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Volumn 57, Issue 5, 2008, Pages 649-673

Resonance of the epidemic threshold in a periodic environment

Author keywords

Epidemic threshold; Perturbation theory; Reproductive value; Resonance; SEIR model

Indexed keywords

ALGORITHM; ANIMAL; ARTICLE; BIOLOGICAL MODEL; COMMUNICABLE DISEASE; DISEASE TRANSMISSION; EPIDEMIOLOGY; HUMAN; PERIODICITY; POPULATION DYNAMICS; SEASON;

EID: 49549125423     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-008-0183-1     Document Type: Article
Times cited : (33)

References (113)
  • 1
    • 0002379564 scopus 로고
    • Contributions to the mathematical theory of epidemics, II. the problem of endemicity
    • W.O. Kermack A.G. McKendrick 1932 Contributions to the mathematical theory of epidemics, II. The problem of endemicity P. Roy. Soc. A 138 55 83
    • (1932) P. Roy. Soc. a , vol.138 , pp. 55-83
    • Kermack, W.O.1    McKendrick, G.A.2
  • 2
    • 0003066251 scopus 로고
    • Transmission and control of arbovirus diseases
    • Society for Industrial and Applied Mathematics Philadelphia
    • Dietz K. (1974). Transmission and control of arbovirus diseases. In: Ludwig, D. and Cooke, K.L. (eds) Proceedings of SIMS Conference on Epidemiology, pp 104-121. Society for Industrial and Applied Mathematics, Philadelphia
    • (1974) Proceedings of SIMS Conference on Epidemiology , pp. 104-121
    • Dietz, K.1    Ludwig, D.2    Cooke, K.L.3
  • 3
    • 0002454064 scopus 로고
    • The incidence of infectious diseases under the influence of seasonal fluctuations
    • Springer Berlin
    • Dietz K. (1976). The incidence of infectious diseases under the influence of seasonal fluctuations. In: Berger, J., Buhler, W., Repges, R. and Tautu, P. (eds) Mathematical Models in Medicine, pp 1-15. Springer, Berlin
    • (1976) Mathematical Models in Medicine , pp. 1-15
    • Dietz, K.1    Berger, J.2    Buhler, W.3    Repges, R.4    Tautu, P.5
  • 4
    • 0002109848 scopus 로고
    • The incidence of infectious diseases under the influence of seasonal fluctuations - Analytical approach
    • Academic Press New York
    • Grossman Z., Gumowski I. and Dietz K. (1977). The incidence of infectious diseases under the influence of seasonal fluctuations - Analytical approach. In: Lakshmikantham, V. (eds) Nonlinear Systems and Applications, pp 525-546. Academic Press, New York
    • (1977) Nonlinear Systems and Applications , pp. 525-546
    • Grossman, Z.1    Gumowski, I.2    Dietz, K.3    Lakshmikantham, V.4
  • 5
    • 0019075237 scopus 로고
    • Oscillatory phenomena in a model of infectious diseases
    • Z. Grossman 1980 Oscillatory phenomena in a model of infectious diseases Theor. Pop. Biol. 18 204 243
    • (1980) Theor. Pop. Biol. , vol.18 , pp. 204-243
    • Grossman, Z.1
  • 6
    • 0020963836 scopus 로고
    • Subharmonic bifurcation in an S-I-R epidemic model
    • H.L. Smith 1983 Subharmonic bifurcation in an S-I-R epidemic model J. Math. Biol. 17 163 177
    • (1983) J. Math. Biol. , vol.17 , pp. 163-177
    • Smith, H.L.1
  • 7
    • 0020956406 scopus 로고
    • Multiple stable subharmonics for a periodic epidemic model
    • H.L. Smith 1983 Multiple stable subharmonics for a periodic epidemic model J. Math. Biol. 17 179 190
    • (1983) J. Math. Biol. , vol.17 , pp. 179-190
    • Smith, H.L.1
  • 8
    • 0021051389 scopus 로고
    • Infinite subharmonic bifurcation in an SEIR epidemic model
    • I.B. Schwartz H.L. Smith 1983 Infinite subharmonic bifurcation in an SEIR epidemic model J. Math. Biol. 18 233 253
    • (1983) J. Math. Biol. , vol.18 , pp. 233-253
    • Schwartz, I.B.1    Smith, H.L.2
  • 9
    • 0021690803 scopus 로고
    • Seasonality and period-doubling bifurcations in an epidemic model
    • J.L. Aron I.B. Schwartz 1984 Seasonality and period-doubling bifurcations in an epidemic model J. Theor. Biol. 110 665 679
    • (1984) J. Theor. Biol. , vol.110 , pp. 665-679
    • Aron, J.L.1    Schwartz, I.B.2
  • 10
    • 0021990877 scopus 로고
    • Multiple stable recurrent outbreaks and predictability in seasonally forced nonlinear epidemic models
    • I.B. Schwartz 1985 Multiple stable recurrent outbreaks and predictability in seasonally forced nonlinear epidemic models J. Math. Biol. 21 347 361
