메뉴 건너뛰기




Volumn 388, Issue 1, 2012, Pages 248-271

The ergodicity and extinction of stochastically perturbed SIR and SEIR epidemic models with saturated incidence

Author keywords

Ergodic property; Exponential stability; It 's formula; SEIR epidemic model; SIR epidemic model; Stochastic Lyapunov function

Indexed keywords


EID: 84455169402     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2011.11.072     Document Type: Article
Times cited : (198)

References (53)
  • 1
    • 77957175423 scopus 로고
    • A preliminary study of the transmission dynamics of the human immunodeficiency virus (HIV), the causative agent of AIDS
    • Anderson R., May R., Medley G., Johnson A. A preliminary study of the transmission dynamics of the human immunodeficiency virus (HIV), the causative agent of AIDS. IMA J. Math. Appl. Med. Biol. 1986, 3:229-263.
    • (1986) IMA J. Math. Appl. Med. Biol. , vol.3 , pp. 229-263
    • Anderson, R.1    May, R.2    Medley, G.3    Johnson, A.4
  • 4
    • 0001064056 scopus 로고
    • Stability in distribution for a class of singular diffusions
    • Gopal K.B., Rabi N.B. Stability in distribution for a class of singular diffusions. Ann. Probab. 1992, 20:312-321.
    • (1992) Ann. Probab. , vol.20 , pp. 312-321
    • Gopal, K.B.1    Rabi, N.B.2
  • 5
    • 0000735971 scopus 로고
    • Harvesting natural populations in a randomly fluctuating environment
    • Beddington J., May R. Harvesting natural populations in a randomly fluctuating environment. Science 1977, 197:463-465.
    • (1977) Science , vol.197 , pp. 463-465
    • Beddington, J.1    May, R.2
  • 6
    • 0031997110 scopus 로고    scopus 로고
    • Stability of epidemic model with time delays influenced by stochastic perturbations
    • Berettaa E., Kolmanovskiib V., Shaikhetc L. Stability of epidemic model with time delays influenced by stochastic perturbations. Math. Comput. Simulation 1998, 45:269-277.
    • (1998) Math. Comput. Simulation , vol.45 , pp. 269-277
    • Berettaa, E.1    Kolmanovskiib, V.2    Shaikhetc, L.3
  • 7
    • 0035425156 scopus 로고    scopus 로고
    • Global asymptotic stability of an SIR epidemic model with distributed time delay
    • Beretta E., Hara T., Ma W., Takeuchi Y. Global asymptotic stability of an SIR epidemic model with distributed time delay. Nonlinear Anal. 2001, 47:4107-4115.
    • (2001) Nonlinear Anal. , vol.47 , pp. 4107-4115
    • Beretta, E.1    Hara, T.2    Ma, W.3    Takeuchi, Y.4
  • 8
    • 0006751822 scopus 로고
    • Conidial discharge and transmission efficiency of Neozygites floridana, an entomopathogenic fungus infecting two-spotted spider mites under laboratory conditions
    • Brown G.C., Hasibuan R. Conidial discharge and transmission efficiency of Neozygites floridana, an entomopathogenic fungus infecting two-spotted spider mites under laboratory conditions. J. Invertebr. Pathol. 1995, 65:10-16.
    • (1995) J. Invertebr. Pathol. , vol.65 , pp. 10-16
    • Brown, G.C.1    Hasibuan, R.2
  • 9
    • 0018041874 scopus 로고
    • A generalisation of the Kermack-McKendrick deterministic epidemic model
    • Capasso V., Serio G. A generalisation of the Kermack-McKendrick deterministic epidemic model. Math. Biosci. 1978, 42:43-61.
    • (1978) Math. Biosci. , vol.42 , pp. 43-61
    • Capasso, V.1    Serio, G.2
  • 11
    • 0036176248 scopus 로고    scopus 로고
    • On the stability properties of a stochastic model for phage-bacteria interaction in open marine environment
    • Carletti M. On the stability properties of a stochastic model for phage-bacteria interaction in open marine environment. Math. Biosci. 2002, 175:117-131.
