메뉴 건너뛰기




Volumn 17, Issue 6, 2012, Pages 2551-2563

Stability analysis of an epidemic model with diffusion and stochastic perturbation

Author keywords

Diffusion; Epidemic model; It 's formula; Lyapunov function; Stochastic perturbation

Indexed keywords

ASYMPTOTIC STABILITY; DIFFUSION; EPIDEMIOLOGY; STOCHASTIC MODELS; STOCHASTIC SYSTEMS;

EID: 84855243526     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2011.10.005     Document Type: Article
Times cited : (20)

References (41)
  • 1
    • 0018656345 scopus 로고
    • Population biology of infectious dieases
    • Anderson R., May R. Population biology of infectious dieases. Part I Nature 1979, 280:361-367.
    • (1979) Part I Nature , vol.280 , pp. 361-367
    • Anderson, R.1    May, R.2
  • 2
    • 33748131158 scopus 로고    scopus 로고
    • Epidemic threshold conditions for seasonally forced SEIR models
    • Ma J., Ma Z. Epidemic threshold conditions for seasonally forced SEIR models. Math Biosci Eng 2006, 3(1):161-172.
    • (2006) Math Biosci Eng , vol.3 , Issue.1 , pp. 161-172
    • Ma, J.1    Ma, Z.2
  • 3
    • 85196152287 scopus 로고    scopus 로고
    • S-I-R epidemic models with directed diffusion in mathematical aspects of human diseases. In: Prato G Da, editior. Appl Math Monographs 3 1992, Giardini Editori, Pisa.
    • Meade D, Milner F. S-I-R epidemic models with directed diffusion in mathematical aspects of human diseases. In: Prato G Da, editior. Appl Math Monographs 3 1992, Giardini Editori, Pisa.
    • Meade, D.1    Milner, F.2
  • 4
    • 0000998185 scopus 로고
    • Contributions to the mathematical theory of epidemics (Part I)
    • Kermack W., McKendrick A. Contributions to the mathematical theory of epidemics (Part I). Proc Roy Soc A 1927, 115:700-721.
    • (1927) Proc Roy Soc A , vol.115 , pp. 700-721
    • Kermack, W.1    McKendrick, A.2
  • 5
    • 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(6):4107-4115.
    • (2001) Nonlinear Anal , vol.47 , Issue.6 , pp. 4107-4115
    • Beretta, E.1    Hara, T.2    Ma, W.3    Takeuchi, Y.4
  • 6
    • 34248562938 scopus 로고    scopus 로고
    • The final size of a SARS epidemic model without quarantine
    • Hsu S., Roeger L. The final size of a SARS epidemic model without quarantine. J Math Anal Appl 2007, 333(2):557-566.
    • (2007) J Math Anal Appl , vol.333 , Issue.2 , pp. 557-566
    • Hsu, S.1    Roeger, L.2
  • 7
    • 39449119838 scopus 로고    scopus 로고
    • The dynamics of a new SIR epidemic model concerning pulse vaccination strategy
    • Meng X., Chen L. The dynamics of a new SIR epidemic model concerning pulse vaccination strategy. Appl Math Comput 2008, 197(2):528-597.
    • (2008) Appl Math Comput , vol.197 , Issue.2 , pp. 528-597
    • Meng, X.1    Chen, L.2
  • 8
    • 41149168534 scopus 로고    scopus 로고
    • Effects of predation on host-pathogen dynamics in SIR models
    • Roy M., Holt R. Effects of predation on host-pathogen dynamics in SIR models. Theor Popul Biol 2008, 73(3):319-331.
    • (2008) Theor Popul Biol , vol.73 , Issue.3 , pp. 319-331
    • Roy, M.1    Holt, R.2
  • 9
    • 67349167681 scopus 로고    scopus 로고
    • The effect of impulsive vaccination on an SIR epidemic model
    • Shi R., Jiang X., Chen L. The effect of impulsive vaccination on an SIR epidemic model. Appl Math Comput 2009, 212(2):305-311.
    • (2009) Appl Math Comput , vol.212 , Issue.2 , pp. 305-311
    • Shi, R.1    Jiang, X.2    Chen, L.3
  • 10
    • 40649091581 scopus 로고    scopus 로고
    • An epidemic model of a vector-borne disease with direct transmission and time delay
    • Wei H., Li X., Martcheva M. An epidemic model of a vector-borne disease with direct transmission and time delay. J Math Anal Appl 2008, 342(2):895-908.
    • (2008) J Math Anal Appl , vol.342 , Issue.2 , pp. 895-908
    • Wei, H.1    Li, X.2    Martcheva, M.3
  • 11
    • 33947212532 scopus 로고    scopus 로고
    • A SIRS epidemic model with infection-age dependence