    • (1985) J. Math. Biol. , vol.21 , pp. 347-361
    • Schwartz, I.B.1
  • 11
    • 77957177075 scopus 로고
    • Can nonlinear dynamics elucidate mechanisms in ecology and epidemiology
    • W.M. Schaffer 1985 Can nonlinear dynamics elucidate mechanisms in ecology and epidemiology IMA J. Math. Appl. Med. Biol. 2 221 252
    • (1985) IMA J. Math. Appl. Med. Biol. , vol.2 , pp. 221-252
    • Schaffer, W.M.1
  • 13
    • 0025196595 scopus 로고
    • Chaos versus noisy periodicity: Alternative hypotheses for childhood epidemics
    • L.F. Olsen W.M. Schaffer 1990 Chaos versus noisy periodicity: alternative hypotheses for childhood epidemics Science 249 499 504
    • (1990) Science , vol.249 , pp. 499-504
    • Olsen, L.F.1    Schaffer, W.M.2
  • 14
    • 0025876128 scopus 로고
    • Chaotic stochasticity: A ubiquitous source of unpredictability in epidemics
    • D.A. Rand H.B. Wilson 1991 Chaotic stochasticity: a ubiquitous source of unpredictability in epidemics P. Roy. Soc. B-Biol. Sci. 246 179 184
    • (1991) P. Roy. Soc. B-Biol. Sci. , vol.246 , pp. 179-184
    • Rand, D.A.1    Wilson, H.B.2
  • 15
    • 0000827513 scopus 로고
    • Chance and chaos in measles dynamics
    • B.T. Grenfell 1992 Chance and chaos in measles dynamics J. Roy. Stat. Soc. B 54 383 398
    • (1992) J. Roy. Stat. Soc. B , vol.54 , pp. 383-398
    • Grenfell, B.T.1
  • 16
    • 0027465252 scopus 로고
    • Chaos and biological complexity in measles dynamics
    • B.M. Bolker B.T. Grenfell 1993 Chaos and biological complexity in measles dynamics P. Roy. Soc. B-Biol. Sci. 251 75 81
    • (1993) P. Roy. Soc. B-Biol. Sci. , vol.251 , pp. 75-81
    • Bolker, B.M.1    Grenfell, B.T.2
  • 17
    • 0027978417 scopus 로고
    • Bifurcation analysis of periodic SEIR and SIR epidemic models
    • Yu.A. Kuznetsov C. Piccardi 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, Yu.A.1    Piccardi, C.2
  • 19
    • 0031066070 scopus 로고    scopus 로고
    • Melnikov analysis of chaos in a simple epidemiological model
    • P. Glendinning L.P. Perry 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.P.2
  • 20
    • 0034723248 scopus 로고    scopus 로고
    • A simple model for complex dynamical transitions in epidemics
    • D.J.D. Earn P. Rohani B.M. Bolker B.T. Grenfell 2000 A simple model for complex dynamical transitions in epidemics Science 287 667 670
    • (2000) Science , vol.287 , pp. 667-670
    • Earn, D.J.D.1    Rohani, P.2    Bolker, B.M.3    Grenfell, B.T.4
  • 21
    • 0347663530 scopus 로고    scopus 로고
    • Seasonally forced disease dynamics explored as switching between attractors
    • M.J. Keeling P. Rohani B.T. Grenfell 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.J.1    Rohani, P.2    Grenfell, B.T.3
  • 22
    • 53149094352 scopus 로고    scopus 로고
    • Understanding the persistence of measles: Reconciling theory, simulation and observation
    • M.J. Keeling B.T. Grenfell 2002 Understanding the persistence of measles: reconciling theory, simulation and observation P. Roy. Soc. B-Biol. Sci. 269 335 343
    • (2002) P. Roy. Soc. B-Biol. Sci. , vol.269 , pp. 335-343
    • Keeling, M.J.1    Grenfell, B.T.2
  • 23
    • 0036369855 scopus 로고    scopus 로고
    • Exciting chaos with noise: Unexpected dynamics in epidemic outbreaks
    • L. Billings I.B. Schwartz 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.B.2
  • 24
    • 0037093075 scopus 로고    scopus 로고
    • The effect of cross-immunity and seasonal forcing in a multi-strain epidemic model
    • M. Kamo A. Sasaki 2002 The effect of cross-immunity and seasonal forcing in a multi-strain epidemic model Physica D 165 228 241
    • (2002) Physica D , vol.165 , pp. 228-241
    • Kamo, M.1    Sasaki, A.2
  • 25
    • 10044287073 scopus 로고    scopus 로고
    • Dynamical resonance can account for seasonality of influenza epidemics
    • J. Dushoff J.B. Plotkin S.A. Levin D.J.D. Earn 2004 Dynamical resonance can account for seasonality of influenza epidemics P. Natl. Acad. Sci. USA 101 16915 16916
    • (2004) P. Natl. Acad. Sci. USA , vol.101 , pp. 16915-16916
    • Dushoff, J.1    Plotkin, J.B.2    Levin, S.A.3    Earn, D.J.D.4
  • 26
    • 1142267538 scopus 로고    scopus 로고
