메뉴 건너뛰기




Volumn 16, Issue 1, 2011, Pages 59-76

Global analysis of a deterministic and stochastic nonlinear SIRS epidemic model

Author keywords

Epidemic model; Global stability; Ito's formula; Lypunov function; Moment exponential stability

Indexed keywords


EID: 79952335417     PISSN: 13925113     EISSN: 23358963     Source Type: Journal    
DOI: 10.15388/na.16.1.14115     Document Type: Article
Times cited : (171)

References (30)
  • 1
    • 4644273929 scopus 로고    scopus 로고
    • Global stability of an SEI epidemic model with general contact rate
    • G. Li, Z. Jin, Global stability of an SEI epidemic model with general contact rate, Chaos Solitons Fractals, 23, pp. 997-1004, 2005.
    • (2005) Chaos Solitons Fractals , vol.23 , pp. 997-1004
    • Li, G.1    Jin, Z.2
  • 3
    • 67349249710 scopus 로고    scopus 로고
    • Global stability of a stage structured epidemic model with a nonlineare incidence
    • M.L. Cai, X.Z. Li, M. Chosh, Global stability of a stage structured epidemic model with a nonlineare incidence, Appl. Math. Comput., 214, pp. 73-82, 2009.
    • (2009) Appl. Math. Comput , vol.214 , pp. 73-82
    • Cai, M.L.1    Li, X.Z.2    Chosh, M.3
  • 4
    • 61449181521 scopus 로고    scopus 로고
    • Analysis of an SEIV epidemic model with a nonlinear incidence rate
    • M.L. Cai, X.Z. Li, Analysis of an SEIV epidemic model with a nonlinear incidence rate, Appl. Math. Modelling, 33, pp. 2919-2926, 2009.
    • (2009) Appl. Math. Modelling , vol.33 , pp. 2919-2926
    • Cai, M.L.1    Li, X.Z.2
  • 7
    • 0017228276 scopus 로고
    • Qualitative analyses of communicable disease models
    • H.W. Hethcote, Qualitative analyses of communicable disease models, Math. Biosci., 28, pp. 335-356, 1976.
    • (1976) Math. Biosci , vol.28 , pp. 335-356
    • Hethcote, H.W.1
  • 8
    • 34547134261 scopus 로고    scopus 로고
    • Global analysis of an epidemic model with nonmonotone incidence rate
    • D. Xiao, S. Ruan, Global analysis of an epidemic model with nonmonotone incidence rate, Math. Biosci., 208, pp. 419-429, 2007.
    • (2007) Math. Biosci , vol.208 , pp. 419-429
    • Xiao, D.1    Ruan, S.2
  • 9
    • 0030544879 scopus 로고    scopus 로고
    • A geometric approach to global-stability problems
    • M.Y. Li, J.S. Muldowney, A geometric approach to global-stability problems, SIAM J. Math. Anal., 27 pp. 1070-1083, 1996.
    • (1996) SIAM J. Math. Anal , vol.27 , pp. 1070-1083
    • Li, M.Y.1    Muldowney, J.S.2
  • 10
    • 0028817626 scopus 로고
    • Global stability for the SEIR model in epidemiology
    • M.Y. Li, J.S. Muldowney, Global stability for the SEIR model in epidemiology, Math. Biosci., 125 pp. 155-164, 1995.
    • (1995) Math. Biosci , vol.125 , pp. 155-164
    • Li, M.Y.1    Muldowney, J.S.2
  • 11
    • 33745222283 scopus 로고    scopus 로고
    • Global stability of an SEIR epidemic model with constant immigration
    • G. Li, W. Wang, Z. Jin, Global stability of an SEIR epidemic model with constant immigration, Chaos Solitons Fractals, 30, pp. 1012-1019, 2006.
    • (2006) Chaos Solitons Fractals , vol.30 , pp. 1012-1019
    • Li, G.1    Wang, W.2    Jin, Z.3
  • 12
    • 33846820429 scopus 로고    scopus 로고
    • Global stability for an special SEIR epidemic model with nonlinear incidence rates
    • C. Sun, Y. Lin, S. Tang, Global stability for an special SEIR epidemic model with nonlinear incidence rates, Chaos Solitons Fractals, 33, pp. 290-297, 2007.
    • (2007) Chaos Solitons Fractals , vol.33 , pp. 290-297
    • Sun, C.1    Lin, Y.2    Tang, S.3
  • 13
    • 67349124783 scopus 로고    scopus 로고
    • Analysis of an HIV/AIDS treatmaent model with a nonlinear incidence
    • L. Cai, J. Wu, Analysis of an HIV/AIDS treatmaent model with a nonlinear incidence, Chaos Solitons Fractals, 41, pp. 175-182, 2009.
    • (2009) Chaos Solitons Fractals , vol.41 , pp. 175-182
    • Cai, L.1    Wu, J.2
  • 14
    • 0031997110 scopus 로고    scopus 로고
    • Stability of epidemic model with time delay influenced by stochastic perturbations
