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Volumn , Issue , 2018, Pages 1-543

Mathematics in Population Biology

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EID: 85194307652     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Book
Times cited : (787)

References (364)
  • 1
    • 0001687872 scopus 로고
    • Analysis of a model representing stagestructured population growth with state-dependent time delay
    • Aiello, W. G., Freedman, H. I., and Wu, J., 1992, Analysis of a model representing stagestructured population growth with state-dependent time delay, SIAM J. Appl. Math. 52, 855-869.
    • (1992) SIAM J. Appl. Math , vol.52 , pp. 855-869
    • Aiello, W.G.1    Freedman, H.I.2    Wu, J.3
  • 3
    • 0003596416 scopus 로고
    • University of Chicago Press, Chicago, IL
    • Allee, W. C., 1931, Animal aggregations, University of Chicago Press, Chicago, IL.
    • (1931) Animal aggregations
    • Allee, W.C.1
  • 8
    • 0000832875 scopus 로고
    • Transmission dynamics and control of infectious disease agents
    • (ed. R. M.Anderson, R. M. May), Life Sciences Research Report, no. 25, Springer, Berlin
    • Anderson, R. M., 1982b, Transmission dynamics and control of infectious disease agents, Population biology of infectious diseases (ed. R. M.Anderson, R. M. May), pp. 1-12, Life Sciences Research Report, no. 25, Springer, Berlin.
    • (1982) Population biology of infectious diseases , pp. 1-12
    • Anderson, R.M.1
  • 9
  • 10
    • 0020004047 scopus 로고
    • Directly transmitted infectious diseases:Control by vaccination
    • Anderson, R. M., and May, R. M., 1982b, Directly transmitted infectious diseases:control by vaccination, Science 215, 1053-1060.
    • (1982) Science , vol.215 , pp. 1053-1060
    • Anderson, R.M.1    May, R.M.2
  • 13
    • 0032188644 scopus 로고    scopus 로고
    • Optimal harvesting for periodic age-dependent population dynamics
    • Anita, S., Iannelli, M., Kim Mi, Y., and Park, E., 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 Mi, Y.3    Park, E.4
  • 15
    • 3042969787 scopus 로고
    • Vector-valued versions of some representation theorems in real analysis
    • (ed. K. D. Bierstedt, A. Pietsch, W. M. Ruess, D. Vogt), Marcel Dekker, NewYork
    • Arendt, W., 1994, Vector-valued versions of some representation theorems in real analysis, Functional analysis (ed. K. D. Bierstedt, A. Pietsch, W. M. Ruess, D. Vogt), pp. 33-50, Marcel Dekker, NewYork.
    • (1994) Functional analysis , pp. 33-50
    • Arendt, W.1
  • 19
    • 84911681078 scopus 로고
    • Simple versus complex epidemiological models
    • (ed. S. A. Levin, T. G. Hallam, L. J. Gross), Springer, Berlin, Heidelberg
    • Aron, J. L., 1989, Simple versus complex epidemiological models, Applied mathematical ecology (ed. S. A. Levin, T. G. Hallam, L. J. Gross), pp. 176-192, Springer, Berlin, Heidelberg.
    • (1989) Applied mathematical ecology , pp. 176-192
    • Aron, J.L.1
  • 20
    • 0021690803 scopus 로고
    • Seasonality and period-doubling bifurcations in an epidemic model
    • Aron, J. L., and Schwartz, I. B., 1984a, 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
  • 21
    • 77957183869 scopus 로고
    • Some new directions for research in epidemic models
    • Aron, J. L., and Schwartz, I. B., 1984b, Some new directions for research in epidemic models, IMA J. Math. Appl. Med. Biol. 1, 267-276.
    • (1984) IMA J. Math. Appl. Med. Biol , vol.1 , pp. 267-276
    • Aron, J.L.1    Schwartz, I.B.2
  • 23
    • 0001274382 scopus 로고
    • Syst`emes d’équations différentielles d’oscillations nonlinéaires
    • Barbalat, I., 1959, Syst`emes d’équations différentielles d’oscillations nonlinéaires, Rev. Roumaine Math. Pures Appl. 4, 267-270.
    • (1959) Rev. Roumaine Math. Pures Appl , vol.4 , pp. 267-270
    • Barbalat, I.1
  • 24
    • 0035218446 scopus 로고    scopus 로고
    • On the controllability of the Lotka-McKendrick model of population dynamics
    • Barbu, V., Iannelli, M., and Martcheva, M., 2001, On the controllability of the Lotka-McKendrick model of population dynamics, J. Math. Analysis Appl. 253, 142-165.
    • (2001) J. Math. Analysis Appl , vol.253 , pp. 142-165
    • Barbu, V.1    Iannelli, M.2    Martcheva, M.3
  • 25
    • 84870415645 scopus 로고    scopus 로고
    • Das Leben Fermats
    • (2001), Deutsche Mathematiker-Vereinigung
    • Barner, K., 2001, Das Leben Fermats, Mitteilungen der DMV, Issue 3 (2001), pp. 12-26, Deutsche Mathematiker-Vereinigung.
    • (2001) Mitteilungen der DMV , Issue.3 , pp. 12-26
    • Barner, K.1
  • 26
    • 0003188315 scopus 로고
    • Measles periodicity and community size
    • A120
    • Bartlett, M. S., 1957, Measles periodicity and community size, J. R. Statist. Soc. A120, 48-70.
    • (1957) J. R. Statist. Soc , pp. 48-70
    • Bartlett, M.S.1
  • 27
    • 0003188313 scopus 로고
    • The critical community size for measles in the United States
    • A123
    • Bartlett, M. S., 1960, The critical community size for measles in the United States, J. R. Statist. Soc. A123, 37-44.
    • (1960) J. R. Statist. Soc , pp. 37-44
    • Bartlett, M.S.1
  • 29
    • 0004178623 scopus 로고
    • reprinted in 1986 by Simon & Schuster
    • Bell, E. T., 1937, Men of mathematics, reprinted in 1986 by Simon & Schuster.
    • (1937) Men of mathematics
    • Bell, E.T.1
  • 30
    • 0001408436 scopus 로고    scopus 로고
    • Asymptotic pseudotrajectories and chain recurrent flows, with applications
    • Benaïm, M., and Hirsch, M.W., 1996, Asymptotic pseudotrajectories and chain recurrent flows, with applications, J. Dyn. Diff. Eqns 8, 141-176.
    • (1996) J. Dyn. Diff. Eqns , vol.8 , pp. 141-176
    • Benaïm, M.1    Hirsch, M.W.2
  • 32
    • 0035111113 scopus 로고    scopus 로고
    • Linking the Allee effect, sexual reproduction, and temperature-dependent sex determination via spatial dynamics
    • Berec, L., Boukal, D. S., and Berec, M., 2002, Linking the Allee effect, sexual reproduction, and temperature-dependent sex determination via spatial dynamics, Am. Naturalist 157, 217-230.
    • (2002) Am. Naturalist , vol.157 , pp. 217-230
    • Berec, L.1    Boukal, D.S.2    Berec, M.3
  • 33
    • 0001992090 scopus 로고
    • Essai d’une nouvelle analyse de la mortalité causée par la petite vérole
    • Bernoulli, D., 1766, Essai d’une nouvelle analyse de la mortalité causée par la petite vérole, Mém. Math. Phys. Acad. Roy. Sci. Paris 1.
    • (1766) Mém. Math. Phys. Acad. Roy. Sci. Paris , pp. 1
    • Bernoulli, D.1
  • 34
    • 0001510308 scopus 로고
    • On the dynamics of exploited fish populations
    • Series 2, HMSO
    • Beverton, R. J. H., and Holt, S. J., 1957, On the dynamics of exploited fish populations, Fishery Investigations Series 2, vol. 19, HMSO.
    • (1957) Fishery Investigations , vol.19
    • Beverton, R.J.H.1    Holt, S.J.2
  • 35
    • 0036399391 scopus 로고    scopus 로고
    • Single species models of the Allee effect: Extinction boundaries, sex ratios and mate encounters
    • Boukal, D. S., and Berec, L., 2002, Single species models of the Allee effect: extinction boundaries, sex ratios and mate encounters, J. Theor. Biol. 218, 375-394.
    • (2002) J. Theor. Biol , vol.218 , pp. 375-394
    • Boukal, D.S.1    Berec, L.2
  • 38
    • 2942679580 scopus 로고    scopus 로고
    • Some directions for mathematical epidemiology
    • (ed. S. Ruan, G.Wolkowicz, and J. Wu), Fields Institute Communications, American Mathematical Society, Providence, RI
    • Brauer, F., and van den Driessche, P., 2002, Some directions for mathematical epidemiology, Dynamical systems and their applications to biology (ed. S. Ruan, G.Wolkowicz, and J. Wu), pp. 95-112, Fields Institute Communications, American Mathematical Society, Providence, RI.
    • (2002) Dynamical systems and their applications to biology , pp. 95-112
    • Brauer, F.1    van den Driessche, P.2
  • 40
    • 77957175569 scopus 로고
    • A general solution of the problem of mixing of subpopulations and its application to risk-and age-structured epidemic models for the spread of AIDS
    • Busenberg, S. N., and Castillo-Chavez, C., 1991, A general solution of the problem of mixing of subpopulations and its application to risk-and age-structured epidemic models for the spread of AIDS, IMA J. Math. Appl. Med. Biol. 8, 1-29.
    • (1991) IMA J. Math. Appl. Med. Biol , vol.8 , pp. 1-29
    • Busenberg, S.N.1    Castillo-Chavez, C.2
  • 43
    • 0000036443 scopus 로고
    • Persistence in dynamical systems
    • Butler, G., and Waltman, P., 1986, Persistence in dynamical systems, J. Diff. Eqns 63, 255-263.
    • (1986) J. Diff. Eqns , vol.63 , pp. 255-263
    • Butler, G.1    Waltman, P.2
  • 47
    • 0024352931 scopus 로고
    • On the role of long incubation periods in the dynamics of acquired immunodeficiency syndrome (AIDS). Part 1: Single population models
    • Castillo-Chavez, C., Cooke, K. L., Huang, W., and Levin, S. A., 1989, On the role of long incubation periods in the dynamics of acquired immunodeficiency syndrome (AIDS). Part 1: single population models, J. Math. Biol. 27, 373-398.