    • External forcing of ecological and epidemiological systems: A resonance approach
    • J. Greenman M. Kamo M. Boots 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
  • 27
    • 4544370028 scopus 로고    scopus 로고
    • The effect of seasonal host birth rates on population dynamics: The importance of resonance
    • J.M. Ireland R.A. Norman J.V. Greenman 2004 The effect of seasonal host birth rates on population dynamics: the importance of resonance J. Theor. Biol. 231 229 238
    • (2004) J. Theor. Biol. , vol.231 , pp. 229-238
    • Ireland, J.M.1    Norman, R.A.2    Greenman, J.V.3
  • 28
    • 18544380939 scopus 로고    scopus 로고
    • Complexity of an SIR epidemic dynamics model with impulsive vaccination control
    • G.Z. Zeng L.S. Chen L.H. Sun 2005 Complexity of an SIR epidemic dynamics model with impulsive vaccination control Chaos Soliton Fract. 26 495 505
    • (2005) Chaos Soliton Fract. , vol.26 , pp. 495-505
    • Zeng, G.Z.1    Chen, L.S.2    Sun, L.H.3
  • 30
    • 33750037356 scopus 로고    scopus 로고
    • Dynamics of infectious diseases and pulse vaccination: Teasing apart the embedded resonance effects
    • M. Choisy J.-F. Guégan P. Rohani 2006 Dynamics of infectious diseases and pulse vaccination: teasing apart the embedded resonance effects Physica D 223 26 35
    • (2006) Physica D , vol.223 , pp. 26-35
    • Choisy, M.1    Guégan, J.-F.2    Rohani, P.3
  • 31
    • 33748982385 scopus 로고    scopus 로고
    • Seasonal infectious disease epidemiology
    • N.C. Grassly C. Fraser 2006 Seasonal infectious disease epidemiology P. Roy. Soc. B-Biol. Sci. 273 2541 2550
    • (2006) P. Roy. Soc. B-Biol. Sci. , vol.273 , pp. 2541-2550
    • Grassly, N.C.1    Fraser, C.2
  • 32
    • 33847252846 scopus 로고    scopus 로고
    • The effect of seasonal host birth rates on disease persistence
    • J.M. Ireland B.D. Mestel R.A. Norman 2007 The effect of seasonal host birth rates on disease persistence Math. Biosci. 206 31 45
    • (2007) Math. Biosci. , vol.206 , pp. 31-45
    • Ireland, J.M.1    Mestel, B.D.2    Norman, R.A.3
  • 33
    • 33847608267 scopus 로고    scopus 로고
    • Seasonally varying epidemics with and without latent period: A comparative simulation study
    • I.A. Moneim 2007 Seasonally varying epidemics with and without latent period: a comparative simulation study Math. Med. Biol. 24 1 15
    • (2007) Math. Med. Biol. , vol.24 , pp. 1-15
    • Moneim, I.A.1
  • 34
    • 34548404314 scopus 로고    scopus 로고
    • The effect of using different types of periodic contact rate on the behaviour of infectious diseases: A simulation study
    • I.A. Moneim 2007 The effect of using different types of periodic contact rate on the behaviour of infectious diseases: a simulation study Comput. Biol. Med. 37 1582 1590
    • (2007) Comput. Biol. Med. , vol.37 , pp. 1582-1590
    • Moneim, I.A.1
  • 35
    • 0002426167 scopus 로고
    • The interpretation of periodicity in disease prevalence
    • H.E. Soper 1929 The interpretation of periodicity in disease prevalence J. Roy. Stat. Soc. 92 34 73
    • (1929) J. Roy. Stat. Soc. , vol.92 , pp. 34-73
    • Soper, H.E.1
  • 36
    • 0019030156 scopus 로고
    • Age- and density-dependent population dynamics in static and variable environments
    • W.S.C. Gurney R.M. Nisbet 1980 Age- and density-dependent population dynamics in static and variable environments Theor. Pop. Biol. 17 321 344
    • (1980) Theor. Pop. Biol. , vol.17 , pp. 321-344
    • Gurney, W.S.C.1    Nisbet, R.M.2
  • 39
    • 0001808481 scopus 로고
    • A contribution to the theory of self-renewing aggregates, with special reference to industrial replacement
    • A.J. Lotka 1939 A contribution to the theory of self-renewing aggregates, with special reference to industrial replacement Ann. Math. Stat. 10 1 25
    • (1939) Ann. Math. Stat. , vol.10 , pp. 1-25
    • Lotka, A.J.1
  • 41
    • 0030266838 scopus 로고    scopus 로고
    • Populations with sinusoidal birth trajectories
    • Y.J. Kim R. Schoen 1996 Populations with sinusoidal birth trajectories Theor. Pop. Biol. 50 105 123
    • (1996) Theor. Pop. Biol. , vol.50 , pp. 105-123
    • Kim, Y.J.1    Schoen, R.2
  • 42
    • 0031405194 scopus 로고    scopus 로고
