메뉴 건너뛰기




Volumn 7, Issue 2, 2011, Pages

First principles modeling of nonlinear incidence rates in seasonal epidemics

Author keywords

[No Author keywords available]

Indexed keywords

EPIDEMIOLOGY; STOCHASTIC MODELS; STOCHASTIC SYSTEMS;

EID: 79952481627     PISSN: 1553734X     EISSN: 15537358     Source Type: Journal    
DOI: 10.1371/journal.pcbi.1001079     Document Type: Article
Times cited : (43)

References (61)
  • 2
    • 0034486891 scopus 로고    scopus 로고
    • The mathematics of infectious diseases
    • Hethcote H, (2000) The mathematics of infectious diseases. SIAM rev 42: 599-653.
    • (2000) SIAM Rev , vol.42 , pp. 599-653
    • Hethcote, H.1
  • 3
    • 0025985745 scopus 로고
    • Some epidemiological models with nonlinear incidence
    • Hethcote H, Driessche P, (1991) Some epidemiological models with nonlinear incidence. J Math Biol 29: 271-287.
    • (1991) J Math Biol , vol.29 , pp. 271-287
    • Hethcote, H.1    Driessche, P.2
  • 4
    • 0028116676 scopus 로고
    • Some Discrete-Time SI, S/R, and S/S Epidemic Models
    • Allen L, (1994) Some Discrete-Time SI, S/R, and S/S Epidemic Models. Math Biosci 124: 83-105.
    • (1994) Math Biosci , vol.124 , pp. 83-105
    • Allen, L.1
  • 5
    • 0033979874 scopus 로고    scopus 로고
    • Comparison of deterministic and stochastic SIS and SIR models in discrete time
    • Allen L, Burgin A, (2000) Comparison of deterministic and stochastic SIS and SIR models in discrete time. Math Biosci 163: 1-33.
    • (2000) Math Biosci , vol.163 , pp. 1-33
    • Allen, L.1    Burgin, A.2
  • 6
    • 0037429355 scopus 로고    scopus 로고
    • Dynamical behavior of an epidemic model with a nonlinear incidence rate
    • Ruan S, Wang W, (2003) Dynamical behavior of an epidemic model with a nonlinear incidence rate. J Differ Equations 188: 135-163.
    • (2003) J Differ Equations , vol.188 , pp. 135-163
    • Ruan, S.1    Wang, W.2
  • 7
    • 27844516471 scopus 로고    scopus 로고
    • Bifurcation Analysis of an SIRS Epidemic Model with Generalized Incidence
    • Alexander M, Moghadas S, (2006) Bifurcation Analysis of an SIRS Epidemic Model with Generalized Incidence. SIAM J App Math 65: 1794-1816.
    • (2006) SIAM J App Math , vol.65 , pp. 1794-1816
    • Alexander, M.1    Moghadas, S.2
  • 8
    • 25144476559 scopus 로고    scopus 로고
    • Non-linear incidence and stability of infectious disease models
    • Korobeinikov A, Maini P, (2005) Non-linear incidence and stability of infectious disease models. Math Med Biol 22: 113-128.
    • (2005) Math Med Biol , vol.22 , pp. 113-128
    • Korobeinikov, A.1    Maini, P.2
  • 9
    • 0034847341 scopus 로고    scopus 로고
    • Modeling epidemics caused by respiratory syncytial virus (RSV)
    • Weber A, Weber M, Milligan P, (2001) Modeling epidemics caused by respiratory syncytial virus (RSV). Math Biosci 172: 95-113.
    • (2001) Math Biosci , vol.172 , pp. 95-113
    • Weber, A.1    Weber, M.2    Milligan, P.3
  • 10
    • 0036590892 scopus 로고    scopus 로고
    • Dynamics of measles epidemics: estimating scaling of transmission rates using a time series SIR model
    • Bjørnstad O, Finkenstädt B, Grenfell B, (2002) Dynamics of measles epidemics: estimating scaling of transmission rates using a time series SIR model. Ecol Monogr 72: 169-184.
