메뉴 건너뛰기




Volumn 8, Issue 3, 2011, Pages 733-752

Stability analysis and application of a mathematical cholera model

Author keywords

Cholera model; Dynamical system; Equilibrium; Stability

Indexed keywords

ARTICLE; CHOLERA; COMPUTER SIMULATION; EPIDEMIC; HUMAN; INCIDENCE; PROPORTIONAL HAZARDS MODEL; RISK ASSESSMENT; RISK FACTOR; STATISTICAL MODEL; STATISTICS; ZIMBABWE;

EID: 79958212835     PISSN: 15471063     EISSN: 15510018     Source Type: Journal    
DOI: 10.3934/mbe.2011.8.733     Document Type: Article
Times cited : (64)

References (42)
  • 2
    • 21344476293 scopus 로고
    • Sensitivity and uncertainty analysis of complex models of disease transmission: An HIV model, as an example
    • S. M. Blower and H. Dowlatabadi, Sensitivity and uncertainty analysis of complex models of disease transmission: An HIV model, as an example, International Statistical Review, 62 (1994), 229-243.
    • (1994) International Statistical Review , vol.62 , pp. 229-243
    • Blower, S.M.1    Dowlatabadi, H.2
  • 3
    • 0018704517 scopus 로고
    • Mathematical model for the 1973 cholera epidemic in the European Mediterranean region
    • V. Capasso and S. L. Paveri-Fontana, A mathematical model for the 1973 cholera epidemic in the european mediterranean region, Revue Dépidémoligié et de Santé Publiqué, 27 (1979), 121-132. (Pubitemid 10233290)
    • (1979) Revue d'Epidemiologie et de Sante Publique , vol.27 , Issue.2 , pp. 121-132
    • Capasso, V.1    Paveri-Fontana, S.L.2
  • 5
    • 33847746157 scopus 로고    scopus 로고
    • Bifurcation analysis of a mathematical model for malaria transmission
    • DOI 10.1137/050638941
    • N. Chitnis, J. M. Cushing and J. M. Hyman, Bifurcation analysis of a mathematical model for malaria transmission, SIAM Journal on Applied Mathematics, 67 (2006), 24-45. (Pubitemid 46384494)
    • (2006) SIAM Journal on Applied Mathematics , vol.67 , Issue.1 , pp. 24-45
    • Chitnis, N.1    Cushing, J.M.2    Hyman, J.M.3
  • 6
    • 2942619997 scopus 로고    scopus 로고
    • Endemic and epidemic dynamics of cholera: The role of the aquatic reservoir
    • C. T. Codeço, Endemic and epidemic dynamics of cholera: The role of the aquatic reservoir, BMC Infectious Diseases, 1, 2001.
    • (2001) BMC Infectious Diseases , vol.1
    • Codeço, C.T.1
  • 7
    • 0027736832 scopus 로고
    • The estimation of the basic reproduction number for infections diseases
    • K. Dietz, The estimation of the basic reproduction number for infections diseases, Statistical Methods in Medical Research, 2 (1993), 23-41.
    • (1993) Statistical Methods in Medical Research , vol.2 , pp. 23-41
    • Dietz, K.1
  • 8
    • 0031992574 scopus 로고    scopus 로고
    • Backwards bifurcations and catastrophe in simple models of fatal diseases
    • J. Dushoff, W. Huang and C. Castillo-Chavez, Backwards bifurcation and catastrophe in simple models of fatal diseases, Journal of Mathematical Biology, 36 (1998), 227-248. (Pubitemid 128735143)
    • (1998) Journal of Mathematical Biology , vol.36 , Issue.3 , pp. 227-248
    • Dushoff, J.1    Huang, W.2    Castillo-Chavez, C.3
  • 9
    • 32044434020 scopus 로고    scopus 로고
    • Hyperinfectivity: A critical element in the ability of V. cholerae to cause epidemics?
    • DOI 10.1371/journal.pmed.0030007, e7
    • D. M. Hartley, J. G. Morris and D. L. Smith, Hyperinfectivity: A critical element in the ability of V. cholerae to cause epidemics?, PLoS Medicine, 3 (2006), 63-69. (Pubitemid 43200633)
    • (2006) PLoS Medicine , vol.3 , Issue.1 , pp. 63-69
    • Hartley, D.M.1    Morris Jr., J.G.2    Smith, D.L.3
  • 12
    • 0034486891 scopus 로고    scopus 로고
    • The mathematics of infectious diseases
    • H. W. Hethcote, The mathematics of infectious diseases, SIAM Review, 42 (2000), 599-653.
    • (2000) SIAM Review , vol.42 , pp. 599-653
    • Hethcote, H.W.1
  • 14
    • 0005157181 scopus 로고
    • Periodic orbits of autonomous ordinary differential equations: Theory and applications
    • B. Li, Periodic orbits of autonomous ordinary differential equations: Theory and applications, Nonlinear Analysis, 5 (1981), 931-958.