    • Exploring cyclic net reproduction
    • R. Schoen Y.J. Kim 1997 Exploring cyclic net reproduction Math. Pop. Stud. 6 277 290
    • (1997) Math. Pop. Stud. , vol.6 , pp. 277-290
    • Schoen, R.1    Kim, Y.J.2
  • 44
    • 0022104238 scopus 로고
    • Population dynamics in variable environments, vi Cyclical environments
    • S. Tuljapurkar 1985 Population dynamics in variable environments, vi Cyclical environments Theor. Pop. Biol. 28 1 17
    • (1985) Theor. Pop. Biol. , vol.28 , pp. 1-17
    • Tuljapurkar, S.1
  • 48
    • 33748152440 scopus 로고    scopus 로고
    • The epidemic threshold of vector borne diseases with seasonality
    • N. Bacaër S. Guernaoui 2006 The epidemic threshold of vector borne diseases with seasonality J. Math. Biol. 53 421 436
    • (2006) J. Math. Biol. , vol.53 , pp. 421-436
    • Bacaër, N.1    Guernaoui, S.2
  • 49
    • 33947541669 scopus 로고    scopus 로고
    • 0 for vector-borne diseases with a periodic vector population
    • 0 for vector-borne diseases with a periodic vector population Bull. Math. Biol. 69 1067 1091
    • (2007) Bull. Math. Biol. , vol.69 , pp. 1067-1091
    • Bacaër, N.1
  • 50
    • 36148974693 scopus 로고    scopus 로고
    • Growth rate and basic reproduction number for population models with a simple periodic factor
    • N. Bacaër R. Ouifki 2007 Growth rate and basic reproduction number for population models with a simple periodic factor Math. Biosci. 210 647 658
    • (2007) Math. Biosci. , vol.210 , pp. 647-658
    • Bacaër, N.1    Ouifki, R.2
  • 51
    • 0000572783 scopus 로고
    • On the integral equation of renewal theory
    • W. Feller 1941 On the integral equation of renewal theory Ann. Math. Stat. 12 243 267
    • (1941) Ann. Math. Stat. , vol.12 , pp. 243-267
    • Feller, W.1
  • 53
    • 24044522878 scopus 로고    scopus 로고
    • General relative entropy inequality: An illustration on growth models
    • P. Michel S. Mischler B. Perthame 2005 General relative entropy inequality: an illustration on growth models J. Math. Pures Appl. 84 1235 1260
    • (2005) J. Math. Pures Appl. , vol.84 , pp. 1235-1260
    • Michel, P.1    Mischler, S.2    Perthame, B.3
  • 54
    • 84937341775 scopus 로고    scopus 로고
    • Application of the demographic potential concept to understanding the Russian population history and prospects: 1897-2100
    • D.M. Ediev 2001 Application of the demographic potential concept to understanding the Russian population history and prospects: 1897-2100 Demogr. Res. 4 289 336
    • (2001) Demogr. Res. , vol.4 , pp. 289-336
    • Ediev, D.M.1
  • 55
    • 35448996934 scopus 로고    scopus 로고
    • On an extension of R.A. Fisher's result on the dynamics of the reproductive value
    • D.M. Ediev 2007 On an extension of R.A. Fisher's result on the dynamics of the reproductive value Theor. Pop. Biol. 72 480 484
    • (2007) Theor. Pop. Biol. , vol.72 , pp. 480-484
    • Ediev, D.M.1
  • 56
    • 0021523081 scopus 로고
    • Renewal theorems for linear periodic Volterra integral equations
    • H.R. Thieme 1984 Renewal theorems for linear periodic Volterra integral equations J. Integ. Equ. 7 253 277
    • (1984) J. Integ. Equ. , vol.7 , pp. 253-277
    • Thieme, H.R.1
  • 57
    • 0040825727 scopus 로고
    • Branching processes in periodically varying environment
    • P. Jagers O. Nerman 1985 Branching processes in periodically varying environment Ann. Probab. 13 254 268
    • (1985) Ann. Probab. , vol.13 , pp. 254-268
    • Jagers, P.1    Nerman, O.2
  • 58
    • 0030825041 scopus 로고    scopus 로고
    • Infectious disease persistence when transmission varies seasonally
    • B.G. Williams C. Dye 1997 Infectious disease persistence when transmission varies seasonally Math. Biosci. 145 77 88
    • (1997) Math. Biosci. , vol.145 , pp. 77-88
    • Williams, B.G.1    Dye, C.2
  • 59
    • 0009999818 scopus 로고
    • The actuarial treatment of official birth records
    • R.A. Fisher 1927 The actuarial treatment of official birth records Eugen. Rev. 19 103 108
    • (1927) Eugen. Rev. , vol.19 , pp. 103-108
    • Fisher, R.A.1
  • 60
    • 49549098418 scopus 로고
    • Correspondance regarding the article "the actuarial treatment of official birth records"