    • (2002) Ecol Monogr , vol.72 , pp. 169-184
    • Bjørnstad, O.1    Finkenstädt, B.2    Grenfell, B.3
  • 11
  • 13
    • 0002454064 scopus 로고
    • The incidence of infectious diseases under the influence of seasonal fluctuations
    • In: Berger J, Bühler W, Repges R, Tautu P, editors, Berlin, Springer-Verlag
    • Dietz K, (1976) The incidence of infectious diseases under the influence of seasonal fluctuations. In: Berger J, Bühler W, Repges R, Tautu P, editors. Proceedings of a Workshop on Mathematical Models in Medicine, Mainz. Lecture Notes in Biomathematics 11 Berlin Springer-Verlag pp. 1-15.
    • (1976) Proceedings of a Workshop on Mathematical Models in Medicine, Mainz. Lecture Notes in Biomathematics 11 , pp. 1-15
    • Dietz, K.1
  • 14
    • 1142267538 scopus 로고    scopus 로고
    • External forcing of ecological and epidemiological systems: a resonance approach
    • Greenman J, Kamo M, Boots M, (2004) External forcing of ecological and epidemiological systems: a resonance approach. Physica D 190: 136-151.
    • (2004) Physica D , vol.190 , pp. 136-151
    • Greenman, J.1    Kamo, M.2    Boots, M.3
  • 15
    • 0347663530 scopus 로고    scopus 로고
    • Seasonally forced disease dynamics explored as switching between attractors
    • Keeling M, Rohani P, Grenfell B, (2001) Seasonally forced disease dynamics explored as switching between attractors. Physica D 148: 317-335.
    • (2001) Physica D , vol.148 , pp. 317-335
    • Keeling, M.1    Rohani, P.2    Grenfell, B.3
  • 16
    • 34047120681 scopus 로고    scopus 로고
    • Seasonal dynamics of recurrent epidemics
    • Stone L, Olinky R, Huppert A, (2007) Seasonal dynamics of recurrent epidemics. Nature 446: 533.
    • (2007) Nature , vol.446 , pp. 533
    • Stone, L.1    Olinky, R.2    Huppert, A.3
  • 17
    • 49649105737 scopus 로고    scopus 로고
    • Inapparent infections and cholera dynamics
    • King A, Ionides E, Pascual M, Bouma M, (2008) Inapparent infections and cholera dynamics. Nature 454: 877-U29.
    • (2008) Nature , vol.454
    • King, A.1    Ionides, E.2    Pascual, M.3    Bouma, M.4
  • 18
    • 15744382069 scopus 로고    scopus 로고
    • Seasonal patterns of infectious diseases
    • Pascual M, Dobson A, (2005) Seasonal patterns of infectious diseases. PLoS Med 2: 18-20.
    • (2005) PLoS Med , vol.2 , pp. 18-20
    • Pascual, M.1    Dobson, A.2
  • 20
    • 1542648303 scopus 로고    scopus 로고
    • Seasonal dynamics of mycoplasmal conjunctivitis in eastern North American house finches
    • Altizer S, Hochachka W, Dhondt A, (2004) Seasonal dynamics of mycoplasmal conjunctivitis in eastern North American house finches. Ecology 73: 309-322.
    • (2004) Ecology , vol.73 , pp. 309-322
    • Altizer, S.1    Hochachka, W.2    Dhondt, A.3
  • 22
    • 0018041874 scopus 로고
    • A generalization of the kermack-mckendrick deterministic epidemic model
    • Capasso V, Serio G, (1978) A generalization of the kermack-mckendrick deterministic epidemic model. Math Biosci 42: 41-61.
    • (1978) Math Biosci , vol.42 , pp. 41-61
    • Capasso, V.1    Serio, G.2
  • 23
    • 0025985745 scopus 로고
    • Some epidemiological models with nonlinear incidence
    • Hethcote H, Driessche P, (1991) Some epidemiological models with nonlinear incidence. J Math Biol 29: 271-287.