    • E. Beretta, V. Kolmanovskii, L. Shaikhet, Stability of epidemic model with time delay influenced by stochastic perturbations, Math. Comput. Simul., 45, pp. 269-277, 1998.
    • (1998) Math. Comput. Simul , vol.45 , pp. 269-277
    • Beretta, E.1    Kolmanovskii, V.2    Shaikhet, L.3
  • 15
    • 22144467632 scopus 로고    scopus 로고
    • Cancer self remission and tumor stability - a stochastic approach
    • R.R. Sarkar, S. Banerjee, Cancer self remission and tumor stability - a stochastic approach, Math. Biosci., 196(1), pp. 65-81, 2005.
    • (2005) Math. Biosci , vol.196 , Issue.1 , pp. 65-81
    • Sarkar, R.R.1    Banerjee, S.2
  • 16
    • 0018041874 scopus 로고
    • A generalization of the Kermack-Mckendrick deterministic epidemic model
    • V. Capasso, G. Serio, A generalization of the Kermack-Mckendrick deterministic epidemic model, Math. Biosci, 42, pp. 41-61, 1978.
    • (1978) Math. Biosci , vol.42 , pp. 41-61
    • Capasso, V.1    Serio, G.2
  • 17
    • 33746594608 scopus 로고    scopus 로고
    • Lyapunov functions and global stability for SIR and SIRS epidemiological models with non-linear transmission
    • A. Korobeinikov, Lyapunov functions and global stability for SIR and SIRS epidemiological models with non-linear transmission, Bull. Math. Biol., 68, pp. 615-626, 2006.
    • (2006) Bull. Math. Biol , vol.68 , pp. 615-626
    • Korobeinikov, A.1
  • 18
    • 25144476559 scopus 로고    scopus 로고
    • Nonlinear incidence and stability of infectious disease models
    • A. Korobeinikov, P.K. Maini, Nonlinear incidence and stability of infectious disease models, Math. Med. Biol., 22, pp. 113-128, 2005.
    • (2005) Math. Med. Biol , vol.22 , pp. 113-128
    • Korobeinikov, A.1    Maini, P.K.2
  • 19
    • 31244431623 scopus 로고    scopus 로고
    • Lyapunov functions and global stability for SIR, SIRS and SIS epidemiological models
    • A. Korobeinikov, G.C. Wake, Lyapunov functions and global stability for SIR, SIRS and SIS epidemiological models, Appl. Math. Lett. 15(8), pp. 955-961, 2002.
    • (2002) Appl. Math. Lett , vol.15 , Issue.8 , pp. 955-961
    • Korobeinikov, A.1    Wake, G.C.2
  • 20
    • 3042703290 scopus 로고    scopus 로고
    • Lyapunov functions and global properties for SEIR and SEIS epidemic models
    • A. Korobeinikov, Lyapunov functions and global properties for SEIR and SEIS epidemic models, Math. Med. Biol. 21(2), pp. 75-83, 2004.
    • (2004) Math. Med. Biol , vol.21 , Issue.2 , pp. 75-83
    • Korobeinikov, A.1
  • 23
    • 0033586169 scopus 로고    scopus 로고
    • Stochastic versions of the LaSalle theorem
    • X. Mao, Stochastic versions of the LaSalle theorem, J. Differ. Equations, 153, pp. 175-195, 1999.
    • (1999) J. Differ. Equations , vol.153 , pp. 175-195
    • Mao, X.1
  • 24
    • 19944381861 scopus 로고    scopus 로고
    • Stability of a stochastic SIR system
    • E. Tornatore, S.M. Buccellato, P. Vetro, Stability of a stochastic SIR system, Physica A, 354, pp. 111-126, 2005.
    • (2005) Physica A , vol.354 , pp. 111-126
    • Tornatore, E.1    Buccellato, S.M.2    Vetro, P.3
  • 25
    • 67649440965 scopus 로고    scopus 로고
    • Stability of SIRS system with random perturbations
    • Q. Lu, Stability of SIRS system with random perturbations, Physica A, 388, pp. 3677-3686, 2009.
    • (2009) Physica A , vol.388 , pp. 3677-3686
    • Lu, Q.1
  • 26
    • 0036845274 scopus 로고    scopus 로고
    • Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
    • P. Van den Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci., 180, pp. 29-48, 2002.
    • (2002) Math. Biosci , vol.180 , pp. 29-48
    • Van den Driessche, P.1    Watmough, J.2
  • 29
    • 0039337197 scopus 로고
    • A strong law of large numbers for local martingales
    • R. Liptser, A strong law of large numbers for local martingales, Stochastics, 3, pp. 217-228, 1980.
    • (1980) Stochastics , vol.3 , pp. 217-228
    • Liptser, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.