    • A.J. Lotka R.A. Fisher 1927 Correspondance regarding the article "The actuarial treatment of official birth records" Eugen. Rev. 19 257 258
    • (1927) Eugen. Rev. , vol.19 , pp. 257-258
    • Lotka, A.J.1    Fisher, R.A.2
  • 61
    • 33745438509 scopus 로고    scopus 로고
    • A theory of Fisher's reproductive value
    • A. Grafen 2006 A theory of Fisher's reproductive value J. Math. Biol. 53 15 60
    • (2006) J. Math. Biol. , vol.53 , pp. 15-60
    • Grafen, A.1
  • 63
    • 0013942563 scopus 로고
    • The moulding of senescence by natural selection
    • W.D. Hamilton 1966 The moulding of senescence by natural selection J. Theor. Biol. 12 12 45
    • (1966) J. Theor. Biol. , vol.12 , pp. 12-45
    • Hamilton, W.D.1
  • 64
    • 0033756222 scopus 로고    scopus 로고
    • Fisher, Medawar, Hamilton and the evolution of aging
    • B. Charlesworth 2000 Fisher, Medawar, Hamilton and the evolution of aging Genetics 156 927 931
    • (2000) Genetics , vol.156 , pp. 927-931
    • Charlesworth, B.1
  • 65
    • 0007358970 scopus 로고
    • The sensitivity of population growth rate to perturbations in the life cycle components
    • L. Demetrius 1969 The sensitivity of population growth rate to perturbations in the life cycle components Math. Biosci. 4 129 136
    • (1969) Math. Biosci. , vol.4 , pp. 129-136
    • Demetrius, L.1
  • 66
    • 0007359765 scopus 로고
    • On the sensitivity of the intrinsic growth rate to changes in the age-specific birth and death rates
    • L.A. Goodman 1971 On the sensitivity of the intrinsic growth rate to changes in the age-specific birth and death rates Theor. Pop. Biol. 2 339 354
    • (1971) Theor. Pop. Biol. , vol.2 , pp. 339-354
    • Goodman, L.A.1
  • 67
    • 0018029760 scopus 로고
    • A general formula for the sensitivity of population growth rate to changes in life history parameters
    • H. Caswell 1978 A general formula for the sensitivity of population growth rate to changes in life history parameters Theor. Pop. Biol. 14 215 230
    • (1978) Theor. Pop. Biol. , vol.14 , pp. 215-230
    • Caswell, H.1
  • 68
    • 34250636321 scopus 로고    scopus 로고
    • Environmental forcing, invasion and control of ecological and epidemiological systems
    • J.V. Greenman R.A. Norman 2007 Environmental forcing, invasion and control of ecological and epidemiological systems J. Theor. Biol. 247 492 506
    • (2007) J. Theor. Biol. , vol.247 , pp. 492-506
    • Greenman, J.V.1    Norman, R.A.2
  • 69
    • 0017104702 scopus 로고
    • A periodicity threshold theorem for epidemics and population growth
    • K.L. Cooke J.L. Kaplan 1976 A periodicity threshold theorem for epidemics and population growth Math. Biosci. 31 87 104
    • (1976) Math. Biosci. , vol.31 , pp. 87-104
    • Cooke, K.L.1    Kaplan, J.L.2
  • 70
    • 0017328061 scopus 로고
    • On periodic solutions of a delay integral equation modelling epidemics
    • H.L. Smith 1977 On periodic solutions of a delay integral equation modelling epidemics J. Math. Biol. 4 69 80
    • (1977) J. Math. Biol. , vol.4 , pp. 69-80
    • Smith, H.L.1
  • 71
    • 0011508129 scopus 로고
    • Periodic solutions of some integral equations from the theory of epidemics
    • Academic Press New York
    • Nussbaum R.D. (1977). Periodic solutions of some integral equations from the theory of epidemics. In: Lakshmikantham, V. (eds) Nonlinear Systems and Applications, pp 235-257. Academic Press, New York
    • (1977) Nonlinear Systems and Applications , pp. 235-257
    • Nussbaum, R.D.1    Lakshmikantham, V.2
  • 72
    • 0000954935 scopus 로고
    • A periodicity threshold theorem for some nonlinear integral equations
    • R.D. Nussbaum 1978 A periodicity threshold theorem for some nonlinear integral equations SIAM J. Math. Anal. 9 356 376
    • (1978) SIAM J. Math. Anal. , vol.9 , pp. 356-376
    • Nussbaum, R.D.1
  • 73
    • 33748131158 scopus 로고    scopus 로고
    • Epidemic threshold conditions for seasonally forced SEIR models
    • J. Ma Z. Ma 2006 Epidemic threshold conditions for seasonally forced SEIR models Math. Biosci. Eng. 3 161 172
    • (2006) Math. Biosci. Eng. , vol.3 , pp. 161-172
    • Ma, J.1    Ma, Z.2
  • 74
    • 0017362713 scopus 로고
    • Measures of fitness and demographic stability
