메뉴 건너뛰기




Volumn 428, Issue , 2015, Pages 140-153

Analysis of the deterministic and stochastic SIRS epidemic models with nonlinear incidence

Author keywords

Extinction; It 's formula; Lyapunov function; Nonlinear incidence; Stationary distribution

Indexed keywords

EPIDEMIOLOGY; LIGHT EXTINCTION; LYAPUNOV FUNCTIONS; STOCHASTIC MODELS; WHITE NOISE;

EID: 84923789423     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2015.01.075     Document Type: Article
Times cited : (78)

References (28)
  • 1
    • 0000998185 scopus 로고
    • Contributions to the mathematical theory of epidemics (Part I)
    • W.O. Kermack, and A.G. McKendrick Contributions to the mathematical theory of epidemics (Part I) Proc. Soc. Lond. Ser. A 115 1927 700 721
    • (1927) Proc. Soc. Lond. Ser. A , vol.115 , pp. 700-721
    • Kermack, W.O.1    McKendrick, A.G.2
  • 2
    • 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 Statist. Probab. Lett. 83 2013 960 968
    • (2013) Statist. Probab. Lett. , vol.83 , pp. 960-968
    • Lahrouz, A.1    Omari, L.2
  • 3
    • 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 Appl. Math. Lett. 34 2014 90 93
    • (2014) Appl. Math. Lett. , vol.34 , pp. 90-93
    • Zhao, Y.1    Jiang, D.2
  • 4
    • 84860842742 scopus 로고    scopus 로고
    • Global stability of SIRS epidemic models with a class of nonlinear incidence rates and distributed delays
    • Y. Enatsu, Y. Nakata, and Y. Muroya Global stability of SIRS epidemic models with a class of nonlinear incidence rates and distributed delays Acta Math. Sci. 32B 3 2012 851 865
    • (2012) Acta Math. Sci. , vol.32 B , Issue.3 , pp. 851-865
    • Enatsu, Y.1    Nakata, Y.2    Muroya, Y.3
  • 5
    • 78651240621 scopus 로고    scopus 로고
    • Global stability of a delayed SIRS epidemic model with a non-monotonic incidence rate
    • Y. Muroya, Y. Enatsu, and Y. Nakata Global stability of a delayed SIRS epidemic model with a non-monotonic incidence rate J. Math. Anal. Appl. 377 2011 1 14
    • (2011) J. Math. Anal. Appl. , vol.377 , pp. 1-14
    • Muroya, Y.1    Enatsu, Y.2    Nakata, Y.3
  • 6
    • 84855868838 scopus 로고    scopus 로고
    • Complete global stability for an SIRS epidemic model with generalized non-linear incidence and vaccination
    • A. Lahrouz, L. Omari, D. Kiouach, and A. Belmaati Complete global stability for an SIRS epidemic model with generalized non-linear incidence and vaccination Appl. Math. Comput. 218 2012 6519 6525
    • (2012) Appl. Math. Comput. , vol.218 , pp. 6519-6525
    • Lahrouz, A.1    Omari, L.2    Kiouach, D.3    Belmaati, A.4
  • 7
    • 67649440965 scopus 로고    scopus 로고
    • Stability of SIRS system with random perturbations
    • Q. Lu Stability of SIRS system with random perturbations Phys. A 388 2009 3677 3686
    • (2009) Phys. A , vol.388 , pp. 3677-3686
    • Lu, Q.1
  • 8
    • 84904883586 scopus 로고    scopus 로고
    • Survival and stationary distribution of a SIR epidemic model with stochastic perturbations
    • Y.L. Zhou, W.G. Zhang, and S.L. Yuan Survival and stationary distribution of a SIR epidemic model with stochastic perturbations Appl. Math. Comput. 244 2014 118 131
    • (2014) Appl. Math. Comput. , vol.244 , pp. 118-131
    • Zhou, Y.L.1    Zhang, W.G.2    Yuan, S.L.3
  • 9
    • 84894574300 scopus 로고    scopus 로고
    • Necessary and sufficient condition for extinction and persistence of SIRS system with random perturbation
    • A. Lahrouz, and A. Settati Necessary and sufficient condition for extinction and persistence of SIRS system with random perturbation Appl. Math. Comput. 233 2014 10 19
    • (2014) Appl. Math. Comput. , vol.233 , pp. 10-19
    • Lahrouz, A.1    Settati, A.2
  • 10
    • 84908507682 scopus 로고    scopus 로고
    • Threshold behaviour of a stochastic SIR model
    • C.Y. Ji, and D.Q. Jiang Threshold behaviour of a stochastic SIR model Appl. Math. Model. 38 2014 5067 5079
    • (2014) Appl. Math. Model. , vol.38 , pp. 5067-5079
    • Ji, C.Y.1    Jiang, D.Q.2
  • 11
    • 84903964640 scopus 로고    scopus 로고
    • On pulse vaccine strategy in a periodic stochastic SIR epidemic model
    • F.Y. Wang, X.Y. Wang, S.W. Zhang, and C.M. Ding On pulse vaccine strategy in a periodic stochastic SIR epidemic model Chaos Solitons Fractals 66 2014 127 135