    • (1991) J Math Biol , vol.29 , pp. 271-287
    • Hethcote, H.1    Driessche, P.2
  • 24
    • 0023070210 scopus 로고
    • Dynamical behavior of epidemiological models with nonlinear incidence rates
    • Liu W, Hethcote H, Levin S, (1987) Dynamical behavior of epidemiological models with nonlinear incidence rates. J Math Biol 25: 359-380.
    • (1987) J Math Biol , vol.25 , pp. 359-380
    • Liu, W.1    Hethcote, H.2    Levin, S.3
  • 25
    • 1542406443 scopus 로고    scopus 로고
    • Bifurcations in an epidemic model with constant removal rate of the infectives
    • Wang W, Ruan S, (2004) Bifurcations in an epidemic model with constant removal rate of the infectives. J Math Anal and Appl 291: 775-793.
    • (2004) J Math Anal and Appl , vol.291 , pp. 775-793
    • Wang, W.1    Ruan, S.2
  • 26
    • 34250220630 scopus 로고    scopus 로고
    • An SIRS model with a nonlinear incidence rate
    • Jin Y, Wang W, Xiao S, (2007) An SIRS model with a nonlinear incidence rate. Chaos Solitons Fractals 34: 1482-1497.
    • (2007) Chaos Solitons Fractals , vol.34 , pp. 1482-1497
    • Jin, Y.1    Wang, W.2    Xiao, S.3
  • 27
    • 0036369855 scopus 로고    scopus 로고
    • Exciting chaos with noise: unexpected dynamics in epidemic outbreaks
    • Billings L, Schwartz I, (2002) Exciting chaos with noise: unexpected dynamics in epidemic outbreaks. J Math Biol 44: 31-48.
    • (2002) J Math Biol , vol.44 , pp. 31-48
    • Billings, L.1    Schwartz, I.2
  • 28
    • 84994053884 scopus 로고    scopus 로고
    • Modeling infectious diseases in humans and animals
    • Keeling M, Rohani P, (2008) Modeling infectious diseases in humans and animals. Clin Infect Dis 47: 864-6.
    • (2008) Clin Infect Dis , vol.47 , pp. 864-866
    • Keeling, M.1    Rohani, P.2
  • 29
    • 42249098829 scopus 로고    scopus 로고
    • An introduction to stochastic epidemic models
    • In: Brauer F, Van den Driessche P, Wu J, editors, Berlin, Springer
    • Allen L, (2008) An introduction to stochastic epidemic models. In: Brauer F, Van den Driessche P, Wu J, editors. Mathematical Epidemiology. Lecture Notes in Mathematics Berlin Springer pp. 81-130.
    • (2008) Mathematical Epidemiology. Lecture Notes in Mathematics , pp. 81-130
    • Allen, L.1
  • 30
    • 0034723248 scopus 로고    scopus 로고
    • A simple model for complex dynamical transitions in epidemics
    • Earn D, Rohani P, Bolker B, Grenfell B, (2000) A simple model for complex dynamical transitions in epidemics. Science 287: 667.
    • (2000) Science , vol.287 , pp. 667
    • Earn, D.1    Rohani, P.2    Bolker, B.3    Grenfell, B.4
  • 32
    • 0027465252 scopus 로고
    • Chaos and biological complexity in measles dynamics
    • Bolker B, Grenfell B, (1993) Chaos and biological complexity in measles dynamics. Proc R Soc Lond B Biol Sci 251: 75-81.
    • (1993) Proc R Soc Lond B Biol Sci , vol.251 , pp. 75-81
    • Bolker, B.1    Grenfell, B.2
  • 33
    • 5544233810 scopus 로고    scopus 로고
    • A weather-driven model of malaria transmission
    • Hoshen M, Morse A, (2004) A weather-driven model of malaria transmission. Malar J 3: 32.
    • (2004) Malar J , vol.3 , pp. 32
    • Hoshen, M.1    Morse, A.2
  • 34
    • 42249097285 scopus 로고    scopus 로고
    • Compartmental models in epidemiology
    • In: Brauer F, Van den Driessche P, Wu J, editors, Berlin, Springer
    • Brauer F, (2008) Compartmental models in epidemiology. In: Brauer F, Van den Driessche P, Wu J, editors. Mathematical Epidemiology. Lecture Notes in Mathematics Berlin Springer pp. 19-80.