    • (1981) Nonlinear Analysis , vol.5 , pp. 931-958
    • Li, B.1
  • 15
    • 4644273929 scopus 로고    scopus 로고
    • Global stability of an SEI epidemic model with general contact rate
    • G. Li and J. Zhen, Global stability of an SEI epidemic model with general contact rate, Chaos Solitons Fractals, 23 (2005), 997-1004.
    • (2005) Chaos Solitons Fractals , vol.23 , pp. 997-1004
    • Li, G.1    Zhen, J.2
  • 16
    • 0032812296 scopus 로고    scopus 로고
    • Global dynamics of a SEIR model with varying total population size
    • DOI 10.1016/S0025-5564(99)00030-9, PII S0025556499000309
    • M. Y. Li, J. R. Graef, L. Wang and J. Karsai, Global dynamics of a SEIR model with varying total population size, Mathematical Biosciences, 160 (1999), 191-213. (Pubitemid 29398860)
    • (1999) Mathematical Biosciences , vol.160 , Issue.2 , pp. 191-213
    • Li, M.Y.1    Graef, J.R.2    Wang, L.3    Karsai, J.4
  • 17
    • 0028817626 scopus 로고
    • Global stability for the SEIR model in epidemiology
    • M. Y. Li and J. S. Muldowney, Global stability for the SEIR model in epidemiology, Mathe- matical Biosciences, 125 (1995), 155-164.
    • (1995) Mathematical Biosciences , vol.125 , pp. 155-164
    • Li, M.Y.1    Muldowney, J.S.2
  • 18
    • 0017226769 scopus 로고
    • A deterministic model for gonorrhea in a nonhomogeneous population
    • A. Lajmanovich and J. Yorke, A deterministic model for gonorrhea in a nonhomogeneous population, Mathematical Biosciences, 28 (1976), 221-236.
    • (1976) Mathematical Biosciences , vol.28 , pp. 221-236
    • Lajmanovich, A.1    Yorke, J.2
  • 19
  • 21
    • 49649105737 scopus 로고    scopus 로고
    • Inapparent infections and cholera dynamics
    • A. A. King, E. L. Lonides, M. Pascual and M. J. Bouma, Inapparent infections and cholera dynamics, Nature, 454 (2008), 877-881.
    • (2008) Nature , vol.454 , pp. 877-881
    • King, A.A.1    Lonides, E.L.2    Pascual, M.3    Bouma, M.J.4
  • 22
    • 45449094504 scopus 로고    scopus 로고
    • A methodology for performing global uncertainty and sensitivity analysis in system biology
    • S. Marino, I. Hogue, C. J. Ray and D. E. Kirschner, A methodology for performing global uncertainty and sensitivity analysis in system biology, Journal of Theoretical Biology, 254 (2008), 178-196.
    • (2008) Journal of Theoretical Biology , vol.254 , pp. 178-196
    • Marino, S.1    Hogue, I.2    Ray, C.J.3    Kirschner, D.E.4
  • 23
    • 66249092824 scopus 로고    scopus 로고
    • Zimbabwe experiences the worst epidemic of cholera in Africa
    • P. R. Mason, Zimbabwe experiences the worst epidemic of cholera in Africa, Journal of Infection in Developing Countries, 3 (2009), 148-151.
    • (2009) Journal of Infection in Developing Countries , vol.3 , pp. 148-151
    • Mason, P.R.1
  • 24
    • 0026491804 scopus 로고
    • Dynamic models of infectious diseases as regulator of population sizes
    • J. Mena-Lorca and H. W. Hethcote, Dynamic models of infectious diseases as regulator of population sizes, Journal of Mathematical Biology, 30 (1992), 693-716.
    • (1992) Journal of Mathematical Biology , vol.30 , pp. 693-716
    • Mena-Lorca, J.1    Hethcote, H.W.2
  • 26
    • 0037099662 scopus 로고    scopus 로고
    • Global stability of a two-stage epidemic model with generalized non-linear incidence
    • DOI 10.1016/S0378-4754(02)00002-2, PII S0378475402000022
    • S. M. Moghadas and A. B. Gumel, Global stability of a two-stage epidemic model with gener- alized non-linear incidence, Mathematics and Computers in Simulation, 60 (2002), 107-118. (Pubitemid 34661523)
    • (2002) Mathematics and Computers in Simulation , vol.60 , Issue.1-2 , pp. 107-118
    • Moghadas, S.M.1    Gumel, A.B.2
  • 29
    • 0036185525 scopus 로고    scopus 로고
    • Cholera and climate: Revisiting the quantitative evidence
    • DOI 10.1016/S1286-4579(01)01533-7, PII S1286457901015337
    • M. Pascual, M. Bouma and A. Dobson, Cholera and climate: Revisiting the quantiative evidence, Microbes and Infections, 4 (2002), 237-245. (Pubitemid 34183499)