    • Zhang Z., Peng J. A SIRS epidemic model with infection-age dependence. J Math Anal Appl 2007, 331(2):1396-1414.
    • (2007) J Math Anal Appl , vol.331 , Issue.2 , pp. 1396-1414
    • Zhang, Z.1    Peng, J.2
  • 12
    • 41949125685 scopus 로고    scopus 로고
    • Global stability of an SIR epidemic model with constant infectious period
    • Zhang F., Li Z., Zhang F. Global stability of an SIR epidemic model with constant infectious period. Appl Math Comput 2008, 199(1):285-291.
    • (2008) Appl Math Comput , vol.199 , Issue.1 , pp. 285-291
    • Zhang, F.1    Li, Z.2    Zhang, F.3
  • 13
    • 54049119675 scopus 로고    scopus 로고
    • Permanence and extinction for a nonautonomous SIRS epidemic model with time delay
    • Zhang T., Teng Z. Permanence and extinction for a nonautonomous SIRS epidemic model with time delay. Appl Math Model 2009, 33(2):1058-1071.
    • (2009) Appl Math Model , vol.33 , Issue.2 , pp. 1058-1071
    • Zhang, T.1    Teng, Z.2
  • 14
    • 0028176208 scopus 로고
    • Partial differential equations in ecology: spatial interactions and population dynamics
    • Holmes E., Lewis M., Banks J., Veit R. Partial differential equations in ecology: spatial interactions and population dynamics. Ecology 1994, 75:17-29.
    • (1994) Ecology , vol.75 , pp. 17-29
    • Holmes, E.1    Lewis, M.2    Banks, J.3    Veit, R.4
  • 18
    • 44749094468 scopus 로고    scopus 로고
    • Dynamics of an HBV model with diffusion and delay
    • Wang K., Wang W., Song S. Dynamics of an HBV model with diffusion and delay. J Theor Biol 2008, 253(1):36-44.
    • (2008) J Theor Biol , vol.253 , Issue.1 , pp. 36-44
    • Wang, K.1    Wang, W.2    Song, S.3
  • 19
    • 33846025992 scopus 로고    scopus 로고
    • Stability of epidemic models with evolution
    • Mulone G., Straughan B., Wang W. Stability of epidemic models with evolution. Studies Appl Math 2007, 118(2):117-132.
    • (2007) Studies Appl Math , vol.118 , Issue.2 , pp. 117-132
    • Mulone, G.1    Straughan, B.2    Wang, W.3
  • 20
    • 0028314994 scopus 로고
    • Asymptotic behaviour of reaction-diffusion systems in population and epidemic models, The role of cross diffusion
    • Capasso V., Liddo A. Asymptotic behaviour of reaction-diffusion systems in population and epidemic models, The role of cross diffusion. J Math Biol 1994, 32:453-463.
    • (1994) J Math Biol , vol.32 , pp. 453-463
    • Capasso, V.1    Liddo, A.2
  • 21
    • 14844315022 scopus 로고    scopus 로고
    • Ratio-dependent predator-prey model: effect of environmental fluctuation and stability
    • Bandyopadhyay M., Chattopadhyay J. Ratio-dependent predator-prey model: effect of environmental fluctuation and stability. Nonlinearity 2005, 18(2):913-936.
    • (2005) Nonlinearity , vol.18 , Issue.2 , pp. 913-936
    • Bandyopadhyay, M.1    Chattopadhyay, J.2
  • 24
    • 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(2):1084-1101.
    • (2008) J Math Anal Appl , vol.341 , Issue.2 , pp. 1084-1101
    • Dalal, N.1    Greenhalgh, D.2    Mao, X.3
  • 25
    • 0028518403 scopus 로고
    • Stochastic stabilisation and destabilisation
    • Mao X. Stochastic stabilisation and destabilisation. Systems Control Lett 1994, 23:279-290.
    • (1994) Systems Control Lett , vol.23 , pp. 279-290
    • Mao, X.1
  • 26
    • 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(1):95-110.
    • (2002) Stochastic Process Appl , vol.97 , Issue.1 , pp. 95-110
    • Mao, X.1    Marion, G.2    Renshaw, E.3
  • 27
    • 0031997110 scopus 로고    scopus 로고
    • Stability of epidemic model with time delays influenced by stochastic perturbations
    • Berettaa E., Kolmanovskiib V., Shaikhet L. Stability of epidemic model with time delays influenced by stochastic perturbations. Math Comput Simu 1998, 45(3-4):269-277.
    • (1998) Math Comput Simu , vol.45 , Issue.3-4 , pp. 269-277
    • Berettaa, E.1    Kolmanovskiib, V.2    Shaikhet, L.3
  • 28