    • L. Demetrius 1977 Measures of fitness and demographic stability P. Natl. Acad. Sci. USA 74 384 386
    • (1977) P. Natl. Acad. Sci. USA , vol.74 , pp. 384-386
    • Demetrius, L.1
  • 75
    • 0003696785 scopus 로고
    • Office of Population Research, Princeton University Princeton
    • Lopez A. (1961). Problems in Stable Population Theory. Office of Population Research, Princeton University, Princeton
    • (1961) Problems in Stable Population Theory
    • Lopez, A.1
  • 77
    • 34047120681 scopus 로고    scopus 로고
    • Seasonal dynamics of recurrent epidemics
    • L. Stone R. Olinky A. Huppert 2007 Seasonal dynamics of recurrent epidemics Nature 446 533 536
    • (2007) Nature , vol.446 , pp. 533-536
    • Stone, L.1    Olinky, R.2    Huppert, A.3
  • 79
    • 0036291194 scopus 로고    scopus 로고
    • Stability properties of pulse vaccination strategy in SEIR epidemic model
    • A. D'Onofrio 2002 Stability properties of pulse vaccination strategy in SEIR epidemic model Math. Biosci. 179 57 72
    • (2002) Math. Biosci. , vol.179 , pp. 57-72
    • D'Onofrio, A.1
  • 80
    • 0037200435 scopus 로고    scopus 로고
    • Pulse vaccination strategy in the SIR epidemic model: Global asymptotic stable eradication in presence of vaccine failures
    • A. D'Onofrio 2002 Pulse vaccination strategy in the SIR epidemic model: global asymptotic stable eradication in presence of vaccine failures Math. Comput. Model. 36 473 489
    • (2002) Math. Comput. Model. , vol.36 , pp. 473-489
    • D'Onofrio, A.1
  • 81
    • 1242264916 scopus 로고    scopus 로고
    • Mixed pulse vaccination strategy in epidemic model with realistically distributed infectious and latent times
    • A. D'Onofrio 2004 Mixed pulse vaccination strategy in epidemic model with realistically distributed infectious and latent times Appl. Math. Comput. 151 181 187
    • (2004) Appl. Math. Comput. , vol.151 , pp. 181-187
    • D'Onofrio, A.1
  • 82
    • 18144413585 scopus 로고    scopus 로고
    • On pulse vaccination strategy in the SIR epidemic model with vertical transmission
    • A. D'Onofrio 2005 On pulse vaccination strategy in the SIR epidemic model with vertical transmission Appl. Math. Lett. 18 729 732
    • (2005) Appl. Math. Lett. , vol.18 , pp. 729-732
    • D'Onofrio, A.1
  • 83
    • 19344365285 scopus 로고    scopus 로고
    • Threshold and stability results for an SIRS epidemic model with a general periodic vaccination strategy
    • I.A. Moneim D. Greenhalgh 2005 Threshold and stability results for an SIRS epidemic model with a general periodic vaccination strategy J. Biol. Syst. 13 131 150
    • (2005) J. Biol. Syst. , vol.13 , pp. 131-150
    • Moneim, I.A.1    Greenhalgh, D.2
  • 84
    • 33847663496 scopus 로고    scopus 로고
    • Use of a periodic vaccination strategy to control the spread of epidemics with seasonally varying contact rate
    • I.A. Moneim D. Greenhalgh 2005 Use of a periodic vaccination strategy to control the spread of epidemics with seasonally varying contact rate Math. Biosci. Eng. 2 591 611
    • (2005) Math. Biosci. Eng. , vol.2 , pp. 591-611
    • Moneim, I.A.1    Greenhalgh, D.2
  • 85
    • 33746833233 scopus 로고    scopus 로고
    • Analysis of a delayed epidemic model with pulse vaccination and saturation incidence
    • S. Gao L. Chen J.J. Nieto A. Torres 2006 Analysis of a delayed epidemic model with pulse vaccination and saturation incidence Vaccine 24 6037 6045
    • (2006) Vaccine , vol.24 , pp. 6037-6045
    • Gao, S.1    Chen, L.2    Nieto, J.J.3    Torres, A.4
  • 86
    • 33847258383 scopus 로고    scopus 로고
    • Impulsive vaccination of an SEIRS model with time delay and varying total population size
    • S. Gao L. Chen Z. Teng 2007 Impulsive vaccination of an SEIRS model with time delay and varying total population size Bull. Math. Biol. 69 731 745
    • (2007) Bull. Math. Biol. , vol.69 , pp. 731-745
    • Gao, S.1    Chen, L.2    Teng, Z.3
  • 87
    • 0029184066 scopus 로고
    • Threshold quantities for helminth infections
    • J.A.P. Heesterbeek M.G. Roberts 1995 Threshold quantities for helminth infections J. Math. Biol. 33 415 434
    • (1995) J. Math. Biol. , vol.33 , pp. 415-434
    • Heesterbeek, J.A.P.1    Roberts, M.G.2