    • (2002) Math. Biosci. , vol.175 , pp. 117-131
    • Carletti, M.1
  • 12
    • 33845457993 scopus 로고    scopus 로고
    • Numerical simulation of a Campbell-like stochastic delay model for bacteriophage infection
    • Carletti M. Numerical simulation of a Campbell-like stochastic delay model for bacteriophage infection. Math. Med. Biol. 2006, 23:297-310.
    • (2006) Math. Med. Biol. , vol.23 , pp. 297-310
    • Carletti, M.1
  • 13
    • 0030318519 scopus 로고    scopus 로고
    • Analysis of an SEIRS epidemic model with two delays
    • Cooke K., van den Driessche P. Analysis of an SEIRS epidemic model with two delays. J. Math. Biol. 1996, 35:240-260.
    • (1996) J. Math. Biol. , vol.35 , pp. 240-260
    • Cooke, K.1    van den Driessche, P.2
  • 15
    • 38949193330 scopus 로고    scopus 로고
    • A stochastic model for internal HIV dynamics
    • Dalal N., Greenhalgh D., Mao X. A stochastic model for internal HIV dynamics. J. Math. Anal. Appl. 2008, 341:1084-1101.
    • (2008) J. Math. Anal. Appl. , vol.341 , pp. 1084-1101
    • Dalal, N.1    Greenhalgh, D.2    Mao, X.3
  • 16
    • 34548612632 scopus 로고    scopus 로고
    • Pulse vaccination in SIRS epidemic model with non-monotonic incidence rate
    • Gakkhar S., Negi K. Pulse vaccination in SIRS epidemic model with non-monotonic incidence rate. Chaos Solitons Fractals 2008, 35:626-638.
    • (2008) Chaos Solitons Fractals , vol.35 , pp. 626-638
    • Gakkhar, S.1    Negi, K.2
  • 17
    • 37349097013 scopus 로고    scopus 로고
    • Pulse vaccination of an SEIR epidemic model with time delay
    • Gao S., Chen L., Teng Z. Pulse vaccination of an SEIR epidemic model with time delay. Nonlinear Anal. Real World Appl. 2008, 9:599-607.
    • (2008) Nonlinear Anal. Real World Appl. , vol.9 , pp. 599-607
    • Gao, S.1    Chen, L.2    Teng, Z.3
  • 18
    • 79955561859 scopus 로고    scopus 로고
    • Seasonality and mixed vaccination strategy in an epidemic model with vertical transmission
    • Gao S., Liu Y., Nieto J.J., Andrade H. Seasonality and mixed vaccination strategy in an epidemic model with vertical transmission. Math. Comput. Simulation 2011, 81:1855-1868.
    • (2011) Math. Comput. Simulation , vol.81 , pp. 1855-1868
    • Gao, S.1    Liu, Y.2    Nieto, J.J.3    Andrade, H.4
  • 20
    • 0029445684 scopus 로고
    • An SIS epidemic model with variable population size and a delay
    • Hethcote H.W., van den Driessche P. An SIS epidemic model with variable population size and a delay. J. Math. Biol. 1995, 34:177-194.
    • (1995) J. Math. Biol. , vol.34 , pp. 177-194
    • Hethcote, H.W.1    van den Driessche, P.2
  • 22
    • 0034486891 scopus 로고    scopus 로고
    • The mathematics of infectious diseases
    • Hethcote H.W. The mathematics of infectious diseases. SIAM Rev. 2000, 42:599-653.
    • (2000) SIAM Rev. , vol.42 , pp. 599-653
    • Hethcote, H.W.1
  • 23
    • 0035439412 scopus 로고    scopus 로고
    • An algorithmic introduction to numerical simulation of stochastic differential equations
    • Higham D. An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Rev. 2001, 43:525-546.