    • (1989) J. Math. Biol , vol.27 , pp. 373-398
    • Castillo-Chavez, C.1    Cooke, K.L.2    Huang, W.3    Levin, S.A.4
  • 49
    • 0001165512 scopus 로고
    • Modeling contact structures in biology
    • (ed. S. A. Levin), Lecture Notes in Biomathematics, Springer, Berlin
    • Castillo-Chavez, C., Velasco-Hernandez, J. X., and Fridman, S., 1994, Modeling contact structures in biology, Frontiers in mathematical biology (ed. S. A. Levin), pp. 454-491, Lecture Notes in Biomathematics, vol. 100, Springer, Berlin.
    • (1994) Frontiers in mathematical biology , vol.100 , pp. 454-491
    • Castillo-Chavez, C.1    Velasco-Hernandez, J.X.2    Fridman, S.3
  • 51
    • 0032526441 scopus 로고    scopus 로고
    • Existence and uniqueness of endemic states for the age-structured S-I-R epidemic model
    • Cha, Y., Iannelli, M., and Milner, F. A., 1998, Existence and uniqueness of endemic states for the age-structured S-I-R epidemic model, Math. Biosci. 150, 177-190.
    • (1998) Math. Biosci , vol.150 , pp. 177-190
    • Cha, Y.1    Iannelli, M.2    Milner, F.A.3
  • 52
    • 33644531192 scopus 로고    scopus 로고
    • Stability change of an epidemic model
    • Cha, Y., Iannelli, M., and Milner, F. A., 2000, Stability change of an epidemic model, Dynamic Syst. Appl. 9, 361-376.
    • (2000) Dynamic Syst. Appl , vol.9 , pp. 361-376
    • Cha, Y.1    Iannelli, M.2    Milner, F.A.3
  • 59
    • 0016045445 scopus 로고
    • Model fertility tables: Variations in the age structure of childbearing in human populations
    • reprinted in Smith, Keyfitz (eds), 1977, pp. 323-331
    • Coale, A. J., and Trussell, T. J., 1974, Model fertility tables: variations in the age structure of childbearing in human populations, Population Index 40, 186-192 (reprinted in Smith, Keyfitz (eds), 1977, pp. 323-331).
    • (1974) Population Index , vol.40 , pp. 186-192
    • Coale, A.J.1    Trussell, T.J.2
  • 61
    • 0001368734 scopus 로고
    • Intrapopulation variation in the body size at metamorphosis and timing of metamorphosis in the bullfrog
    • Collins, J. P., 1979, Intrapopulation variation in the body size at metamorphosis and timing of metamorphosis in the bullfrog, Rana castesbeiana, Ecology 60, 738-749.
    • (1979) Rana castesbeiana, Ecology , vol.60 , pp. 738-749
    • Collins, J.P.1
  • 62
    • 0020864346 scopus 로고
    • Effect of food and density on development of typical and cannibalistic salamander larvae in Ambystoma tigrinum nebulosum
    • Collins, J. P., and Cheek, J. E., 1983, Effect of food and density on development of typical and cannibalistic salamander larvae in Ambystoma tigrinum nebulosum, Amer. Zool. 23, 77-84.
    • (1983) Amer. Zool , vol.23 , pp. 77-84
    • Collins, J.P.1    Cheek, J.E.2
  • 63
    • 0027144186 scopus 로고
    • Shaping intraspecific variation:Development, ecology and the evolution of morphology and life history variation in tiger salamanders
    • Collins, J. P., Zerba, K. E., and Sredl, M. J., 1993, Shaping intraspecific variation:development, ecology and the evolution of morphology and life history variation in tiger salamanders, Genetica 89, 167-183.
    • (1993) Genetica , vol.89 , pp. 167-183
    • Collins, J.P.1    Zerba, K.E.2    Sredl, M.J.3
  • 64
    • 4644238532 scopus 로고
    • Functional differential equations: Some models and perturbation problems
    • (ed. J. K. Hale, J. P. LaSalle), Academic Press, NewYork
    • Cooke, K. L., 1967, Functional differential equations: some models and perturbation problems, Differential equations and dynamical systems (ed. J. K. Hale, J. P. LaSalle), pp. 167-183, Academic Press, NewYork.
    • (1967) Differential equations and dynamical systems , pp. 167-183
    • Cooke, K.L.1
  • 65
    • 0033209987 scopus 로고    scopus 로고
    • Interaction of maturation delay and nonlinear birth in population and epidemic models
    • Erratum, 2002, J. Math. Biol. 45, 470
    • Cooke, K. L., van den Driessche, P., and Zou, X, 1999, Interaction of maturation delay and nonlinear birth in population and epidemic models, J. Math. Biol. 39, 332-352 (Erratum, 2002, J. Math. Biol. 45, 470).
    • (1999) J. Math. Biol , vol.39 , pp. 332-352
    • Cooke, K.L.1    van den Driessche, P.2    Zou, X.3
  • 67
    • 0028974630 scopus 로고
    • Experimentally induced transitions in the dynamics behaviour of insect populations
    • Costantino, R. F., Cushing, J. M., Dennis, B., and Desharnais, R. A., 1995, Experimentally induced transitions in the dynamics behaviour of insect populations, Nature 375, 227-230.
    • (1995) Nature , vol.375 , pp. 227-230
    • Costantino, R.F.1    Cushing, J.M.2    Dennis, B.3    Desharnais, R.A.4
  • 70
    • 0001219907 scopus 로고
    • Local and global stability for population models
    • Cull, P., 1986, Local and global stability for population models, Biological Cybernetics 54, 141-149.
    • (1986) Biological Cybernetics , vol.54 , pp. 141-149
    • Cull, P.1
  • 71
    • 85194347660 scopus 로고    scopus 로고
    • CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, PA
    • Cushing, J. M., 1998, An introduction to structured population dynamics, CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 71, SIAM, Philadelphia, PA.
    • (1998) An introduction to structured population dynamics , vol.71
    • Cushing, J.M.1
  • 72
    • 0030302697 scopus 로고    scopus 로고
    • An interdisciplinary approach to understanding nonlinear ecological dynamics
    • Cushing, J. M., Dennis, B., Desharnais, R. A., and Costantino, F. R., 1996, An interdisciplinary approach to understanding nonlinear ecological dynamics, Ecological Modeling 91, 111-119.
    • (1996) Ecological Modeling , vol.91 , pp. 111-119
    • Cushing, J.M.1    Dennis, B.2    Desharnais, R.A.3    Costantino, F.R.4
  • 74
    • 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, Nat. Resource Modeling 3, 481-538.
    • (1989) Nat. Resource Modeling , vol.3 , pp. 481-538
    • Dennis, B.1
  • 75
    • 0028976114 scopus 로고
    • Nonlinear demographic dynamics: Mathematical models, statistical methods, and biological experiments
    • Dennis, B., Desharnais, R. A., Cushing, J. M., and Costantino, R. F., 1995, Nonlinear demographic dynamics: mathematical models, statistical methods, and biological experiments, Ecol. Monogr. 65, 261-281.
    • (1995) Ecol. Monogr , vol.65 , pp. 261-281
    • Dennis, B.1    Desharnais, R.A.2    Cushing, J.M.3    Costantino, R.F.4
  • 76
    • 0021412055 scopus 로고
    • The gamma distribution and weighted multinomial gamma distributions as models of population abundance
    • Dennis, B., and Patil, G. P., 1984, The gamma distribution and weighted multinomial gamma distributions as models of population abundance, Math. Biosci. 68, 187-212.
    • (1984) Math. Biosci , vol.68 , pp. 187-212
    • Dennis, B.1    Patil, G.P.2
  • 77
    • 0000724325 scopus 로고    scopus 로고
    • Agentle approach to physiologically structured population models
    • (ed. S. Tuljapurkar, H. Caswell), Chapman and Hall, NewYork
    • de Roos, A. M., 1997, Agentle approach to physiologically structured population models, Structured population models in marine, freshwater, and terrestrial systems (ed. S. Tuljapurkar, H. Caswell), pp. 119-204, Chapman and Hall, NewYork.
    • (1997) Structured population models in marine, freshwater, and terrestrial systems , pp. 119-204
    • de Roos, A.M.1
  • 78
    • 0037460860 scopus 로고    scopus 로고
    • Emergent Allee effects in top predators feeding on structured prey population
    • B270
    • de Roos, A. M., Persson, L., and Thieme, H. R., 2003, Emergent Allee effects in top predators feeding on structured prey population, Proc. R. Soc. Lond. B270, 611-618.
    • (2003) Proc. R. Soc. Lond , pp. 611-618
    • de Roos, A.M.1    Persson, L.2    Thieme, H.R.3
  • 83
    • 0026344644 scopus 로고
    • The basic reproduction ratio for sexually transmitted diseases, I, Theoretical considerations
    • Diekmann, O., Dietz, K., and Heesterbeek, J. A. P., 1991, The basic reproduction ratio for sexually transmitted diseases, I, Theoretical considerations, Math. Biosci. 107, 325-339.
    • (1991) Math. Biosci , vol.107 , pp. 325-339
    • Diekmann, O.1    Dietz, K.2    Heesterbeek, J.A.P.3
  • 84
    • 0035433541 scopus 로고    scopus 로고
    • On the formulation and analysis of general deterministic structured population models, II, Nonlinear theory
    • Diekmann, O., Gyllenberg, M., Huang, H., Kirkilionis, M., Metz, J. A. J., and Thieme, H. R., 2001, On the formulation and analysis of general deterministic structured population models, II, Nonlinear theory, J. Math. Biol. 43, 157-189.