    • 19944381861 scopus 로고    scopus 로고
    • Stability of a stochastic SIR system
    • Tornatore E., Buccellato S., Vetro P. Stability of a stochastic SIR system. Phys A 2005, 354:111-126.
    • (2005) Phys A , vol.354 , pp. 111-126
    • Tornatore, E.1    Buccellato, S.2    Vetro, P.3
  • 29
    • 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(1):235-244.
    • (2009) J Math Anal Appl , vol.360 , Issue.1 , pp. 235-244
    • Yu, J.1    Jiang, D.2    Shi, N.3
  • 30
    • 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(2):506-515.
    • (2010) Appl Math Comput , vol.217 , Issue.2 , pp. 506-515
    • Meng, X.1
  • 31
    • 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(1):162-180.
    • (2010) J Math Anal Appl , vol.372 , Issue.1 , pp. 162-180
    • Jiang, D.1    Ji, C.2    Shi, N.3    Yu, J.4
  • 32
    • 0347600676 scopus 로고    scopus 로고
    • Numerical simulation of stochastic ordinary differential equations in biomathematical modelling
    • Carletti M., Burrage K., Burrage P. Numerical simulation of stochastic ordinary differential equations in biomathematical modelling. Math Comput Simulat 2004, 64:271-277.
    • (2004) Math Comput Simulat , vol.64 , pp. 271-277
    • Carletti, M.1    Burrage, K.2    Burrage, P.3
  • 33
    • 34547134261 scopus 로고    scopus 로고
    • Global analysis of an epidemic model with nonmonotone incidence rate
    • Xiao D., Ruan S. Global analysis of an epidemic model with nonmonotone incidence rate. Math Biosci 2007, 208(2):419-429.
    • (2007) Math Biosci , vol.208 , Issue.2 , pp. 419-429
    • Xiao, D.1    Ruan, S.2
  • 34
    • 0022649243 scopus 로고
    • Pattern sensitivity to boundary and initial conditions in reaction-diffusion models
    • Arcuri P., Murray J. Pattern sensitivity to boundary and initial conditions in reaction-diffusion models. J Math Biol 1986, 24(2):141-165.
    • (1986) J Math Biol , vol.24 , Issue.2 , pp. 141-165
    • Arcuri, P.1    Murray, J.2
  • 35
    • 78049383134 scopus 로고    scopus 로고
    • Complex patterns in a predator-prey model with self and cross-diffusion
    • Wang W., Lin Y., Zhang L., Rao F., Tan Y. Complex patterns in a predator-prey model with self and cross-diffusion. Commun Nonlinear Sci Numer Simulat 2011, 16:2006-2015.
    • (2011) Commun Nonlinear Sci Numer Simulat , vol.16 , pp. 2006-2015
    • Wang, W.1    Lin, Y.2    Zhang, L.3    Rao, F.4    Tan, Y.5
  • 36
    • 0003460899 scopus 로고
    • Geometric theory of semilinear parabolic equations
    • Springer-Verlag
    • Henry D. Geometric theory of semilinear parabolic equations. Lecture Notes in Mathematics 1981, Springer-Verlag.
    • (1981) Lecture Notes in Mathematics
    • Henry, D.1
  • 38
    • 77957351473 scopus 로고    scopus 로고
    • Global stability of a nonlinear stochastic predator-prey system with Beddington-DeAngelis functional response
    • Liu M., Wang K. Global stability of a nonlinear stochastic predator-prey system with Beddington-DeAngelis functional response. Commun Nonlinear Sci Numer Simulat 2011, 16(3):1114-1121.
    • (2011) Commun Nonlinear Sci Numer Simulat , vol.16 , Issue.3 , pp. 1114-1121
    • Liu, M.1    Wang, K.2
  • 39
    • 34249314701 scopus 로고    scopus 로고
    • Stochastic population dynamics under regime switching
    • Luo Q., Mao X. Stochastic population dynamics under regime switching. J Math Anal Appl 2007, 334(1):69-84.
    • (2007) J Math Anal Appl , vol.334 , Issue.1 , pp. 69-84
    • Luo, Q.1    Mao, X.2
  • 40
    • 79955964883 scopus 로고    scopus 로고
    • Asymptotic properties of a stochastic predator-prey system with Holling II functional response
    • Lv J., Wang K. Asymptotic properties of a stochastic predator-prey system with Holling II functional response. Commun Nonlinear Sci Numer Simulat 2011, 16(10):4037-4048.
    • (2011) Commun Nonlinear Sci Numer Simulat , vol.16 , Issue.10 , pp. 4037-4048
    • Lv, J.1    Wang, K.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.