    • (2001) SIAM Rev. , vol.43 , pp. 525-546
    • Higham, D.1
  • 24
    • 78149359955 scopus 로고    scopus 로고
    • Stochastic Lotka-Volterra models with multiple delays
    • Hu Y., Wu F., Huang C. Stochastic Lotka-Volterra models with multiple delays. J. Math. Anal. Appl. 2011, 375:42-57.
    • (2011) J. Math. Anal. Appl. , vol.375 , pp. 42-57
    • Hu, Y.1    Wu, F.2    Huang, C.3
  • 25
    • 24644508416 scopus 로고    scopus 로고
    • Exclusion and persistence in deterministic and stochastic chemostat models
    • Imhof L., Walcher S. Exclusion and persistence in deterministic and stochastic chemostat models. J. Differential Equations 2005, 217:26-53.
    • (2005) J. Differential Equations , vol.217 , pp. 26-53
    • Imhof, L.1    Walcher, S.2
  • 26
    • 79955483757 scopus 로고    scopus 로고
    • Dynamics of a stochastic density dependent predator-prey system with Beddington-DeAngelis functional response
    • Ji C., Jiang D. Dynamics of a stochastic density dependent predator-prey system with Beddington-DeAngelis functional response. J. Math. Anal. Appl. 2011, 381:441-453.
    • (2011) J. Math. Anal. Appl. , vol.381 , pp. 441-453
    • Ji, C.1    Jiang, D.2
  • 27
    • 79952616171 scopus 로고    scopus 로고
    • Multigroup SIR epidemic model with stochastic perturbation
    • Ji C., Jiang D., Shi N. Multigroup SIR epidemic model with stochastic perturbation. Phys. A 2011, 390:1747-1762.
    • (2011) Phys. A , vol.390 , pp. 1747-1762
    • Ji, C.1    Jiang, D.2    Shi, N.3
  • 28
    • 77955268021 scopus 로고    scopus 로고
    • The long time behavior of DI SIR epidemic model with stochastic perturbation
    • Jiang D., Ji C., Shi N., Yu J. The long time behavior of DI SIR epidemic model with stochastic perturbation. J. Math. Anal. Appl. 2010, 372:162-180.
    • (2010) J. Math. Anal. Appl. , vol.372 , pp. 162-180
    • Jiang, D.1    Ji, C.2    Shi, N.3    Yu, J.4
  • 29
    • 79955469778 scopus 로고    scopus 로고
    • Asymptotic behavior of global positive solution to a stochastic SIR model
    • Jiang D., Yu J., Ji C., Shi N. Asymptotic behavior of global positive solution to a stochastic SIR model. Math. Comput. Modelling 2011, 54:221-232.
    • (2011) Math. Comput. Modelling , vol.54 , pp. 221-232
    • Jiang, D.1    Yu, J.2    Ji, C.3    Shi, N.4
  • 30
    • 34250220630 scopus 로고    scopus 로고
    • An SIRS model with a nonlinear incidence rate
    • Jin Y., Wang W., Xiao S. An SIRS model with a nonlinear incidence rate. Chaos Solitons Fractals 2007, 34:1482-1497.
    • (2007) Chaos Solitons Fractals , vol.34 , pp. 1482-1497
    • Jin, Y.1    Wang, W.2    Xiao, S.3
  • 31
    • 34547655762 scopus 로고    scopus 로고
    • Global properties of infectious disease models with nonlinear incidence
    • Korobeinikov A. Global properties of infectious disease models with nonlinear incidence. Bull. Math. Biol. 2007, 69:1871-1886.
    • (2007) Bull. Math. Biol. , vol.69 , pp. 1871-1886
    • Korobeinikov, A.1
  • 33
    • 18444376767 scopus 로고    scopus 로고
    • Global stability of an SEIR epidemic model with infectious force in latent, infected and immune period
    • Li G., Jin Z. Global stability of an SEIR epidemic model with infectious force in latent, infected and immune period. Chaos Solitons Fractals 2005, 25:1177-1184.