    • (2001) J. Math. Biol , vol.43 , pp. 157-189
    • Diekmann, O.1    Gyllenberg, M.2    Huang, H.3    Kirkilionis, M.4    Metz, J.A.J.5    Thieme, H.R.6
  • 85
    • 0000201875 scopus 로고    scopus 로고
    • On the formulations and analysis of general deterministic structured population models, I, Linear Theory
    • Diekmann, O., Gyllenberg, M., Metz, J. A. J., and Thieme, H. R., 1998, On the formulations and analysis of general deterministic structured population models, I, Linear Theory, J. Math. Biol. 36, 349-388.
    • (1998) J. Math. Biol , vol.36 , pp. 349-388
    • Diekmann, O.1    Gyllenberg, M.2    Metz, J.A.J.3    Thieme, H.R.4
  • 86
    • 84972525241 scopus 로고
    • Perturbing semigroups by solving Stieltjes renewal equations
    • Diekmann, O., Gyllenberg, M., and Thieme, H. R., 1993, Perturbing semigroups by solving Stieltjes renewal equations, Diff. Int. Eqns 6, 155-181.
    • (1993) Diff. Int. Eqns , vol.6 , pp. 155-181
    • Diekmann, O.1    Gyllenberg, M.2    Thieme, H.R.3
  • 87
    • 84972545683 scopus 로고
    • Perturbing evolutionary systems by step responses and cumulative outputs
    • Diekmann, O., Gyllenberg, M., and Thieme, H. R., 1995a, Perturbing evolutionary systems by step responses and cumulative outputs, Diff. Int. Eqns 8, 1205-1244.
    • (1995) Diff. Int. Eqns , vol.8 , pp. 1205-1244
    • Diekmann, O.1    Gyllenberg, M.2    Thieme, H.R.3
  • 89
    • 0025159677 scopus 로고
    • On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations
    • Diekmann, O., Heesterbeek, J. A. P., and Metz, J. A. J., 1990, On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations, J. Math. Biol. 28, 365-382.
    • (1990) J. Math. Biol , vol.28 , pp. 365-382
    • Diekmann, O.1    Heesterbeek, J.A.P.2    Metz, J.A.J.3
  • 90
    • 0026064784 scopus 로고
    • Patterns in the effects of infectious diseases on population growth
    • Diekmann, O., and Kretzschmar, M., 1991, Patterns in the effects of infectious diseases on population growth, J. Math. Biol. 29, 539-570.
    • (1991) J. Math. Biol , vol.29 , pp. 539-570
    • Diekmann, O.1    Kretzschmar, M.2
  • 92
    • 0022593199 scopus 로고
    • Simple mathematical models for cannibalism: A critique and a new approach
    • Diekmann, O., Nisbet, R. M., Gurney, W. S. C., and van den Bosch, F., 1986, Simple mathematical models for cannibalism: a critique and a new approach, Math. Biosci. 78, 21-46.
    • (1986) Math. Biosci , vol.78 , pp. 21-46
    • Diekmann, O.1    Nisbet, R.M.2    Gurney, W.S.C.3    van den Bosch, F.4
  • 94
    • 0003066251 scopus 로고
    • Transmission and control of arbovirus diseases
    • (ed. D. Ludwig, K. L. Cooke), SIAM, Philadelphia, PA
    • Dietz, K., 1975, Transmission and control of arbovirus diseases, Epidemiology (ed. D. Ludwig, K. L. Cooke), pp. 104-119, SIAM, Philadelphia, PA.
    • (1975) Epidemiology , pp. 104-119
    • Dietz, K.1
  • 95
    • 0002454064 scopus 로고
    • The incidence of infectious diseases under the influence of seasonal fluctuations
    • (ed. J. Berger, W. Bühler, R. Repges, P. Tautu), Lecture Notes in Biomathematics, Springer, Heidelberg
    • Dietz, K., 1976, The incidence of infectious diseases under the influence of seasonal fluctuations, Mathematical models in medicine (ed. J. Berger, W. Bühler, R. Repges, P. Tautu), pp. 1-15, Lecture Notes in Biomathematics, vol. 11, Springer, Heidelberg.
    • (1976) Mathematical models in medicine , vol.11 , pp. 1-15
    • Dietz, K.1
  • 96
    • 0001778313 scopus 로고
    • Overall population patterns in the transmission cycle of infectious disease agents
    • (ed. R. M. Anderson, R. M. May), Life Sciences Research Report, no. 25, Springer, Berlin
    • Dietz, K., 1982, Overall population patterns in the transmission cycle of infectious disease agents, Population biology of infectious diseases (ed. R. M. Anderson, R. M. May), pp. 1-12, Life Sciences Research Report, no. 25, Springer, Berlin.
    • (1982) Population biology of infectious diseases , pp. 1-12
    • Dietz, K.1
  • 97
    • 0011053510 scopus 로고
    • The first epidemic model: A historical note on P. D. En’ko
    • Dietz, K., 1988, The first epidemic model: a historical note on P. D. En’ko, Austral. J. Statist. 30A, 56-65.
    • (1988) Austral. J. Statist , vol.30A , pp. 56-65
    • Dietz, K.1
  • 98
    • 0002736422 scopus 로고
    • Some problems in the theory of infectious disease transmission and control
    • (ed. D. Mollison), Cambridge University Press, Cambridge
    • Dietz, K., 1995, Some problems in the theory of infectious disease transmission and control, Epidemic models. Their structure and relation to data (ed. D. Mollison), pp. 3-16, Cambridge University Press, Cambridge.
    • (1995) Epidemic models. Their structure and relation to data , pp. 3-16
    • Dietz, K.1
  • 99
    • 0036847088 scopus 로고    scopus 로고
    • Daniel Bernoulli’s epidemiological model revisited
    • Dietz, K., and Heesterbeek, J. A. P., 2002, Daniel Bernoulli’s epidemiological model revisited, Math. Biosci. 180, 1-21.
    • (2002) Math. Biosci , vol.180 , pp. 1-21
    • Dietz, K.1    Heesterbeek, J.A.P.2
  • 100
    • 0002836854 scopus 로고
    • Mathematical models for infectious disease statistics
    • The ISI Centenary Volume (ed. A. C. Atkinson, S. E. Fienberg), Springer, NewYork
    • Dietz, K., and Schenzle, D., 1985, Mathematical models for infectious disease statistics, A celebration of statistics, The ISI Centenary Volume (ed. A. C. Atkinson, S. E. Fienberg), Springer, NewYork.
    • (1985) A celebration of statistics
    • Dietz, K.1    Schenzle, D.2
  • 102
    • 0001755071 scopus 로고
    • AUTO: A program for the automatic bifurcation analysis of autonomous systems
    • Doedel, E., 1981, AUTO: a program for the automatic bifurcation analysis of autonomous systems, Cong. Num. 30, 265-284.
    • (1981) Cong. Num , vol.30 , pp. 265-284
    • Doedel, E.1
  • 105
    • 0003756370 scopus 로고
    • Holt, Rinehart and Winston, NewYork (1965) and Dover, NewYork (1995)
    • Edwards, R. E., 1965, 1995, Functional analysis, Holt, Rinehart and Winston, NewYork (1965) and Dover, NewYork (1995).
    • (1965) Functional analysis
    • Edwards, R.E.1
  • 108
    • 0035649220 scopus 로고    scopus 로고
    • Estimation of the basic reproduction number for infectious diseases from age-stratified serological survey data (with discussion)
    • Farrington, C. P., Kanaan, M. N., and Gay, N. J., 2001, Estimation of the basic reproduction number for infectious diseases from age-stratified serological survey data (with discussion), J. Royal Statist. Soc. C; Appl. Statistics 50, 251-283.
    • (2001) J. Royal Statist. Soc. C; Appl. Statistics , vol.50 , pp. 251-283
    • Farrington, C.P.1    Kanaan, M.N.2    Gay, N.J.3
  • 109
    • 0000572783 scopus 로고
    • On the integral equation of renewal theory
    • reprinted in Smith, Keyfitz (eds), 1977, pp. 131-156
    • Feller, W., 1941, On the integral equation of renewal theory, Ann. Math. Statistics 12, 243-267 (reprinted in Smith, Keyfitz (eds), 1977, pp. 131-156).
    • (1941) Ann. Math. Statistics , vol.12 , pp. 243-267
    • Feller, W.1
  • 111
    • 85194335629 scopus 로고    scopus 로고
    • Stability of periodic solutions in an epidemiological model
    • (ed. Z. Chen, S. N. Chow and K. Li), Springer, Singapore, NewYork
    • Feng, Z., 1999, Stability of periodic solutions in an epidemiological model, Bifurcation theory and its numerical analysis (ed. Z. Chen, S. N. Chow and K. Li), pp. 69-78, Springer, Singapore, NewYork.
    • (1999) Bifurcation theory and its numerical analysis , pp. 69-78
    • Feng, Z.1
  • 112
    • 0029014859 scopus 로고
    • Recurrent outbreaks of childhood diseases revisited:The impact of isolation
    • Feng, Z., and Thieme, H. R., 1995, Recurrent outbreaks of childhood diseases revisited:the impact of isolation, Math. Biosci. 128, 93-130.
    • (1995) Math. Biosci , vol.128 , pp. 93-130
    • Feng, Z.1    Thieme, H.R.2
  • 113
    • 0034923771 scopus 로고    scopus 로고
    • Endemic models with arbitrarily distributed periods of infection, I, General theory
    • Feng, Z., and Thieme, H. R., 2000a, Endemic models with arbitrarily distributed periods of infection, I, General theory, SIAM J. Appl. Math. 61, 803-833.
    • (2000) SIAM J. Appl. Math , vol.61 , pp. 803-833
    • Feng, Z.1    Thieme, H.R.2
  • 114
    • 0034927101 scopus 로고    scopus 로고
    • Endemic models with arbitrarily distributed periods of infection, II, Fast disease dynamics and permanent recovery
    • Feng, Z., and Thieme, H. R., 2000b, Endemic models with arbitrarily distributed periods of infection, II, Fast disease dynamics and permanent recovery, SIAM J. Appl. Math. 61, 983-1012.