    • (2002) Microbes and Infection , vol.4 , Issue.2 , pp. 237-245
    • Pascual, M.1    Bouma, M.J.2    Dobson, A.P.3
  • 30
    • 33745604544 scopus 로고    scopus 로고
    • Hyperinfectivity in cholera: A new mechanism for an old epidemiological model?
    • M. Pascual, K. Koelle and A. Dobson, Hyperinfectivity in cholera: A new mechanism for an old epidemiological model? , PLoS Medicine, 3 (2006), 931-933.
    • (2006) PLoS Medicine , vol.3 , pp. 931-933
    • Pascual, M.1    Koelle, K.2    Dobson, A.3
  • 31
    • 0012460662 scopus 로고    scopus 로고
    • A method to estimate the incidence of communicable diseases under seasonal fluctuations with application to cholera
    • DOI 10.1016/S0096-3003(99)00212-X, PII S009630039900212X
    • E. Pourabbas, A. d'Onofrio and M. Rafanelli, A method to estimate the incidence of commu- nicable diseases under seasonal uctuations with application to cholera, Applied Mathematics and Computation, 118 (2001), 161-174. (Pubitemid 33592916)
    • (2001) Applied Mathematics and Computation , vol.118 , Issue.2-3 , pp. 161-174
    • Pourabbas, E.1    D'Onofrio, A.2    Rafanelli, M.3
  • 32
    • 41949112171 scopus 로고    scopus 로고
    • Backward bifurcation and multiple equilibria in epidemic models with structured immunity
    • T. C. Reluga, J. Medlock and A. S. Perelson, Backward bifurcation and multiple equilibria in epidemic models with structured immunity, Journal of Theoretical Biology, 252 (2008), 155-165.
    • (2008) Journal of Theoretical Biology , vol.252 , pp. 155-165
    • Reluga, T.C.1    Medlock, J.2    Perelson, A.S.3
  • 33
    • 0026846319 scopus 로고
    • Reproduction numbers and the stability of equilibria of SI models for heterogeneous populations
    • C. P. Simon and J. A. Jacquez, Reproduction numbers and the stability of equilibria of SI models for heterogeneous populations, SIAM Journal on Applied Mathematics, 52 (1992), 541-576.
    • (1992) SIAM Journal on Applied Mathematics , vol.52 , pp. 541-576
    • Simon, C.P.1    Jacquez, J.A.2
  • 35
    • 84923059547 scopus 로고    scopus 로고
    • An introduction to dynamical systems and neuronal dynamics
    • Springer, Berlin/Heidelberg
    • D. Terman, An introduction to dynamical systems and neuronal dynamics, in \Tutorials in Mathematical Biosciences I," Springer, Berlin/Heidelberg, 2005.
    • (2005) Tutorials in Mathematical Biosciences I
    • Terman, D.1
  • 37
    • 0036845274 scopus 로고    scopus 로고
    • Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
    • DOI 10.1016/S0025-5564(02)00108-6, PII S0025556402001086
    • P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180 (2002), 29-48. (Pubitemid 35304346)
    • (2002) Mathematical Biosciences , vol.180 , pp. 29-48
    • Van Den Driessche, P.1    Watmough, J.2
  • 38
    • 34548598462 scopus 로고    scopus 로고
    • Estimates of the reproduction numbers of Spanish influenza using morbidity data
    • DOI 10.1093/ije/dym071
    • E. Vynnycky, A. Trindall and P. Mangtani, Estimates of the reproduction numbers of spanish inuenza using morbidity data, International Journal of Epidemiology, 36 (2007), 881-889. (Pubitemid 47394158)
    • (2007) International Journal of Epidemiology , vol.36 , Issue.4 , pp. 881-889
    • Vynnycky, E.1    Trindall, A.2    Mangtani, P.3
  • 39
    • 0042828944 scopus 로고    scopus 로고
    • Global dynamics of an SEIR epidemic model with saturating contact rate
    • DOI 10.1016/S0025-5564(03)00087-7
    • J. Zhang and Z. Ma, Global dynamics of an SEIR epidemic model with saturating contact rate, Mathematical Biosciences, 185 (2003), 15-32. (Pubitemid 37046573)
    • (2003) Mathematical Biosciences , vol.185 , Issue.1 , pp. 15-32
    • Zhang, J.1    Ma, Z.2
  • 41
    • 84858613793 scopus 로고    scopus 로고
    • Available from
    • The Wikipedia, Available from: http://en.wikipedia.org.
    • The Wikipedia
  • 42
    • 84858621095 scopus 로고    scopus 로고
    • World Health Organization Available from
    • World Health Organization, Available from: http://www.who.org.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.