  • 88
    • 0343506610 scopus 로고
    • Threshold quantities for infectious diseases in periodic environments
    • J.A.P. Heesterbeek M.G. Roberts 1995 Threshold quantities for infectious diseases in periodic environments J. Biol. Syst. 3 779 787
    • (1995) J. Biol. Syst. , vol.3 , pp. 779-787
    • Heesterbeek, J.A.P.1    Roberts, M.G.2
  • 89
    • 0029667003 scopus 로고    scopus 로고
    • Vector-borne diseases and the basic reproduction number: A case study of African horse sickness
    • C.C. Lord M.E.J. Woolhouse J.A.P. Heesterbeek P.S. Mellor 1996 Vector-borne diseases and the basic reproduction number: a case study of African horse sickness Med. Vet. Entomol. 10 19 28
    • (1996) Med. Vet. Entomol. , vol.10 , pp. 19-28
    • Lord, C.C.1    Woolhouse, M.E.J.2    Heesterbeek, J.A.P.3    Mellor, P.S.4
  • 90
    • 0031591148 scopus 로고    scopus 로고
    • A simulation model of the infection cycle of Leishmania mexicana in Neotoma micropus
    • S. Kerr W.E. Grant N.O. Dronen Jr 1997 A simulation model of the infection cycle of Leishmania mexicana in Neotoma micropus Ecol. Model. 98 187 197
    • (1997) Ecol. Model. , vol.98 , pp. 187-197
    • Kerr, S.1    Grant, W.E.2    Dronen Jr., N.O.3
  • 91
    • 2942619997 scopus 로고    scopus 로고
    • Endemic and epidemic dynamics of cholera: The role of the aquatic reservoir
    • C.T. Codeço 2001 Endemic and epidemic dynamics of cholera: The role of the aquatic reservoir BMC Infect. Dis. 289 2801 2810
    • (2001) BMC Infect. Dis. , vol.289 , pp. 2801-2810
    • Codeço, C.T.1
  • 92
    • 3943111029 scopus 로고    scopus 로고
    • Seasonal population dynamics and behaviour of insects in models of vector-borne pathogens
    • C. Lord 2004 Seasonal population dynamics and behaviour of insects in models of vector-borne pathogens Physiol. Entomol. 29 214 222
    • (2004) Physiol. Entomol. , vol.29 , pp. 214-222
    • Lord, C.1
  • 93
    • 33750703973 scopus 로고    scopus 로고
    • Threshold conditions for a non-autonomous epidemic system describing the population dynamics of dengue
    • F.A.B. Coutinho M.N. Burattini L.F. Lopez E. Massad 2006 Threshold conditions for a non-autonomous epidemic system describing the population dynamics of dengue Bull. Math. Biol. 68 2263 2282
    • (2006) Bull. Math. Biol. , vol.68 , pp. 2263-2282
    • Coutinho, F.A.B.1    Burattini, M.N.2    Lopez, L.F.3    Massad, E.4
  • 94
    • 0031750774 scopus 로고    scopus 로고
    • The dynamics of an infectious disease in a population with birth pulses
    • M.G. Roberts R.R. Kao 1998 The dynamics of an infectious disease in a population with birth pulses Math. Biosci. 149 23 36
    • (1998) Math. Biosci. , vol.149 , pp. 23-36
    • Roberts, M.G.1    Kao, R.R.2
  • 95
    • 0036483349 scopus 로고    scopus 로고
    • Density-dependent birth rate, birth pulses and their population dynamics consequences
    • S. Tang L. Chen 2002 Density-dependent birth rate, birth pulses and their population dynamics consequences J. Math. Biol. 44 185 199
    • (2002) J. Math. Biol. , vol.44 , pp. 185-199
    • Tang, S.1    Chen, L.2
  • 96
    • 33746638486 scopus 로고    scopus 로고
    • A multi-patch epidemic model with periodic demography, direct and indirect transmission and variable maturation rate
    • C. Wolf F. Sauvage D. Pontier M. Langlais 2006 A multi-patch epidemic model with periodic demography, direct and indirect transmission and variable maturation rate Math. Pop. Stud. 13 153 177
    • (2006) Math. Pop. Stud. , vol.13 , pp. 153-177
    • Wolf, C.1    Sauvage, F.2    Pontier, D.3    Langlais, M.4
  • 97
    • 34547666538 scopus 로고    scopus 로고
    • Epidemiological effects of seasonal oscillations in birth rates
    • D. He D.J.D. Earn 2007 Epidemiological effects of seasonal oscillations in birth rates Theor. Pop. Biol. 72 274 291
    • (2007) Theor. Pop. Biol. , vol.72 , pp. 274-291
    • He, D.1    Earn, D.J.D.2
  • 98
    • 35648967095 scopus 로고    scopus 로고
    • On a nonautonomous SEIRS model in epidemiology
    • doi: 10.1007/s11538-007-9231-z
    • Zhang, T., Teng, Z.: On a nonautonomous SEIRS model in epidemiology. Bull. Math. Biol. (2007) doi: 10.1007/s11538-007-9231-z
    • (2007) Bull. Math. Biol.