    • (2000) SIAM J. Appl. Math , vol.61 , pp. 983-1012
    • Feng, Z.1    Thieme, H.R.2
  • 115
    • 0001269939 scopus 로고
    • Global Hopf bifurcation forVolterra integral equations
    • Fiedler, B., 1986, Global Hopf bifurcation forVolterra integral equations, SIAM J. Math. Analysis 17, 911-932.
    • (1986) SIAM J. Math. Analysis , vol.17 , pp. 911-932
    • Fiedler, B.1
  • 116
    • 0000980087 scopus 로고
    • APoincaré-Bendixson theorem for scalar reaction diffusion equations
    • Fiedler, B., and Mallet-Paret, J., 1989, APoincaré-Bendixson theorem for scalar reaction diffusion equations, Arch. Ration. Mech. Analysis 107, 325-345.
    • (1989) Arch. Ration. Mech. Analysis , vol.107 , pp. 325-345
    • Fiedler, B.1    Mallet-Paret, J.2
  • 118
    • 84968495017 scopus 로고
    • Uniformly persistent semidynamical systems
    • Fonda, A., 1988, Uniformly persistent semidynamical systems, Proc. Am. Math. Soc. 104, 111-116.
    • (1988) Proc. Am. Math. Soc , vol.104 , pp. 111-116
    • Fonda, A.1
  • 119
    • 0003111841 scopus 로고
    • Cannibalism in natural populations
    • Fox, L. R., 1975, Cannibalism in natural populations, A. Rev. Ecol. Syst. 6, 87-106.
    • (1975) A. Rev. Ecol. Syst , vol.6 , pp. 87-106
    • Fox, L.R.1
  • 120
    • 4243218457 scopus 로고
    • Analysis of age-structure models
    • (ed. T. G. Hallam, S. A. Levin), Springer, Berlin
    • Frauenthal, J. C., 1986, Analysis of age-structure models, Mathematical ecology. An introduction (ed. T. G. Hallam, S. A. Levin), pp. 117-147, Springer, Berlin.
    • (1986) Mathematical ecology. An introduction , pp. 117-147
    • Frauenthal, J.C.1
  • 121
    • 84966258595 scopus 로고
    • Persistence definitions and their connections
    • Freedman, H. I., and Moson, P., 1990, Persistence definitions and their connections, Proc. Am. Math. Soc. 109, 1025-1032.
    • (1990) Proc. Am. Math. Soc , vol.109 , pp. 1025-1032
    • Freedman, H.I.1    Moson, P.2
  • 122
    • 0029012360 scopus 로고
    • Four SEI endemic models with periodicity and separatrices
    • Gao, L., Mena-Lorca, J., and Hethcote, H. W., 1995, Four SEI endemic models with periodicity and separatrices, Math. Biosci. 128, 157-184.
    • (1995) Math. Biosci , vol.128 , pp. 157-184
    • Gao, L.1    Mena-Lorca, J.2    Hethcote, H.W.3
  • 124
    • 0015760853 scopus 로고
    • Global models of growth and competition
    • Gilpin, M. E., and Ayala, F. J., 1973, Global models of growth and competition, Proc. Nat. Acad. Sci. USA 70, 3590-3593.
    • (1973) Proc. Nat. Acad. Sci. USA , vol.70 , pp. 3590-3593
    • Gilpin, M.E.1    Ayala, F.J.2
  • 125
    • 0003293418 scopus 로고
    • On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. In a letter to Francis Batley, esq
    • Gompertz, B., 1825, On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. In a letter to Francis Batley, esq., Phil. Trans. R. Soc. Lond. 115, 513-585.
    • (1825) Phil. Trans. R. Soc. Lond , vol.115 , pp. 513-585
    • Gompertz, B.1
  • 126
    • 84967958213 scopus 로고
    • Incubation period of measles (letter to editor)
    • Goodall, E. W., 1931, Incubation period of measles (letter to editor), Brit. Med. J. 1, 73-74.
    • (1931) Brit. Med. J , vol.1 , pp. 73-74
    • Goodall, E.W.1
  • 127
    • 0025160594 scopus 로고
    • Vaccination compaigns for common childhood diseases
    • Greenhalgh, D., 1990, Vaccination compaigns for common childhood diseases, Math. Biosci. 100, 201-240.
    • (1990) Math. Biosci , vol.100 , pp. 201-240
    • Greenhalgh, D.1
  • 128
    • 0028046641 scopus 로고
    • Some bounds on estimates for reproductive ratios from the age-specific force of infection
    • Greenhalgh, D., and Dietz, K., 1994, Some bounds on estimates for reproductive ratios from the age-specific force of infection, Math. Biosci. 124, 9-57.
    • (1994) Math. Biosci , vol.124 , pp. 9-57
    • Greenhalgh, D.1    Dietz, K.2
  • 131
    • 0019075237 scopus 로고
    • Oscillatory phenomena in a model of infectious diseases
    • Grossman, Z., 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
  • 132
    • 0002109848 scopus 로고
    • The incidence of infectious diseases under the influence of seasonal fluctuations-analytic approach
    • Academic Press, San Diego, CA
    • Grossman, Z., Gumowski, I., and Dietz, K., 1977, The incidence of infectious diseases under the influence of seasonal fluctuations-analytic approach, Nonlinear systems and applications to life sciences, pp. 525-546, Academic Press, San Diego, CA.
    • (1977) Nonlinear systems and applications to life sciences , pp. 525-546
    • Grossman, Z.1    Gumowski, I.2    Dietz, K.3
  • 134
    • 0031397178 scopus 로고    scopus 로고
    • Continuous versus discrete single species population models with adjustable reproductive strategies
    • Gyllenberg, M., Hanski, I., and Lindström, T., 1997, Continuous versus discrete single species population models with adjustable reproductive strategies, Bull. Math. Biol. 59, 679-705.
    • (1997) Bull. Math. Biol , vol.59 , pp. 679-705
    • Gyllenberg, M.1    Hanski, I.2    Lindström, T.3
  • 135
    • 0029055539 scopus 로고
    • A core group model for disease transmission
    • Hadeler, K. P., and Castillo-Chavez, C., 1995, A core group model for disease transmission, Math. Biosci. 128, 41-55.
    • (1995) Math. Biosci , vol.128 , pp. 41-55
    • Hadeler, K.P.1    Castillo-Chavez, C.2
  • 136
    • 0021678649 scopus 로고
    • Population dynamics of killing parasites which reproduce in the host
    • Hadeler, K. P., and Dietz, K., 1984, Population dynamics of killing parasites which reproduce in the host, J. Math. Biol. 21, 45-65.
    • (1984) J. Math. Biol , vol.21 , pp. 45-65
    • Hadeler, K.P.1    Dietz, K.2
  • 137
    • 0001620170 scopus 로고    scopus 로고
    • Optimal vaccination patterns in age-structured populations, II, Optimal strategies
    • (ed. V. Isham, G. Medley), Cambridge University Press, Cambridge
    • Hadeler, K. P., and Müller, J., 1996, Optimal vaccination patterns in age-structured populations, II, Optimal strategies, Model for infectious human diseases: their structure and relation to data (ed. V. Isham, G. Medley), pp. 102-114, Cambridge University Press, Cambridge.
    • (1996) Model for infectious human diseases: Their structure and relation to data , pp. 102-114
    • Hadeler, K.P.1    Müller, J.2
  • 138
    • 0017439216 scopus 로고
    • Periodic solutions of difference-differential equations
    • Hadeler, K. P., and Tomiuk, J., 1977, Periodic solutions of difference-differential equations, Arch. Ration. Mech. Analysis 65, 87-96.
    • (1977) Arch. Ration. Mech. Analysis , vol.65 , pp. 87-96
    • Hadeler, K.P.1    Tomiuk, J.2
  • 143
    • 0000802631 scopus 로고
    • Persistence in infinite-dimensional systems
    • Hale, J. K., and Waltman, P., 1989, Persistence in infinite-dimensional systems, SIAM J. Math. Analysis 20, 388-395.
    • (1989) SIAM J. Math. Analysis , vol.20 , pp. 388-395
    • Hale, J.K.1    Waltman, P.2
  • 144
    • 0002787307 scopus 로고
    • Population dynamics in a homogeneous environment
    • (ed.T. G. Hallam, S.A. Levin), Biomathematics, Springer, Berlin
    • Hallam, T. G., 1986, Population dynamics in a homogeneous environment, Mathematical ecology (ed.T. G. Hallam, S.A. Levin), pp. 61-94, Biomathematics, vol. 17, Springer, Berlin.
    • (1986) Mathematical ecology , vol.17 , pp. 61-94
    • Hallam, T.G.1
  • 145
    • 0021217861 scopus 로고
    • Effects of toxicants on populations: A qualitative approach, III, Environmental and food chain pathways
    • Hallam, T. G., and De Luna, J. L., 1984, Effects of toxicants on populations: a qualitative approach, III, Environmental and food chain pathways, J. Theor. Biol. 109, 411-429.
    • (1984) J. Theor. Biol , vol.109 , pp. 411-429
    • Hallam, T.G.1    De Luna, J.L.2
  • 146
    • 0006268607 scopus 로고
    • Effects of toxicants on aquatic populations
    • (ed. S. A. Levin, T. G. Hallam, L. J. Gross), Springer, Berlin
    • Hallam, T. G., Lassiter, R. R., and Kooijman, S. A. L. M., 1989, Effects of toxicants on aquatic populations, Applied mathematical ecology (ed. S. A. Levin, T. G. Hallam, L. J. Gross), pp. 352-382, Springer, Berlin.
    • (1989) Applied mathematical ecology , pp. 352-382
    • Hallam, T.G.1    Lassiter, R.R.2    Kooijman, S.A.L.M.3
  • 147
    • 0002643627 scopus 로고
    • Density dependence in single-species populations
    • Hassell, M. P., 1975, Density dependence in single-species populations, J. Animal Ecol. 44, 283-295.
    • (1975) J. Animal Ecol , vol.44 , pp. 283-295
    • Hassell, M.P.1
  • 150
    • 0036025407 scopus 로고    scopus 로고
    • A brief history of R0 and a recipe for its calculation
    • Heesterbeek, J. A. P., 2002, A brief history of R0 and a recipe for its calculation, Acta Biotheoretica 50, 189-204.
