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Volumn 21, Issue 7, 2016, Pages 2363-2378

Stationary distribution of stochastic SIRS epidemic model with standard incidence

Author keywords

Asymptotic stability; Diffusion process; Markov semigroups; Stationary distribution

Indexed keywords


EID: 84990842341     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2016051     Document Type: Article
Times cited : (7)

References (30)
  • 1
    • 0018656345 scopus 로고
    • Population biology of infectious diseases I
    • R. M. Anderson and R. M. May, Population biology of infectious diseases I, Nature, 280 (1979), 361-367.
    • (1979) Nature , vol.280 , pp. 361-367
    • Anderson, R.M.1    May, R.M.2
  • 2
    • 0018357820 scopus 로고
    • Population biology of infectious diseases II
    • R. M. Anderson and R. M. May, Population biology of infectious diseases II, Nature, 280 (1979), 455-461.
    • (1979) Nature , vol.280 , pp. 455-461
    • Anderson, R.M.1    May, R.M.2
  • 5
    • 33847299320 scopus 로고
    • Décroissance exponentielle du noyau de la chaleur sur la diagonale (II)
    • G.B. Arous and R. Léandre, Décroissance exponentielle du noyau de la chaleur sur la diagonale (II), Probab. Theory Relat. Fields, 90 (1991), 377-402.
    • (1991) Probab. Theory Relat. Fields , vol.90 , pp. 377-402
    • Arous, G.B.1    Léandre, R.2
  • 7
    • 0025112636 scopus 로고
    • Analysis of a disease transmission model in a population with varying size
    • S. Busenberg and P. van den Driessche, Analysis of a disease transmission model in a population with varying size, J. Math. Biol., 28 (1990), 257-270.
    • (1990) J. Math. Biol. , vol.28 , pp. 257-270
    • Busenberg, S.1    Van Den Driessche, P.2
  • 8
    • 33750368835 scopus 로고    scopus 로고
    • A stochastic model of AIDS and condom use
    • N. Dalal, D. Greenhalgh and X. Mao, 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
  • 9
    • 79960370338 scopus 로고    scopus 로고
    • A stochastic differential equation SIS epidemic model
    • A. Gray, D. Greenhalgh, L. Hu, X. Mao and J. Pan, 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
  • 11
    • 0034486891 scopus 로고    scopus 로고
    • The mathematics of infectious diseases
    • H. W. Hethcote, The mathematics of infectious diseases, SIAM Rev., 42 (2000), 599-653.
    • (2000) SIAM Rev. , vol.42 , pp. 599-653
    • Hethcote, H.W.1
  • 12
    • 0035439412 scopus 로고    scopus 로고
    • An algorithmic introduction to numerical simulation of stochastic differential equations
    • D. J. Higham, An algorithmic introduction to numerical simulation of stochastic differential equations, SIAM Rev., 43 (2001), 525-546.
    • (2001) SIAM Rev. , vol.43 , pp. 525-546
    • Higham, D.J.1
  • 13
    • 84355161643 scopus 로고    scopus 로고
    • Dynamics of a multigroup SIR epidemic model with stochastic perturbation
    • C. Ji, D. Jiang, Q. Yang and N. Z. Shi, Dynamics of a multigroup SIR epidemic model with stochastic perturbation, Automatica, 48 (2012), 121-131.
    • (2012) Automatica , vol.48 , pp. 121-131
    • Ji, C.1    Jiang, D.2    Yang, Q.3    Shi, N.Z.4
  • 14
    • 0000998185 scopus 로고
    • Contribution to mathematical theory of epidemics
    • W. O. Kermack and A. G. McKendrick, Contribution to mathematical theory of epidemics, P. Roy. Soc. Lond. A Math., 115 (1927), 700-721.
    • (1927) P. Roy. Soc. Lond. A Math. , vol.115 , pp. 700-721
    • Kermack, W.O.1    McKendrick, A.G.2
  • 15
    • 79952335417 scopus 로고    scopus 로고
    • Global analysis of a deterministic and stochastic nonlinear SIRS epidemic model
    • A. Lahrouz, L. Omari and D. Kiouach, Global analysis of a deterministic and stochastic nonlinear SIRS epidemic model, Nonlinear Anal. Model. Control, 16 (2011), 59-76.
    • (2011) Nonlinear Anal. Model. Control , vol.16 , pp. 59-76
    • Lahrouz, A.1    Omari, L.2    Kiouach, D.3
  • 16
    • 84873535867 scopus 로고    scopus 로고
    • Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence
    • A. Lahrouz and L. Omari, Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence, Statistics & Probability Letters, 83 (2013), 960-968.
    • (2013) Statistics & Probability Letters , vol.83 , pp. 960-968
    • Lahrouz, A.1    Omari, L.2
  • 17
    • 0032812296 scopus 로고    scopus 로고
    • Global dynamics of a SEIR model with varying total population size