    • (2008) Mathematical Epidemiology. Lecture Notes in Mathematics , pp. 19-80
    • Brauer, F.1
  • 35
    • 0027429258 scopus 로고
    • A disease transmission model in a nonconstant population
    • Derrick W, Driessche P, (1993) A disease transmission model in a nonconstant population. J Math Biol 31: 495-512.
    • (1993) J Math Biol , vol.31 , pp. 495-512
    • Derrick, W.1    Driessche, P.2
  • 36
    • 0000236256 scopus 로고
    • Periodicity in epidemiological models
    • In: Gross L, Hallam TG, Levin SA, editors, Berlin, Springer
    • Hethcote H, Levin SA, (1989) Periodicity in epidemiological models. In: Gross L, Hallam TG, Levin SA, editors. Applied Mathematical Ecology 18 Berlin Springer pp. 193-211.
    • (1989) Applied Mathematical Ecology 18 , pp. 193-211
    • Hethcote, H.1    Levin, S.A.2
  • 37
    • 0000604313 scopus 로고
    • Allee effects: population growth, critical density, and the chance of extinction
    • Dennis B, (1989) Allee effects: population growth, critical density, and the chance of extinction. Natural Resource Modeling 3: 481-538.
    • (1989) Natural Resource Modeling , vol.3 , pp. 481-538
    • Dennis, B.1
  • 39
    • 13144257707 scopus 로고    scopus 로고
    • The genetic theory of adaptation: a brief history
    • Orr H, (2005) The genetic theory of adaptation: a brief history. Nat Rev Genet 6: 119-127.
    • (2005) Nat Rev Genet , vol.6 , pp. 119-127
    • Orr, H.1
  • 41
    • 33644839515 scopus 로고    scopus 로고
    • Sampling variability and estimates of density dependence: a composite-likelihood approach
    • Lele S, (2006) Sampling variability and estimates of density dependence: a composite-likelihood approach. Ecology 87: 189-202.
    • (2006) Ecology , vol.87 , pp. 189-202
    • Lele, S.1
  • 42
    • 33747072045 scopus 로고    scopus 로고
    • Estimating density dependence, process noise, and observation error
    • Dennis B, Ponciano J, Lele S, Taper M, Staples D, (2006) Estimating density dependence, process noise, and observation error. Ecol Monogr 76: 323-341.
    • (2006) Ecol Monogr , vol.76 , pp. 323-341
    • Dennis, B.1    Ponciano, J.2    Lele, S.3    Taper, M.4    Staples, D.5
  • 47
    • 0031345518 scopus 로고    scopus 로고
    • Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization
    • Zhu C, Byrd R, Lu P, Nocedal J, (1997) Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization. ACM Trans Math Softw 23: 550-560.
    • (1997) ACM Trans Math Softw , vol.23 , pp. 550-560
    • Zhu, C.1    Byrd, R.2    Lu, P.3    Nocedal, J.4
  • 48
    • 0000888026 scopus 로고
    • Information theory and an extension of the likelihood ratio principle
    • In: Kotz S, NL J, editors, Berlin, Springer
    • Akaike H, (1992) Information theory and an extension of the likelihood ratio principle. In: Kotz S, NL J, editors. Breakthroughs in Statistics I Berlin Springer pp. 610-624.
    • (1992) Breakthroughs in Statistics I , pp. 610-624
    • Akaike, H.1
  • 50
    • 0000120766 scopus 로고
    • Estimating the dimension of a model
    • Schwarz G, (1978) Estimating the dimension of a model. Ann Stat 6: 461-464.
    • (1978) Ann Stat , vol.6 , pp. 461-464
    • Schwarz, G.1
  • 51
    • 0020072418 scopus 로고
    • Measles in England and Wales-I: An analysis of factors underlying seasonal patterns
    • Fine P, Clarkson J, (1982) Measles in England and Wales-I: An analysis of factors underlying seasonal patterns. Int J Epidemiol 11: 5.