    • (2002) Acta Biotheoretica , vol.50 , pp. 189-204
    • Heesterbeek, J.A.P.1
  • 151
    • 0027488382 scopus 로고
    • The saturating contact rate in marriage and epidemic models
    • Heesterbeek, J. A. P., and Metz, J. A. J., 1993, The saturating contact rate in marriage and epidemic models, J. Math. Biol. 31, 529-539.
    • (1993) J. Math. Biol , vol.31 , pp. 529-539
    • Heesterbeek, J.A.P.1    Metz, J.A.J.2
  • 152
    • 0040864462 scopus 로고
    • Asymptotic behavior
    • (ed. Ph. Clément, H. J. A. M. Heijmans, S. Angenent, C. J. van Duijn, B. de Pagter), North-Holland, Amsterdam
    • Heijmans, H. J. A. M., and de Pagter, B., 1987, Asymptotic behavior, One-parameter semigroups (ed. Ph. Clément, H. J. A. M. Heijmans, S. Angenent, C. J. van Duijn, B. de Pagter), pp. 213-233, North-Holland, Amsterdam.
    • (1987) One-parameter semigroups , pp. 213-233
    • Heijmans, H.J.A.M.1    de Pagter, B.2
  • 153
    • 0017228276 scopus 로고
    • Qualitative analysis for communicable disease models
    • Hethcote, H. W., 1976, Qualitative analysis for communicable disease models, Math. Biosci. 28, 335-356.
    • (1976) Math. Biosci , vol.28 , pp. 335-356
    • Hethcote, H.W.1
  • 154
    • 0000824569 scopus 로고
    • Three basic epidemiological models
    • (ed. S. A. Levin, T. G. Hallam, L. J. Gross), Biomathematics, Springer, Berlin
    • Hethcote, H. W., 1989a, Three basic epidemiological models, Applied mathematical ecology (ed. S. A. Levin, T. G. Hallam, L. J. Gross), pp. 119-144, Biomathematics, vol. 18, Springer, Berlin.
    • (1989) Applied mathematical ecology , vol.18 , pp. 119-144
    • Hethcote, H.W.1
  • 155
    • 0040436404 scopus 로고
    • Rubella
    • (ed. S. A. Levin, T. G. Hallam, L. J. Gross), Biomathematics, Springer, Berlin
    • Hethcote, H.W., 1989b, Rubella, Applied mathematical ecology (ed. S. A. Levin, T. G. Hallam, L. J. Gross), pp. 212-234, Biomathematics, vol. 18, Springer, Berlin.
    • (1989) Applied mathematical ecology , vol.18 , pp. 212-234
    • Hethcote, H.W.1
  • 156
    • 0000751578 scopus 로고
    • A thousand and one epidemic models
    • (ed. S. A. Levin), Lecture Notes in Biomathematics, Springer, Berlin
    • Hethcote, H.W., 1994, A thousand and one epidemic models, Frontiers in mathematical biology (ed. S. A. Levin), pp. 504-515, Lecture Notes in Biomathematics, vol. 100, Springer, Berlin.
    • (1994) Frontiers in mathematical biology , vol.100 , pp. 504-515
    • Hethcote, H.W.1
  • 157
    • 0002530264 scopus 로고
    • Modeling heterogeneous mixing in infectious disease dynamics
    • (ed. V. Isham, G. Medley), Cambridge University Press, Cambridge
    • Hethcote, H.W., 1995, Modeling heterogeneous mixing in infectious disease dynamics, Models for infectious human diseases. Their structure and relation to data (ed. V. Isham, G. Medley), Cambridge University Press, Cambridge.
    • (1995) Models for infectious human diseases. Their structure and relation to data
    • Hethcote, H.W.1
  • 158
    • 0034486891 scopus 로고    scopus 로고
    • The mathematics of infectious disease
    • Hethcote, H.W., 2000, The mathematics of infectious disease, SIAM Rev. 42, 599-653.
    • (2000) SIAM Rev , vol.42 , pp. 599-653
    • Hethcote, H.W.1
  • 159
    • 0000236256 scopus 로고
    • Periodicity in epidemiological models
    • (ed. S. A. Levin, T. G. Hallam, L. J. Gross), Biomathematics, Springer, Berlin
    • Hethcote, H.W., and Levin, S. A., 1989, Periodicity in epidemiological models, Applied mathematical ecology (ed. S. A. Levin, T. G. Hallam, L. J. Gross), pp. 193-211, Biomathematics, vol. 18, Springer, Berlin.
    • (1989) Applied mathematical ecology , vol.18 , pp. 193-211
    • Hethcote, H.W.1    Levin, S.A.2
  • 161
    • 0021984692 scopus 로고
    • Stability of the endemic equilibrium in epidemic models with subpopulations
    • Hethcote, H. W., and Thieme, H. R., 1985, Stability of the endemic equilibrium in epidemic models with subpopulations, Math. Biosci. 75, 205-227.
    • (1985) Math. Biosci , vol.75 , pp. 205-227
    • Hethcote, H.W.1    Thieme, H.R.2
  • 164
    • 0036846383 scopus 로고    scopus 로고
    • Effects of quarantine in six endemic models for infectious diseases
    • Hethcote, H.W., Zhien, M., and Shengbing, L., 2002, Effects of quarantine in six endemic models for infectious diseases, Math. Biosci. 180, 141-160.
    • (2002) Math. Biosci , vol.180 , pp. 141-160
    • Hethcote, H.W.1    Zhien, M.2    Shengbing, L.3
  • 166
    • 0024099079 scopus 로고
    • The epidemiology of AIDS in the US
    • Heyward, W. L., and Curran, J.W., 1988, The epidemiology of AIDS in the US, Scient. Amer. 259(4), 72-81.
    • (1988) Scient. Amer , vol.259 , Issue.4 , pp. 72-81
    • Heyward, W.L.1    Curran, J.W.2
  • 167
    • 0001015290 scopus 로고
    • Systems of differential equations which are competitive or cooperative, IV, Structural stability in three dimensional systems
    • Hirsch, M.W., 1990, Systems of differential equations which are competitive or cooperative, IV, Structural stability in three dimensional systems, SIAM J. Math. Analysis 21, 1225-1234.
    • (1990) SIAM J. Math. Analysis , vol.21 , pp. 1225-1234
    • Hirsch, M.W.1
  • 168
    • 84990581010 scopus 로고
    • Differential equation models for some parasitic infections: Methods for the study of asymptotic behavior
    • Hirsch, W. M., Hanisch, H., and Gabriel, J.-P., 1985, Differential equation models for some parasitic infections: methods for the study of asymptotic behavior, Commun. Pure Appl. Math. 38, 733-753.
    • (1985) Commun. Pure Appl. Math , vol.38 , pp. 733-753
    • Hirsch, W.M.1    Hanisch, H.2    Gabriel, J.-P.3
  • 170
    • 0000446081 scopus 로고
    • Stable periodic solutions for the hypercycle system
    • Hofbauer, J., Mallet-Paret, J., and Smith, H. L., 1991, Stable periodic solutions for the hypercycle system, J. Dyn. Diff. Eqns 3, 423-436.
    • (1991) J. Dyn. Diff. Eqns , vol.3 , pp. 423-436
    • Hofbauer, J.1    Mallet-Paret, J.2    Smith, H.L.3
  • 173
    • 0002366911 scopus 로고
    • The functional response of predators to prey density and its role in mimicry and population regulation
    • Holling, C. S., 1965, The functional response of predators to prey density and its role in mimicry and population regulation, Mem. Ent. Soc. Canada 45, 1-60.
    • (1965) Mem. Ent. Soc. Canada , vol.45 , pp. 1-60
    • Holling, C.S.1
  • 174
    • 0002366911 scopus 로고
    • The functional response of invertebrate predators to prey density
    • Holling, C. S., 1966, The functional response of invertebrate predators to prey density, Mem. Entom. Soc. Can. 48.
    • (1966) Mem. Entom. Soc. Can , pp. 48
    • Holling, C.S.1
  • 176
    • 33746358042 scopus 로고
    • Asymptotic stability in singular perturbation problems, II, Problems having matched asymptotic expansion solutions
    • Hoppensteadt, F. C., 1974, Asymptotic stability in singular perturbation problems, II, Problems having matched asymptotic expansion solutions, J. Diff. Eqns 15, 510-521.
    • (1974) J. Diff. Eqns , vol.15 , pp. 510-521
    • Hoppensteadt, F.C.1
  • 179
    • 1642311106 scopus 로고
    • Aproblem in the theory of epidemics
    • Hoppensteadt, F. C., and Waltman, P., 1970, Aproblem in the theory of epidemics, Math. Biosci. 9, 71-91.
    • (1970) Math. Biosci , vol.9 , pp. 71-91
    • Hoppensteadt, F.C.1    Waltman, P.2
  • 180
    • 0011252924 scopus 로고
    • A problem in the theory of epidemics, II
    • Hoppensteadt, F. C., and Waltman, P., 1971, A problem in the theory of epidemics, II, Math. Biosci. 12, 133-145.
    • (1971) Math. Biosci , vol.12 , pp. 133-145
    • Hoppensteadt, F.C.1    Waltman, P.2
  • 182
    • 0000723140 scopus 로고
    • Stability and bifurcation for a multiple-group model for the dynamics of HIV/AIDS transmission
    • Huang, W., Cooke, K. L., and Castillo-Chavez, C., 1992, Stability and bifurcation for a multiple-group model for the dynamics of HIV/AIDS transmission, SIAM J. Appl. Math. 52, 835-854.
    • (1992) SIAM J. Appl. Math , vol.52 , pp. 835-854
    • Huang, W.1    Cooke, K.L.2    Castillo-Chavez, C.3
  • 184
    • 0001439703 scopus 로고
    • A theorem on average Lyapunov functions
    • Hutson, V., 1984, A theorem on average Lyapunov functions, Monatsh. Math. 98, 267-275.