    • (2005) Chaos Solitons Fractals , vol.25 , pp. 1177-1184
    • Li, G.1    Jin, Z.2
  • 34
    • 64549114893 scopus 로고    scopus 로고
    • Global stability of an SIRS epidemic model with transport-related infection
    • Liu J., Zhou Y. Global stability of an SIRS epidemic model with transport-related infection. Chaos Solitons Fractals 2009, 40:145-158.
    • (2009) Chaos Solitons Fractals , vol.40 , pp. 145-158
    • Liu, J.1    Zhou, Y.2
  • 35
    • 73449103156 scopus 로고    scopus 로고
    • The dynamics of spreading and immune strategies of sexually transmitted diseases on scale-free network
    • Lou J., Ruggeri T. The dynamics of spreading and immune strategies of sexually transmitted diseases on scale-free network. J. Math. Anal. Appl. 2010, 365:210-219.
    • (2010) J. Math. Anal. Appl. , vol.365 , pp. 210-219
    • Lou, J.1    Ruggeri, T.2
  • 36
    • 77957103197 scopus 로고    scopus 로고
    • A one-parameter family of stationary solutions in the susceptible-infected-susceptible epidemic model
    • Lucas A.R. A one-parameter family of stationary solutions in the susceptible-infected-susceptible epidemic model. J. Math. Anal. Appl. 2011, 374:258-271.
    • (2011) J. Math. Anal. Appl. , vol.374 , pp. 258-271
    • Lucas, A.R.1
  • 37
    • 77955662616 scopus 로고    scopus 로고
    • Stability of a novel stochastic epidemic model with double epidemic hypothesis
    • Meng X. Stability of a novel stochastic epidemic model with double epidemic hypothesis. Appl. Math. Comput. 2010, 217:506-515.
    • (2010) Appl. Math. Comput. , vol.217 , pp. 506-515
    • Meng, X.1
  • 39
    • 0242563961 scopus 로고    scopus 로고
    • Environmental Brownian noise suppresses explosions in population dynamics
    • Mao X., Marion G., Renshaw E. Environmental Brownian noise suppresses explosions in population dynamics. Stochastic Process. Appl. 2002, 97:95-110.
    • (2002) Stochastic Process. Appl. , vol.97 , pp. 95-110
    • Mao, X.1    Marion, G.2    Renshaw, E.3
  • 40
    • 79952481627 scopus 로고    scopus 로고
    • First principles modeling of nonlinear incidence rates in seasonal epidemics
    • art. No. e1001079
    • Ponciano J.M., Capistrán M.A. First principles modeling of nonlinear incidence rates in seasonal epidemics. PLoS Comput. Biol. 2011, 7. art. No. e1001079.
    • (2011) PLoS Comput. Biol. , vol.7
    • Ponciano, J.M.1    Capistrán, M.A.2
  • 42
    • 0030438088 scopus 로고    scopus 로고
    • A stochastic model for the HIV epidemic in homosexual populations involving age and race
    • Tan W., Zhu X. A stochastic model for the HIV epidemic in homosexual populations involving age and race. Math. Comput. Modelling 1996, 24:67-105.
    • (1996) Math. Comput. Modelling , vol.24 , pp. 67-105
    • Tan, W.1    Zhu, X.2
  • 43
    • 0030433650 scopus 로고    scopus 로고
    • A stochastic model of the HIV epidemic for heterosexual transmission involving married couples and prostitutes: I. The probabilities of HIV transmission and pair formation
    • Tan W., Zhu X. A stochastic model of the HIV epidemic for heterosexual transmission involving married couples and prostitutes: I. The probabilities of HIV transmission and pair formation. Math. Comput. Modelling 1996, 24:47-107.
    • (1996) Math. Comput. Modelling , vol.24 , pp. 47-107
    • Tan, W.1    Zhu, X.2
  • 44
    • 0031540057 scopus 로고    scopus 로고
    • A stochastic model of the HIV epidemic for heterosexual transmission involving married couples and prostitutes: II. The chain multinomial model of the HIV epidemic
    • Tan W., Zhu X. A stochastic model of the HIV epidemic for heterosexual transmission involving married couples and prostitutes: II. The chain multinomial model of the HIV epidemic. Math. Comput. Modelling 1997, 26:17-92.