    • (2014) Chaos Solitons Fractals , vol.66 , pp. 127-135
    • Wang, F.Y.1    Wang, X.Y.2    Zhang, S.W.3    Ding, C.M.4
  • 12
    • 77955768838 scopus 로고    scopus 로고
    • Analysis of an SIR model with bilinear incidence rate
    • J. Wang, J. Zhang, and Z. Jin Analysis of an SIR model with bilinear incidence rate Nonlinear Anal. RWA 11 2010 2390 2402
    • (2010) Nonlinear Anal. RWA , vol.11 , pp. 2390-2402
    • Wang, J.1    Zhang, J.2    Jin, Z.3
  • 13
    • 0018041874 scopus 로고
    • A generalization of the Kermack-Mckendrick deterministic epidemic model
    • V. Capasso, and G. Serio A generalization of the Kermack-Mckendrick deterministic epidemic model Math. Biosci. 42 1978 43 61
    • (1978) Math. Biosci. , vol.42 , pp. 43-61
    • Capasso, V.1    Serio, G.2
  • 14
    • 0037429355 scopus 로고    scopus 로고
    • Dynamical behavior of an epidemic model with a nonlinear incidence rate
    • S. Ruan, and W. Wang Dynamical behavior of an epidemic model with a nonlinear incidence rate J. Differential Equations 188 2003 135 163
    • (2003) J. Differential Equations , vol.188 , pp. 135-163
    • Ruan, S.1    Wang, W.2
  • 15
    • 0022298258 scopus 로고
    • Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models
    • W.M. Liu, S.A. Levin, and Y. Iwasa Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models J. Math. Biol. 23 1986 187 204
    • (1986) J. Math. Biol. , vol.23 , pp. 187-204
    • Liu, W.M.1    Levin, S.A.2    Iwasa, Y.3
  • 17
    • 84903693036 scopus 로고    scopus 로고
    • Dynamics of the deterministic and stochastic SIQS epidemic model with non-linear incidence
    • X.B. Zhang, H.F. Huo, H. Xiang, and X.Y. Meng Dynamics of the deterministic and stochastic SIQS epidemic model with non-linear incidence Appl. Math. Comput. 243 2014 546 558
    • (2014) Appl. Math. Comput. , vol.243 , pp. 546-558
    • Zhang, X.B.1    Huo, H.F.2    Xiang, H.3    Meng, X.Y.4
  • 18
    • 48049122424 scopus 로고    scopus 로고
    • Stability analysis and optimal vaccination of an SIR epidemic model
    • G. Zaman, Y.H. Kang, and I.H. Jung Stability analysis and optimal vaccination of an SIR epidemic model Biosystems 93 2008 240 249
    • (2008) Biosystems , vol.93 , pp. 240-249
    • Zaman, G.1    Kang, Y.H.2    Jung, I.H.3
  • 19
    • 84864974814 scopus 로고    scopus 로고
    • The behavior of an SIR epidemic model with stochastic perturbation
    • C.Y. Ji, D.Q. Jiang, and N.Z. Shi The behavior of an SIR epidemic model with stochastic perturbation Stoch. Anal. Appl. 30 2012 755 773
    • (2012) Stoch. Anal. Appl. , vol.30 , pp. 755-773
    • Ji, C.Y.1    Jiang, D.Q.2    Shi, N.Z.3
  • 20
    • 79955469778 scopus 로고    scopus 로고
    • Asymptotic behavior of global positive solution to a stochastic SIR model
    • D.Q. Jiang, J.J. Yu, C.Y. Ji, and N.Z. Shi Asymptotic behavior of global positive solution to a stochastic SIR model Math. Comput. Modelling 54 2011 221 232
    • (2011) Math. Comput. Modelling , vol.54 , pp. 221-232
    • Jiang, D.Q.1    Yu, J.J.2    Ji, C.Y.3    Shi, N.Z.4
  • 21
    • 84879092827 scopus 로고    scopus 로고
    • Long-time behavior of perturbed SIR model by white noise
    • Y.G. Lin, and D.Q. Jiang Long-time behavior of perturbed SIR model by white noise Discrete Contin. Dyn. Syst. Ser. B 18 2013 1873 1887
    • (2013) Discrete Contin. Dyn. Syst. Ser. B , vol.18 , pp. 1873-1887
    • Lin, Y.G.1    Jiang, D.Q.2
  • 22
    • 0036846383 scopus 로고    scopus 로고
    • Effects of quarantine in six endemic models for infectious diseases
    • H. Herbert, Z. Ma, and S. Liao Effects of quarantine in six endemic models for infectious diseases Math. Biosci. 180 2002 141 160
    • (2002) Math. Biosci. , vol.180 , pp. 141-160
    • Herbert, H.1    Ma, Z.2    Liao, S.3
  • 28
    • 47049084345 scopus 로고    scopus 로고
    • Asymptotic properties of hybrid diffusion systems
    • C. Zhu, and G. Yin Asymptotic properties of hybrid diffusion systems SIAM J. Control Optim. 46 2007 1155 1179
    • (2007) SIAM J. Control Optim. , vol.46 , pp. 1155-1179
    • Zhu, C.1    Yin, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.