    • (1984) Monatsh. Math , vol.98 , pp. 267-275
    • Hutson, V.1
  • 185
    • 0026616222 scopus 로고
    • Permanence in dynamical systems
    • Hutson, V., and Schmitt, K., 1992, Permanence in dynamical systems, Math. Biosci. 111, 1-71.
    • (1992) Math. Biosci , vol.111 , pp. 1-71
    • Hutson, V.1    Schmitt, K.2
  • 188
    • 0024467542 scopus 로고
    • Weak ergodicity of population evolution processes
    • Inaba, H., 1989, Weak ergodicity of population evolution processes, Math. Biosci. 96, 195-219.
    • (1989) Math. Biosci , vol.96 , pp. 195-219
    • Inaba, H.1
  • 189
    • 0025118998 scopus 로고
    • Threshold and stability results for an age-structured epidemic model
    • Inaba, H., 1990, Threshold and stability results for an age-structured epidemic model, J. Math. Biol. 28, 411-434.
    • (1990) J. Math. Biol , vol.28 , pp. 411-434
    • Inaba, H.1
  • 191
    • 0001121830 scopus 로고
    • Oscillations in singularly perturbed delay equations
    • ed. C. K. R. T. Jones, U. Kirchgraber, H. O. Walther, Springer, Berlin
    • Ivanov, A. F., and Sharkovsky, A. N., 1991, Oscillations in singularly perturbed delay equations, Dynamics reported, vol. I (ed. C. K. R. T. Jones, U. Kirchgraber, H. O. Walther), pp. 164-224, Springer, Berlin.
    • (1991) Dynamics reported , vol.1 , pp. 164-224
    • Ivanov, A.F.1    Sharkovsky, A.N.2
  • 192
    • 0000337775 scopus 로고
    • Core groups and R0s for subgroups in heterogeneous SIS and SI models
    • (ed. D. Mollison), Cambridge University Press, Cambridge
    • Jacquez, J. A., Simon, C. P., and Koopman, J., 1995, Core groups and R0s for subgroups in heterogeneous SIS and SI models, Epidemic models: their structure and relation to data (ed. D. Mollison), pp. 279-301, Cambridge University Press, Cambridge.
    • (1995) Epidemic models: Their structure and relation to data , pp. 279-301
    • Jacquez, J.A.1    Simon, C.P.2    Koopman, J.3
  • 196
    • 0032518718 scopus 로고    scopus 로고
    • Effect of variability in infectious period on the persistence and spatial spread of infectious diseases
    • Keeling, M. J., and Grenfell, B. T., 1998, Effect of variability in infectious period on the persistence and spatial spread of infectious diseases, Math. Biosci. 147, 207-226.
    • (1998) Math. Biosci , vol.147 , pp. 207-226
    • Keeling, M.J.1    Grenfell, B.T.2
  • 198
    • 0000998185 scopus 로고
    • Contributions to the mathematical theory of epidemics: Part I (1927)
    • (reprinted in Bull. Math Biol. 53 (1991), 33-55); Part II (1932) Proc. R. Soc. Lond. A138, 55-85 (reprinted in Bull. Math Biol. 53 (1991), 57-87); Part III (1933) Proc. R. Soc. Lond. A141, 94-122 (reprinted in Bull. Math Biol. 53 (1991), 89-118); Part IV (1937) J. Hyg. Camb. 37, 172-187; Part V (1939) J. Hyg. Camb. 39, 271-288
    • Kermack, W. O., and McKendrick, A. G., 1927-1939, Contributions to the mathematical theory of epidemics: Part I (1927) Proc. R. Soc. Lond. A115, 700-721 (reprinted in Bull. Math Biol. 53 (1991), 33-55); Part II (1932) Proc. R. Soc. Lond. A138, 55-85 (reprinted in Bull. Math Biol. 53 (1991), 57-87); Part III (1933) Proc. R. Soc. Lond. A141, 94-122 (reprinted in Bull. Math Biol. 53 (1991), 89-118); Part IV (1937) J. Hyg. Camb. 37, 172-187; Part V (1939) J. Hyg. Camb. 39, 271-288.
    • (1927) Proc. R. Soc. Lond , vol.A115 , pp. 700-721
    • Kermack, W.O.1    McKendrick, A.G.2
  • 202
    • 0024631334 scopus 로고
    • On the equality of average age and average expectation of remaining life in a stationary population
    • Kim, Y. J., and Aron, J. L., 1989, On the equality of average age and average expectation of remaining life in a stationary population, SIAM Rev. 31, 110-113.
    • (1989) SIAM Rev , vol.31 , pp. 110-113
    • Kim, Y.J.1    Aron, J.L.2
  • 203
    • 0037968401 scopus 로고
    • The refractory model: The logistic curve and the history of population ecology
    • Kingsland, S. E., 1982, The refractory model: the logistic curve and the history of population ecology, Q. Rev. Biol. 57, 29-52.
    • (1982) Q. Rev. Biol , vol.57 , pp. 29-52
    • Kingsland, S.E.1
  • 209
    • 0001643309 scopus 로고
    • Population dynamics on the basis of budgets
    • (ed. J. A. J. Metz, O. Diekmann), Lecture Notes in Biomathematics, Springer, Berlin
    • Kooijman, S.A. L. M., 1986, Population dynamics on the basis of budgets, The dynamics of physiologically structured populations (ed. J. A. J. Metz, O. Diekmann), pp. 267-297, Lecture Notes in Biomathematics, vol. 68, Springer, Berlin.
    • (1986) The dynamics of physiologically structured populations , vol.68 , pp. 267-297
    • Kooijman, S.A.L.M.1
  • 211
    • 0021283893 scopus 로고
    • On the dynamics of chemically stressed populations: The deduction of population consequences from effects on individuals
    • Kooijman, S. A. L. M., and Metz, J. A. J., 1984, On the dynamics of chemically stressed populations: the deduction of population consequences from effects on individuals, Ecotox. Env. Saf. 8, 254-274.
    • (1984) Ecotox. Env. Saf , vol.8 , pp. 254-274
    • Kooijman, S.A.L.M.1    Metz, J.A.J.2
  • 214
    • 0000998396 scopus 로고    scopus 로고
    • Positive nonlinear difference equations
    • Krause, U., 1997, Positive nonlinear difference equations, Nonlinear Analysis TMA 30, 301-308.
    • (1997) Nonlinear Analysis TMA , vol.30 , pp. 301-308
    • Krause, U.1
  • 215
    • 0036234426 scopus 로고    scopus 로고
    • Vaccination strategies and backward bifurcation in an age-since-infection structured model
    • Kribs-Zaleta, C. M., and Martcheva, M., 2002, Vaccination strategies and backward bifurcation in an age-since-infection structured model, Math. Biosci. 177-178, 317-322.
    • (2002) Math. Biosci , vol.177-178 , pp. 317-322
    • Kribs-Zaleta, C.M.1    Martcheva, M.2
  • 216
    • 0343238366 scopus 로고    scopus 로고
    • A simple vaccination model with multiple endemic states
    • Kribs-Zaleta, C. M., and Velasco-Hernández, J. X., 2000, A simple vaccination model with multiple endemic states, Math. Biosci. 164, 183-201.
    • (2000) Math. Biosci , vol.164 , pp. 183-201
    • Kribs-Zaleta, C.M.1    Velasco-Hernández, J.X.2
  • 217
    • 0000671790 scopus 로고
    • Global stability of Gause-type predator-prey systems
    • Kuang, Y., 1990, Global stability of Gause-type predator-prey systems, J. Math. Biol. 28, 463-474.
    • (1990) J. Math. Biol , vol.28 , pp. 463-474
    • Kuang, Y.1
  • 219
    • 0017226769 scopus 로고
    • A deterministic model for gonorrhea in a nonhomogeneous population
    • Lajmanovich, A., and Yorke, J. A., 1976, A deterministic model for gonorrhea in a nonhomogeneous population, Math. Biosci. 28, 221-236.
    • (1976) Math. Biosci , vol.28 , pp. 221-236
    • Lajmanovich, A.1    Yorke, J.A.2
  • 220
    • 29244451624 scopus 로고
    • Grouping in population models
    • (ed. D. Mollison), Cambridge University Press, Cambridge
    • Levin, S. A., 1995, Grouping in population models, Epidemic models: their structure and relation to data (ed. D. Mollison), pp. 271-278, Cambridge University Press, Cambridge.
    • (1995) Epidemic models: Their structure and relation to data , pp. 271-278
    • Levin, S.A.1
  • 222
    • 0028817626 scopus 로고
    • Global stability for the SEIR model in epidemiology
    • Li, M.Y., and Muldowney, J. S., 1995, Global stability for the SEIR model in epidemiology, Math. Biosci. 125, 155-164.
    • (1995) Math. Biosci , vol.125 , pp. 155-164
    • Li, M.Y.1    Muldowney, J.S.2
  • 224
    • 0036222772 scopus 로고    scopus 로고
    • Global dynamics of an SEIR epidemic model with vertical transmission
    • Li, M. Y., Smith, H. L., and Wang, L., 2001, Global dynamics of an SEIR epidemic model with vertical transmission, SIAM J. Appl. Math. 62, 58-69.
    • (2001) SIAM J. Appl. Math , vol.62 , pp. 58-69
    • Li, M.Y.1    Smith, H.L.2    Wang, L.3
  • 226
    • 0025931684 scopus 로고
    • On the uniqueness of endemic equilibria of an HIV/AIDS transmission model for a heterogeneous population
    • Lin, X., 1991, On the uniqueness of endemic equilibria of an HIV/AIDS transmission model for a heterogeneous population, J. Math. Biol. 29, 779-790.
    • (1991) J. Math. Biol , vol.29 , pp. 779-790
    • Lin, X.1
  • 227
    • 0009418458 scopus 로고
    • Global stability of the endemic equilibrium and uniform persistence in epidemic models with subpopulations
    • B34
    • Lin, X., and So, J.W.-H., 1993, Global stability of the endemic equilibrium and uniform persistence in epidemic models with subpopulations, J. Austral. Math. Soc. B34, 282-295.