    • (1997) Math. Comput. Modelling , vol.26 , pp. 17-92
    • Tan, W.1    Zhu, X.2
  • 45
    • 0032529108 scopus 로고    scopus 로고
    • A state space model for the HIV epidemic in homosexual populations and some applications
    • Tan W., Xiang Z. A state space model for the HIV epidemic in homosexual populations and some applications. Math. Biosci. 1998, 152:29-61.
    • (1998) Math. Biosci. , vol.152 , pp. 29-61
    • Tan, W.1    Xiang, Z.2
  • 46
    • 0036845274 scopus 로고    scopus 로고
    • Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
    • van den Driessche P., Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 2002, 180:29-48.
    • (2002) Math. Biosci. , vol.180 , pp. 29-48
    • van den Driessche, P.1    Watmough, J.2
  • 47
    • 80052891454 scopus 로고    scopus 로고
    • Global stability of two-scale network human epidemic dynamic model
    • Wanduku D., Ladde G.S. Global stability of two-scale network human epidemic dynamic model. Neural Parallel Sci. Comput. 2011, 19:65-90.
    • (2011) Neural Parallel Sci. Comput. , vol.19 , pp. 65-90
    • Wanduku, D.1    Ladde, G.S.2
  • 48
    • 80054938816 scopus 로고    scopus 로고
    • Global properties of a two-scale network stochastic delayed human epidemic dynamic model
    • Wanduku D., Ladde G.S. Global properties of a two-scale network stochastic delayed human epidemic dynamic model. Nonlinear Anal. Real World Appl. 2012, 13:794-816.
    • (2012) Nonlinear Anal. Real World Appl. , vol.13 , pp. 794-816
    • Wanduku, D.1    Ladde, G.S.2
  • 49
    • 80054965082 scopus 로고    scopus 로고
    • Global asymptotic stability and a property of the SIS model on bipartite networks
    • Wen L., Zhong J. Global asymptotic stability and a property of the SIS model on bipartite networks. Nonlinear Anal. Real World Appl. 2012, 13:967-976.
    • (2012) Nonlinear Anal. Real World Appl. , vol.13 , pp. 967-976
    • Wen, L.1    Zhong, J.2
  • 50
    • 79955575035 scopus 로고    scopus 로고
    • A note on asymptotic behaviors of stochastic population model with Allee effect
    • Yang Q., Jiang D. A note on asymptotic behaviors of stochastic population model with Allee effect. Appl. Math. Model. 2011, 35:4611-4619.
    • (2011) Appl. Math. Model. , vol.35 , pp. 4611-4619
    • Yang, Q.1    Jiang, D.2
  • 51
    • 68049121846 scopus 로고    scopus 로고
    • Global stability of two-group SIR model with random perturbation
    • Yu J., Jiang D., Shi N. Global stability of two-group SIR model with random perturbation. J. Math. Anal. Appl. 2009, 360:235-244.
    • (2009) J. Math. Anal. Appl. , vol.360 , pp. 235-244
    • Yu, J.1    Jiang, D.2    Shi, N.3
  • 52
    • 77955513015 scopus 로고    scopus 로고
    • Global threshold property in an epidemic model for disease with latency spreading in a heterogeneous host population
    • Yuan Z., Zou X. Global threshold property in an epidemic model for disease with latency spreading in a heterogeneous host population. Nonlinear Anal. Real World Appl. 2010, 11:3479-3490.
    • (2010) Nonlinear Anal. Real World Appl. , vol.11 , pp. 3479-3490
    • Yuan, Z.1    Zou, X.2
  • 53
    • 47049084345 scopus 로고    scopus 로고
    • Asymptotic properties of hybrid diffusion systems
    • Zhu C., Yin G. Asymptotic properties of hybrid diffusion systems. SIAM J. Control Optim. 2007, 46(4):1155-1179.
    • (2007) SIAM J. Control Optim. , vol.46 , Issue.4 , pp. 1155-1179
    • Zhu, C.1    Yin, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.