    • Zhang, T.1    Teng, Z.2
  • 99
    • 33750325602 scopus 로고    scopus 로고
    • A periodic epidemic model in a patchy environment
    • F. Zhang X. Zhao 2007 A periodic epidemic model in a patchy environment J. Math. Anal. Appl. 325 496 516
    • (2007) J. Math. Anal. Appl. , vol.325 , pp. 496-516
    • Zhang, F.1    Zhao, X.2
  • 100
    • 0000751578 scopus 로고
    • A thousand and one epidemic models
    • Springer Berlin
    • Hethcote H. (1994). A thousand and one epidemic models. In: Levin, S. (eds) Frontiers in Mathematical Biology, pp 504-515. Springer, Berlin
    • (1994) Frontiers in Mathematical Biology , pp. 504-515
    • Hethcote, H.1    Levin, S.2
  • 101
    • 0032188644 scopus 로고    scopus 로고
    • Optimal harvesting for periodic age-dependent population dynamics
    • S. Anita M. Iannelli M.-Y. Kim E.-J. Park 1998 Optimal harvesting for periodic age-dependent population dynamics SIAM J. Appl. Math. 58 1648 1666
    • (1998) SIAM J. Appl. Math. , vol.58 , pp. 1648-1666
    • Anita, S.1    Iannelli, M.2    Kim, M.-Y.3    Park, E.-J.4
  • 102
    • 1842452891 scopus 로고    scopus 로고
    • Optimal harvesting control problem for linear periodic age-dependent population dynamics
    • Z. Luo W. Li M. Wang 2004 Optimal harvesting control problem for linear periodic age-dependent population dynamics Appl. Math. Comput. 151 789 800
    • (2004) Appl. Math. Comput. , vol.151 , pp. 789-800
    • Luo, Z.1    Li, W.2    Wang, M.3
  • 103
    • 33747044664 scopus 로고    scopus 로고
    • Harvesting can increase severity of wildlife disease epidemics
    • M. Choisy P. Rohani 2006 Harvesting can increase severity of wildlife disease epidemics P. Roy. Soc. B-Biol. Sci. 273 2025 2034
    • (2006) P. Roy. Soc. B-Biol. Sci. , vol.273 , pp. 2025-2034
    • Choisy, M.1    Rohani, P.2
  • 105
    • 9644278189 scopus 로고    scopus 로고
    • Asymptotic behavior of an SI epidemic model with pulse removal
    • K.M. Fuhrman I.G. Lauko G.A. Pinter 2004 Asymptotic behavior of an SI epidemic model with pulse removal Math. Comput. Model. 40 371 386
    • (2004) Math. Comput. Model. , vol.40 , pp. 371-386
    • Fuhrman, K.M.1    Lauko, I.G.2    Pinter, G.A.3
  • 106
    • 33845735615 scopus 로고    scopus 로고
    • A pest management SI model with periodic biological and chemical control concern
    • J. Jiao L. Chen 2006 A pest management SI model with periodic biological and chemical control concern Appl. Math. Comput. 183 1018 1026
    • (2006) Appl. Math. Comput. , vol.183 , pp. 1018-1026
    • Jiao, J.1    Chen, L.2
  • 107
    • 38549168852 scopus 로고    scopus 로고
    • Analysis of a Monod-Haldene type food chain chemostat with seasonally variably pulsed input and washout
    • F. Wang G. Pang J. Hui 2008 Analysis of a Monod-Haldene type food chain chemostat with seasonally variably pulsed input and washout J. Math. Chem. 43 601 619
    • (2008) J. Math. Chem. , vol.43 , pp. 601-619
    • Wang, F.1    Pang, G.2    Hui, J.3
  • 108
    • 26044466998 scopus 로고    scopus 로고
    • Periodically varying antiviral therapies: Conditions for global stability of the virus free state
    • A. D'Onofrio 2005 Periodically varying antiviral therapies: conditions for global stability of the virus free state Appl. Math. Comput. 168 945 953
    • (2005) Appl. Math. Comput. , vol.168 , pp. 945-953
    • D'Onofrio, A.1
  • 109
    • 33646205051 scopus 로고    scopus 로고
    • Role of parametric resonance in virological failure during HIV treatment interruption therapy
    • R. Breban S. Blower 2006 Role of parametric resonance in virological failure during HIV treatment interruption therapy Lancet 367 1285 1289
    • (2006) Lancet , vol.367 , pp. 1285-1289
    • Breban, R.1    Blower, S.2
  • 110
    • 4444221249 scopus 로고    scopus 로고
    • Tumour eradication by antiangiogenic therapy: Analysis and extensions of the model by Hahnfeldt et al. (1999)
    • A. D'Onofrio A. Gandolfi 2004 Tumour eradication by antiangiogenic therapy: analysis and extensions of the model by Hahnfeldt et al. (1999) Math. Biosci. 191 159 184
    • (2004) Math. Biosci. , vol.191 , pp. 159-184
    • D'Onofrio, A.1    Gandolfi, A.2
  • 111
    • 23144445934 scopus 로고    scopus 로고
    • A general framework for modeling tumor-immune system competition and immunotherapy: Mathematical analysis and biomedical inferences
    • A. D'Onofrio 2005 A general framework for modeling tumor-immune system competition and immunotherapy: mathematical analysis and biomedical inferences Physica D 208 220 235
    • (2005) Physica D , vol.208 , pp. 220-235
    • D'Onofrio, A.1
  • 112
    • 33750446670 scopus 로고    scopus 로고
    • The response to antiangiogenic anticancer drugs that inhibit endothelial cell proliferation
    • A. D'Onofrio A. Gandolfi 2006 The response to antiangiogenic anticancer drugs that inhibit endothelial cell proliferation Appl. Math. Comput. 181 1155 1162
    • (2006) Appl. Math. Comput. , vol.181 , pp. 1155-1162
    • D'Onofrio, A.1    Gandolfi, A.2
  • 113
    • 38049036434 scopus 로고    scopus 로고
    • On the long-term fitness of cells in periodically switching environments
    • N.-N. Pang W.-J. Tzeng 2008 On the long-term fitness of cells in periodically switching environments Bull. Math. Biol. 70 210 235
    • (2008) Bull. Math. Biol. , vol.70 , pp. 210-235
    • Pang, N.-N.1    Tzeng, W.-J.2


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