.1    Cui, J.2    Liu, M.3    Liu, S.4
  • 16
    • 84873535867 scopus 로고    scopus 로고
    • Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence
    • [16] Lahrouz, A., Omari, L., Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence. Statist. Probab. Lett. 83 (2013), 960–968.
    • (2013) Statist. Probab. Lett. , vol.83 , pp. 960-968
    • Lahrouz, A.1    Omari, L.2
  • 17
    • 84872020070 scopus 로고    scopus 로고
    • Extinction and recurrence of multi-group SEIR epidemic models with stochastic perturbations
    • [17] Yang, Q., Mao, X., Extinction and recurrence of multi-group SEIR epidemic models with stochastic perturbations. Nonlinear Anal. RWA 14 (2013), 1434–1456.
    • (2013) Nonlinear Anal. RWA , vol.14 , pp. 1434-1456
    • Yang, Q.1    Mao, X.2
  • 18
    • 84884672931 scopus 로고    scopus 로고
    • Dynamics of a two-prey one predator system in random environments
    • [18] Liu, M., Wang, K., Dynamics of a two-prey one predator system in random environments. J. Nonlinear Sci. 23 (2013), 751–775.
    • (2013) J. Nonlinear Sci. , vol.23 , pp. 751-775
    • Liu, M.1    Wang, K.2
  • 19
    • 70450222692 scopus 로고    scopus 로고
    • Epidemic modelling: Aspects where stochastic epidemic models: A survey
    • [19] Britton, T., Lindenstrand, D., Epidemic modelling: Aspects where stochastic epidemic models: A survey. Math. Biosci. 22 (2010), 109–116.
    • (2010) Math. Biosci. , vol.22 , pp. 109-116
    • Britton, T.1    Lindenstrand, D.2
  • 20
    • 0026360185 scopus 로고
    • Reproduction numbers and thresholds in stochastic epidemic models I. homogeneous populations
    • [20] Jacquez, J.A., O'Neill, P., Reproduction numbers and thresholds in stochastic epidemic models I. homogeneous populations. Math. Biosci. 107 (1991), 161–186.
    • (1991) Math. Biosci. , vol.107 , pp. 161-186
    • Jacquez, J.A.1    O'Neill, P.2
  • 21
    • 0029175103 scopus 로고
    • Stochastic epidemics: major outbreaks and the duration of the endemic period
    • [21] van Herwaarden, O.A., Grasman, J., Stochastic epidemics: major outbreaks and the duration of the endemic period. J. Math. Biol. 33 (1995), 581–601.
    • (1995) J. Math. Biol. , vol.33 , pp. 581-601
    • van Herwaarden, O.A.1    Grasman, J.2
  • 22
    • 0036293119 scopus 로고    scopus 로고
    • Stochastic models of some endemic infections
    • [22] Näsell, I., Stochastic models of some endemic infections. Math. Biosci. 179 (2002), 1–19.
    • (2002) Math. Biosci. , vol.179 , pp. 1-19
    • Näsell, I.1
  • 23
    • 19944381861 scopus 로고    scopus 로고
    • Stability of a stochastic SIR system
    • [23] Tornatore, E., Buccellato, S.M., Vetro, P., Stability of a stochastic SIR system. Physica A 354 (2005), 111–126.
    • (2005) Physica A , vol.354 , pp. 111-126
    • Tornatore, E.1    Buccellato, S.M.2    Vetro, P.3
  • 24
    • 33750368835 scopus 로고    scopus 로고
    • A stochastic model of AIDS and condom use
    • [24] Dalal, N., Greenhalgh, D., Mao, X., A stochastic model of AIDS and condom use. J. Math. Anal. Appl. 325 (2007), 36–53.
    • (2007) J. Math. Anal. Appl. , vol.325 , pp. 36-53
    • Dalal, N.1    Greenhalgh, D.2    Mao, X.3
  • 25
    • 38949193330 scopus 로고    scopus 로고
    • A stochastic model for internal HIV dynamics
    • [25] Dalal, N., Greenhalgh, D., Mao, X., A stochastic model for internal HIV dynamics. J. Math. Anal. Appl. 341 (2008), 1084–1101.
    • (2008) J. Math. Anal. Appl. , vol.341 , pp. 1084-1101
    • Dalal, N.1    Greenhalgh, D.2    Mao, X.3
  • 26
    • 77955268021 scopus 로고    scopus 로고
    • The long time behavior of DI SIR epidemic model with stochastic perturbation
    • [26] Jiang, D., Ji, C., Shi, N., Yu, J., The long time behavior of DI SIR epidemic model with stochastic perturbation. J. Math. Anal. Appl. 372 (2010), 162–180.
    • (2010) J. Math. Anal. Appl. , vol.372 , pp. 162-180
    • Jiang, D.1    Ji, C.2    Shi, N.3    Yu, J.4
  • 27
    • 84872028049 scopus 로고    scopus 로고
    • Dynamics of positive solutions to SIR and SEIR epidemic models with saturated incidence rates
    • [27] Liu, Z., Dynamics of positive solutions to SIR and SEIR epidemic models with saturated incidence rates. Nonlinear Anal. RWA 14 (2013), 1286–1299.
    • (2013) Nonlinear Anal. RWA , vol.14 , pp. 1286-1299
    • Liu, Z.1
  • 28
    • 84916882895 scopus 로고    scopus 로고
    • Threshold behavior in a stochastic SIS epidemic model with standard incidence
    • [28] Lin, Y., Jiang, D., Threshold behavior in a stochastic SIS epidemic model with standard incidence. J. Dynam. Differential Equations 26 (2014), 1079–1094.
    • (2014) J. Dynam. Differential Equations , vol.26 , pp. 1079-1094
    • Lin, Y.1    Jiang, D.2
  • 29
    • 84887260929 scopus 로고    scopus 로고
    • Stationary distribution of a stochastic SIS epidemic model with vaccination
    • [29] Lin, Y., Jiang, D., Wang, S., Stationary distribution of a stochastic SIS epidemic model with vaccination. Physica A 394 (2014), 187–197.
    • (2014) Physica A , vol.394 , pp. 187-197
    • Lin, Y.1    Jiang, D.2    Wang, S.3
  • 30
    • 24644508416 scopus 로고    scopus 로고
    • Exclusion and persistence in deterministic and stochastic chemostat models
    • [30] Imhof, L., Walcher, S., Exclusion and persistence in deterministic and stochastic chemostat models. J. Differential Equations 217 (2005), 26–53.
    • (2005) J. Differential Equations , vol.217 , pp. 26-53
    • Imhof, L.1    Walcher, S.2
  • 31
    • 0003649950 scopus 로고
    • Stochastic Stability of Differential Equations
    • Sijthoff and Noordhoff Alphen aan den Rijn, The Netherlands
    • [31] Has'minskii, R.Z., Stochastic Stability of Differential Equations. 1980, Sijthoff and Noordhoff, Alphen aan den Rijn, The Netherlands.
    • (1980)
    • Has'minskii, R.Z.1


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