    • (1993) J. Austral. Math. Soc , pp. 282-295
    • Lin, X.1    So, J.W.-H.2
  • 228
    • 0027358312 scopus 로고
    • Dose-dependent latent period and periodicity of infectious diseases
    • Liu, W.-M., 1993, Dose-dependent latent period and periodicity of infectious diseases, J. Math. Biol. 31, 487-494.
    • (1993) J. Math. Biol , vol.31 , pp. 487-494
    • Liu, W.-M.1
  • 229
    • 85194304632 scopus 로고
    • Models for recurrent outbreaks of infectious diseases
    • (ed. O. Arino, D. Axelrod, M. Kimmel, M. Langlais), Wuerz, Winnipeg
    • Liu, W.-M., 1995, Models for recurrent outbreaks of infectious diseases, Mathematical population dynamics: analysis of heterogeneity, vol. 1, Theory of epidemics (ed. O. Arino, D. Axelrod, M. Kimmel, M. Langlais), pp. 119-130, Wuerz, Winnipeg.
    • (1995) Mathematical population dynamics: Analysis of heterogeneity, vol. 1, Theory of epidemics , pp. 119-130
    • Liu, W.-M.1
  • 230
    • 0023070210 scopus 로고
    • Dynamical behavior of epidemiological models with nonlinear incidence rates
    • Liu, W.-M., Hethcote, H.W., and Levin, S. A., 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.-M.1    Hethcote, H.W.2    Levin, S.A.3
  • 231
    • 0028180350 scopus 로고
    • The role of prey in controlling expression of a trophic polymorphism in Ambystoma tigrinum nebulosum
    • Loeb, M. L. G., Collins, J. P., and Maret, T. J., 1994, The role of prey in controlling expression of a trophic polymorphism in Ambystoma tigrinum nebulosum, Functional Ecology 8, 151-158.
    • (1994) Functional Ecology , vol.8 , pp. 151-158
    • Loeb, M.L.G.1    Collins, J.P.2    Maret, T.J.3
  • 232
    • 0015739604 scopus 로고
    • Recurrent outbreaks of measles, chickenpox and mumps, I, Seasonal variation in contact rates
    • London, W. P., and Yorke, J. A., 1973a, Recurrent outbreaks of measles, chickenpox and mumps, I, Seasonal variation in contact rates, American J. Epidem. 98, 453-468.
    • (1973) American J. Epidem , vol.98 , pp. 453-468
    • London, W.P.1    Yorke, J.A.2
  • 233
    • 0015711463 scopus 로고
    • Recurrent outbreaks of measles, chickenpox and mumps, II, Systematic differences in contact rates and stochastic effects
    • London, W. P., and Yorke, J. A., 1973b, Recurrent outbreaks of measles, chickenpox and mumps, II, Systematic differences in contact rates and stochastic effects, American J. Epidem. 98, 468-482.
    • (1973) American J. Epidem , vol.98 , pp. 468-482
    • London, W.P.1    Yorke, J.A.2
  • 234
    • 0002467390 scopus 로고
    • Relation between birth rates and death rates
    • reprinted in Smith, Keyfitz (eds), 1977, pp. 93-95
    • Lotka, A. L., 1907, Relation between birth rates and death rates, Science 26, 21-22 (reprinted in Smith, Keyfitz (eds), 1977, pp. 93-95).
    • (1907) Science , vol.26 , pp. 21-22
    • Lotka, A.L.1
  • 235
    • 0001487973 scopus 로고
    • The stability of the normal age distribution
    • reprinted in Smith, Keyfitz (eds), 1977, pp. 101-107
    • Lotka, A. J., 1922, The stability of the normal age distribution, Proc. Nat. Acad. Sci. 8, 339-345 (reprinted in Smith, Keyfitz (eds), 1977, pp. 101-107).
    • (1922) Proc. Nat. Acad. Sci , vol.8 , pp. 339-345
    • Lotka, A.J.1
  • 237
    • 0002382886 scopus 로고    scopus 로고
    • Death stalks a continent
    • McGeary, J., 2001, Death stalks a continent, Time 157(6), 36-45.
    • (2001) Time , vol.157 , Issue.6 , pp. 36-45
    • McGeary, J.1
  • 238
    • 0002277320 scopus 로고
    • Applications of mathematics to medical problems
    • McKendrick, A. G., 1926, Applications of mathematics to medical problems, Proc. Edinb. Math. Soc. 14, 98-130.
    • (1926) Proc. Edinb. Math. Soc , vol.14 , pp. 98-130
    • McKendrick, A.G.1
  • 239
    • 18844434923 scopus 로고
    • The rate of multiplication of microorganisms:A mathematical study
    • McKendrick, A. G., and Kesava Pai, M., 1911, The rate of multiplication of microorganisms:a mathematical study, Proc. R. Soc. Edinb. 31, 649-655.
    • (1911) Proc. R. Soc. Edinb , vol.31 , pp. 649-655
    • McKendrick, A.G.1    Kesava Pai, M.2
  • 241
    • 0000774870 scopus 로고
    • On the law of mortality
    • Makeham, W. M., 1867, On the law of mortality, J. Inst. Actuaries 13, 325-367.
    • (1867) J. Inst. Actuaries , vol.13 , pp. 325-367
    • Makeham, W.M.1
  • 242
    • 0030102885 scopus 로고    scopus 로고
    • The Poincaré-Bendixson theorem for monotone cyclic feedback systems with delay
    • Mallet-Paret, J., and Sell, G. R., 1996, The Poincaré-Bendixson theorem for monotone cyclic feedback systems with delay, J. Diff. Eqns 125, 441-489.
    • (1996) J. Diff. Eqns , vol.125 , pp. 441-489
    • Mallet-Paret, J.1    Sell, G.R.2
  • 243
    • 0001051330 scopus 로고
    • The Poincaré-Bendixson theorem for monotone cyclic feedback systems
    • Mallet-Paret, J., and Smith, H. L., 1990, The Poincaré-Bendixson theorem for monotone cyclic feedback systems, J. Dyn. Diff. Eqns 2, 367-421.
    • (1990) J. Dyn. Diff. Eqns , vol.2 , pp. 367-421
    • Mallet-Paret, J.1    Smith, H.L.2
  • 244
    • 0004269732 scopus 로고
    • Harmondsworth, Middlesex (republished by Penguin, NewYork, in 1970)
    • Malthus, T., 1798, An essay on the principle of population, Harmondsworth, Middlesex (republished by Penguin, NewYork, in 1970).
    • (1798) An essay on the principle of population
    • Malthus, T.1
  • 245
    • 0024101420 scopus 로고
    • The international epidemiology of AIDS
    • Mann, J. M., Chin, J., Piot, P., and Quinn, Th., 1988, The international epidemiology of AIDS, Scient. Amer. 259(4), 82-89.
    • (1988) Scient. Amer , vol.259 , Issue.4 , pp. 82-89
    • Mann, J.M.1    Chin, J.2    Piot, P.3    Quinn, T.4
  • 246
    • 0000484858 scopus 로고    scopus 로고
    • Effect of prey vulnerability on population size structure of a gape-limited predator
    • Maret, T. J., and Collins, J. P., 1996, Effect of prey vulnerability on population size structure of a gape-limited predator, Ecology 77, 320-324.
    • (1996) Ecology , vol.77 , pp. 320-324
    • Maret, T.J.1    Collins, J.P.2
  • 247
    • 0004218542 scopus 로고
    • Charles Scribner’s Sons, NewYork
    • Marks, G., and Beatty, W. K., 1976, Epidemics, Charles Scribner’s Sons, NewYork.
    • (1976) Epidemics
    • Marks, G.1    Beatty, W.K.2
  • 248
    • 0032913251 scopus 로고    scopus 로고
    • Exponential growth in age-structured two-sex populations
    • Martcheva, M., 1999, Exponential growth in age-structured two-sex populations, Math. Biosci. 157, 1-22.
    • (1999) Math. Biosci , vol.157 , pp. 1-22
    • Martcheva, M.1
  • 249
    • 85194327763 scopus 로고    scopus 로고
    • Progression age enhanced backward bifurcation in an epidemic model with super-infection
    • n.d, to appear
    • Martcheva, M., and Thieme, H. R., n.d., Progression age enhanced backward bifurcation in an epidemic model with super-infection, J. Math. Biol., to appear.
    • J. Math. Biol.
    • Martcheva, M.1    Thieme, H.R.2
  • 251
    • 3142754314 scopus 로고
    • Introduction
    • (ed. R. M. Anderson, R. M. May), Life Sciences Research Report, no. 25, Springer, Berlin
    • May, R. M., 1982, Introduction, Population biology of infectious diseases (ed. R. M. Anderson, R. M. May), pp. 1-12, Life Sciences Research Report, no. 25, Springer, Berlin.
    • (1982) Population biology of infectious diseases , pp. 1-12
    • May, R.M.1
  • 252
    • 0342421174 scopus 로고
    • The transmission dynamics of human immunodeficiency virus (HIV)
    • (ed. S. A. Levin, T. G. Hallam, L. J. Gross), Biomathematics, Springer, Berlin
    • May, R. M., and Anderson, R. M., 1989, The transmission dynamics of human immunodeficiency virus (HIV), Applied mathematical ecology (ed. S. A. Levin, T. G. Hallam, L. J. Gross), Biomathematics, vol. 18, Springer, Berlin.
    • (1989) Applied mathematical ecology , vol.18
    • May, R.M.1    Anderson, R.M.2
  • 253
  • 255
    • 0036846365 scopus 로고    scopus 로고
    • Detecting autocatalytic dynamics in data modeled by a compartmental model
    • Merrill, S. J., and Murphy, B. M., 2002, Detecting autocatalytic dynamics in data modeled by a compartmental model, Math. Biosci. 180, 255-262.
    • (2002) Math. Biosci , vol.180 , pp. 255-262
    • Merrill, S.J.1    Murphy, B.M.2
  • 259
    • 0000870544 scopus 로고
    • Die Kinetik der Invertinwirkung
    • Michaelis, L., and Menten, M. I., 1913, Die Kinetik der Invertinwirkung, Biochem. Z. 49, 333-369.