    • M. Li, J. Graef, L. Wang and J. Karsai, Global dynamics of a SEIR model with varying total population size, Mathematical Biosciences, 160 (1999), 191-213.
    • (1999) Mathematical Biosciences , vol.160 , pp. 191-213
    • Li, M.1    Graef, J.2    Wang, L.3    Karsai, J.4
  • 19
    • 84862784882 scopus 로고    scopus 로고
    • The asymptotic behavior of stochastically perturbed DI SIR epidemic models with saturated incidences
    • H. Liu, Q. Yang and D. Jiang, The asymptotic behavior of stochastically perturbed DI SIR epidemic models with saturated incidences, Automatica, 48 (2012), 820-825.
    • (2012) Automatica , vol.48 , pp. 820-825
    • Liu, H.1    Yang, Q.2    Jiang, D.3
  • 20
    • 84872028049 scopus 로고    scopus 로고
    • Dynamics of positive solutions to SIR and SEIR epidemic models with saturated incidence rates
    • Z. Liu, Dynamics of positive solutions to SIR and SEIR epidemic models with saturated incidence rates, Nonlinear Analysis: Real World Applications, 14 (2013), 1286-1299.
    • (2013) Nonlinear Analysis: Real World Applications , vol.14 , pp. 1286-1299
    • Liu, Z.1
  • 22
    • 0031260781 scopus 로고    scopus 로고
    • Stability of Markov semigroups and applications to parabolic systems
    • K. Pichór and R. Rudnicki, Stability of Markov semigroups and applications to parabolic systems, J. Math. Anal. Appl., 215 (1997), 56-74.
    • (1997) J. Math. Anal. Appl. , vol.215 , pp. 56-74
    • Pichór, K.1    Rudnicki, R.2
  • 23
    • 0141799906 scopus 로고    scopus 로고
    • Long-time behaviour of a stochastic prey-predator model
    • R. Rudnicki, Long-time behaviour of a stochastic prey-predator model, Stochastic Process. Appl., 108 (2003), 93-107.
    • (2003) Stochastic Process. Appl. , vol.108 , pp. 93-107
    • Rudnicki, R.1
  • 24
    • 33847295610 scopus 로고    scopus 로고
    • Influence of stochastic perturbation on prey-predator systems
    • R. Rudnicki and K. Pichór, Influence of stochastic perturbation on prey-predator systems, Math. Biosci., 206 (2007), 108-119.
    • (2007) Math. Biosci. , vol.206 , pp. 108-119
    • Rudnicki, R.1    Pichór, K.2
  • 25
    • 0000395295 scopus 로고
    • On the Support of Diffusion Processes with Applications to the Strong Maximum Principle
    • University of California Press, Berkeley
    • D. W. Stroock and S. R. S. Varadhan, On the Support of Diffusion Processes with Applications to the Strong Maximum Principle, Proc. Sixth Berkeley Symposium on Mathematical Statistics and Probability, vol. III, University of California Press, Berkeley, 1972.
    • (1972) Proc. Sixth Berkeley Symposium on Mathematical Statistics and Probability , vol.3
    • Stroock, D.W.1    Varadhan, S.R.S.2
  • 27
    • 84455169402 scopus 로고    scopus 로고
    • The ergodicity and extinction of stochastically perturbed SIR and SEIR epidemic models with saturated incidence
    • Q. Yang, D. Jiang and N. Shi, The ergodicity and extinction of stochastically perturbed SIR and SEIR epidemic models with saturated incidence, Journal of Mathematical Analysis and Applications, 388 (2012), 248-271.
    • (2012) Journal of Mathematical Analysis and Applications , vol.388 , pp. 248-271
    • Yang, Q.1    Jiang, D.2    Shi, N.3
  • 28
    • 84901917506 scopus 로고    scopus 로고
    • The threshold of a stochastic SIRS epidemic model with saturated incidence
    • Y. Zhao and D. Jiang, The threshold of a stochastic SIRS epidemic model with saturated incidence, Applied Mathematical Letter, 34 (2014), 90-93.
    • (2014) Applied Mathematical Letter , vol.34 , pp. 90-93
    • Zhao, Y.1    Jiang, D.2
  • 29
    • 84983048127 scopus 로고    scopus 로고
    • The threshold of a stochastic SIRS epidemic model in a population with varying size
    • Y. Zhao, D. Jiang, X. Mao and A. Gray, The threshold of a stochastic SIRS epidemic model in a population with varying size, Discrete Continuous Dynam. Systems - B, 20 (2015), 1277-1295.
    • (2015) Discrete Continuous Dynam. Systems - B , vol.20 , pp. 1277-1295
    • Zhao, Y.1    Jiang, D.2    Mao, X.3    Gray, A.4
  • 30
    • 84883134834 scopus 로고    scopus 로고
    • The extinction and persistence of the stochastic SIS epidemic model with vaccination
    • Y. Zhao, D. Jiang and D. O'Regan, The extinction and persistence of the stochastic SIS epidemic model with vaccination, Physica A, 392 (2013), 4916-4927.
    • (2013) Physica A , vol.392 , pp. 4916-4927
    • Zhao, Y.1    Jiang, D.2    O'Regan, D.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.