    • (1982) Int J Epidemiol , vol.11 , pp. 5
    • Fine, P.1    Clarkson, J.2
  • 52
    • 9244230097 scopus 로고    scopus 로고
    • Population time series: process variability, observation errors, missing values, lags, and hidden states
    • Clark J, Bjørnstad O, (2004) Population time series: process variability, observation errors, missing values, lags, and hidden states. Ecology 85: 3140-3150.
    • (2004) Ecology , vol.85 , pp. 3140-3150
    • Clark, J.1    Bjørnstad, O.2
  • 53
    • 0027978417 scopus 로고
    • Bifurcation analysis of periodic SEIR and SIR epidemic models
    • Kuznetsov Y, Piccardi C, (1994) Bifurcation analysis of periodic SEIR and SIR epidemic models. J Math Biol 32: 109-121.
    • (1994) J Math Biol , vol.32 , pp. 109-121
    • Kuznetsov, Y.1    Piccardi, C.2
  • 55
    • 0031670568 scopus 로고    scopus 로고
    • Complex population dynamics in the real world: modeling the influence of time-varying parameters and time lags
    • Zeng Z, Nowierski R, Taper M, Dennis B, Kemp W, (1998) Complex population dynamics in the real world: modeling the influence of time-varying parameters and time lags. Ecology 79: 2193-2209.
    • (1998) Ecology , vol.79 , pp. 2193-2209
    • Zeng, Z.1    Nowierski, R.2    Taper, M.3    Dennis, B.4    Kemp, W.5
  • 56
    • 0031066070 scopus 로고    scopus 로고
    • Melnikov analysis of chaos in a simple epidemiological model
    • Glendinning P, Perry L, (1997) Melnikov analysis of chaos in a simple epidemiological model. J Math Biol 35: 359-373.
    • (1997) J Math Biol , vol.35 , pp. 359-373
    • Glendinning, P.1    Perry, L.2
  • 57
    • 33750164370 scopus 로고    scopus 로고
    • Melnikov analysis of chaos in a general epidemiological model
    • Diallo O, Koné Y, (2007) Melnikov analysis of chaos in a general epidemiological model. Nonlinear Anal Real World Appl 8: 20-26.
    • (2007) Nonlinear Anal Real World Appl , vol.8 , pp. 20-26
    • Diallo, O.1    Koné, Y.2
  • 58
    • 1642341634 scopus 로고    scopus 로고
    • Periodicity in an epidemic model with a generalized non-linear incidence
    • Alexander M, Moghadas S, (2004) Periodicity in an epidemic model with a generalized non-linear incidence. Math Biosci 189: 75-96.
    • (2004) Math Biosci , vol.189 , pp. 75-96
    • Alexander, M.1    Moghadas, S.2
  • 59
    • 33746747003 scopus 로고    scopus 로고
    • Popper, Bayes and the inverse problem
    • Tarantola A, (2006) Popper, Bayes and the inverse problem. Nat Phys 2: 492-494.
    • (2006) Nat Phys , vol.2 , pp. 492-494
    • Tarantola, A.1
  • 60
    • 70350365793 scopus 로고    scopus 로고
    • Parameter Estimation of Some Epidemic Models. The Case of Recurrent Epidemics Caused by Respiratory Syncytial Virus
    • Capistrán M, Moreles M, Lara B, (2009) Parameter Estimation of Some Epidemic Models. The Case of Recurrent Epidemics Caused by Respiratory Syncytial Virus. Bull Math Biol 71: 1890-1901.
    • (2009) Bull Math Biol , vol.71 , pp. 1890-1901
    • Capistrán, M.1    Moreles, M.2    Lara, B.3
  • 61
    • 0031748527 scopus 로고    scopus 로고
    • Respiratory syncytial virus infection in tropical and developing countries
    • Weber M, Mulholland E, Greenwood B, (1998) Respiratory syncytial virus infection in tropical and developing countries. Trop Med Int Health 3: 268-280.
    • (1998) Trop Med Int Health , vol.3 , pp. 268-280
    • Weber, M.1    Mulholland, E.2    Greenwood, B.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.