    • (1913) Biochem. Z , vol.49 , pp. 333-369
    • Michaelis, L.1    Menten, M.I.2
  • 260
    • 0000703838 scopus 로고
    • Asymptotically autonomous semiflows, chain recurrence and Lyapunov functions
    • Mischaikow, K., Smith, H. L., and Thieme, H. R., 1995, Asymptotically autonomous semiflows, chain recurrence and Lyapunov functions, Trans. Am. Math. Soc. 347, 1669-1685.
    • (1995) Trans. Am. Math. Soc , vol.347 , pp. 1669-1685
    • Mischaikow, K.1    Smith, H.L.2    Thieme, H.R.3
  • 264
    • 0000369563 scopus 로고
    • La technique de culture continue, théorie et applications
    • Monod, J., 1950, La technique de culture continue, théorie et applications, Annales l’Institut Pasteur 79, 390-401.
    • (1950) Annales l’Institut Pasteur , vol.79 , pp. 390-401
    • Monod, J.1
  • 265
    • 84880990802 scopus 로고
    • Compound matrices and ordinary differential equations
    • Muldowney, J. S., 1990, Compound matrices and ordinary differential equations, Rocky Mountain J. Math. 20, 857-872.
    • (1990) Rocky Mountain J. Math , vol.20 , pp. 857-872
    • Muldowney, J.S.1
  • 266
    • 0032153822 scopus 로고    scopus 로고
    • Optimal vaccination patterns in age structured populations
    • Müller, J., 1998, Optimal vaccination patterns in age structured populations, SIAM J. Appl. Math. 59, 222-241.
    • (1998) SIAM J. Appl. Math , vol.59 , pp. 222-241
    • Müller, J.1
  • 269
    • 0342823455 scopus 로고
    • Lecture Notes in Biomathematics, Springer, Berlin
    • Nåsell, I., 1985, Hybrid models of tropical infections, Lecture Notes in Biomathematics, vol. 59, Springer, Berlin.
    • (1985) Hybrid models of tropical infections , vol.59
    • Nåsell, I.1
  • 270
    • 24544434555 scopus 로고    scopus 로고
    • Endemicity, persistence, and quasi-stationarity
    • (ed. C. Castillo-Chavez, with S. Blower, P. van den Driessche, D. Kirschner, A.-A. Yakubu), Springer, NewYork
    • Nåsell, I., 2002, Endemicity, persistence, and quasi-stationarity, Mathematical approaches for emerging and reemerging infectious diseases: models, an introduction (ed. C. Castillo-Chavez, with S. Blower, P. van den Driessche, D. Kirschner, A.-A. Yakubu), Springer, NewYork.
    • (2002) Mathematical approaches for emerging and reemerging infectious diseases: Models, an introduction
    • Nåsell, I.1
  • 272
    • 85194306241 scopus 로고    scopus 로고
    • Remarks on an environmental control problem
    • (ed. M. A. Horn, G. Simonett, G. F.Webb), Vanderbilt University Press, Nashville, TN
    • Navarova, N., and Thieme, H. R., 1998, Remarks on an environmental control problem, Mathematical models in medical and health sciences (ed. M. A. Horn, G. Simonett, G. F.Webb), pp. 267-279, Vanderbilt University Press, Nashville, TN.
    • (1998) Mathematical models in medical and health sciences , pp. 267-279
    • Navarova, N.1    Thieme, H.R.2
  • 273
    • 27144497625 scopus 로고    scopus 로고
    • A nonlinear extension of the Coale-Lopez theorem
    • Nesemann, T., 1999, A nonlinear extension of the Coale-Lopez theorem, Positivity 3, 135-148.
    • (1999) Positivity , vol.3 , pp. 135-148
    • Nesemann, T.1
  • 274
    • 0001992543 scopus 로고    scopus 로고
    • Delay-differential equations for structured populations
    • (ed. S. Tuljapurkar, H. Caswell), Chapman and Hall, NewYork
    • Nisbet, R. M., 1997, Delay-differential equations for structured populations, Structured population models in marine, freshwater, and terrestrial systems (ed. S. Tuljapurkar, H. Caswell), pp. 90-118, Chapman and Hall, NewYork.
    • (1997) Structured population models in marine, freshwater, and terrestrial systems , pp. 90-118
    • Nisbet, R.M.1
  • 277
    • 0000962996 scopus 로고
    • Population dynamic consequences of competition within and between age classes
    • Nisbet, R. M., and Onyiah, L. C., 1994, Population dynamic consequences of competition within and between age classes, J. Math. Biol. 32, 329-344.
    • (1994) J. Math. Biol , vol.32 , pp. 329-344
    • Nisbet, R.M.1    Onyiah, L.C.2
  • 278
    • 84960555068 scopus 로고
    • Natural selection and Mendelian variation
    • Norton, H. T. J., 1928, Natural selection and Mendelian variation, Proc. Lond. Math. Soc. 28, 1-45.
    • (1928) Proc. Lond. Math. Soc , vol.28 , pp. 1-45
    • Norton, H.T.J.1
  • 280
    • 0000036624 scopus 로고
    • Some nonlinear weak ergodic theorems
    • Nussbaum, R. D., 1990, Some nonlinear weak ergodic theorems, SIAM J. Math. Analysis 21, 436-460.
    • (1990) SIAM J. Math. Analysis , vol.21 , pp. 436-460
    • Nussbaum, R.D.1
  • 281
    • 0024029039 scopus 로고
    • Oscillations and chaos in epidemics:A nonlinear dynamic study of six childhood diseases in Copenhagen, Denmark
    • Olsen, L. F., Truty, G. L., and Schaffer, W. M., 1988, Oscillations and chaos in epidemics:a nonlinear dynamic study of six childhood diseases in Copenhagen, Denmark, Theor. Pop. Biol. 33, 344-370.
    • (1988) Theor. Pop. Biol , vol.33 , pp. 344-370
    • Olsen, L.F.1    Truty, G.L.2    Schaffer, W.M.3
  • 284
    • 0028254942 scopus 로고
    • Kin recognition and cannibalism in polyphenic salamanders
    • Pfennig, D.W., Sherman, P.W., and Collins, J. P., 1994, Kin recognition and cannibalism in polyphenic salamanders, Behav. Ecol. 5, 225-232.
    • (1994) Behav. Ecol , vol.5 , pp. 225-232
    • Pfennig, D.W.1    Sherman, P.W.2    Collins, J.P.3
  • 286
    • 0000994468 scopus 로고
    • The evolution and dynamics of intraspecific predation
    • Polis, G. A., 1981, The evolution and dynamics of intraspecific predation, A. Rev. Ecol. Syst. 12, 225-251.
    • (1981) A. Rev. Ecol. Syst , vol.12 , pp. 225-251
    • Polis, G.A.1
  • 288
  • 289
    • 0025031240 scopus 로고
    • Population models for diseases with no recovery
    • Pugliese, A., 1990, Population models for diseases with no recovery, J. Math. Biol. 28, 65-82.
    • (1990) J. Math. Biol , vol.28 , pp. 65-82
    • Pugliese, A.1
  • 291
    • 0016033048 scopus 로고
    • An interpretation of the modern rise of populations in Europe-a critique
    • Razzell, P. E., 1974, An interpretation of the modern rise of populations in Europe-a critique, Pop. Studies 28, 5-17.
    • (1974) Pop. Studies , vol.28 , pp. 5-17
    • Razzell, P.E.1
  • 293
    • 0000001728 scopus 로고
    • Computation and interpretation of biological studies of fish populations
    • Ricker, W. E., 1975, Computation and interpretation of biological studies of fish populations, Bull. Fish. Res. Bd. Canada 191.
    • (1975) Bull. Fish. Res. Bd. Canada , pp. 191
    • Ricker, W.E.1
  • 297
    • 0033587464 scopus 로고    scopus 로고
    • Persistence and extinction in two species reactiondiffusion systems with delays
    • Ruan, S., and Zhao, X.-Q., 1999, Persistence and extinction in two species reactiondiffusion systems with delays, J. Diff. Eqns 156, 71-92.
    • (1999) J. Diff. Eqns , vol.156 , pp. 71-92
    • Ruan, S.1    Zhao, X.-Q.2
  • 298
    • 0001183798 scopus 로고
    • The distribution of incubation periods of infectious diseases
    • Sartwell, P. E., 1950, The distribution of incubation periods of infectious diseases, Am. J. Hyg. 51, 310-318.
    • (1950) Am. J. Hyg , vol.51 , pp. 310-318
    • Sartwell, P.E.1
  • 299
    • 0013886534 scopus 로고
    • The incubation period and the dynamics of infectious disease
    • Sartwell, P. E., 1966, The incubation period and the dynamics of infectious disease, Am. J. Epid. 83, 204-318.
    • (1966) Am. J. Epid , vol.83 , pp. 204-318
    • Sartwell, P.E.1
  • 301
    • 77957177075 scopus 로고
    • Can nonlinear dynamics help us infer mechanisms in ecology and epidemiology?
    • Schaffer, W. M., 1985, Can nonlinear dynamics help us infer 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
  • 302
    • 0021912738 scopus 로고
    • Nearly one dimensional dynamics in an epidemic
    • Schaffer, W. M., and Kot, M., 1985, Nearly one dimensional dynamics in an epidemic, J. Theor. Biol. 112, 403-427.
    • (1985) J. Theor. Biol , vol.112 , pp. 403-427
    • Schaffer, W.M.1    Kot, M.2
  • 303
    • 77957185501 scopus 로고
    • An age-structured model of pre-and postvaccination measles transmission
    • Schenzle, D., 1984, An age-structured model of pre-and postvaccination measles transmission, IMA J. Math. Appl. Med. Biol. 1, 169-191.
    • (1984) IMA J. Math. Appl. Med. Biol , vol.1 , pp. 169-191
    • Schenzle, D.1
  • 304
    • 0021051389 scopus 로고
    • Infinite subharmonic bifurcations in an SEIR epidemic model
    • Schwartz, I. B., and Smith, H. L., 1983, Infinite subharmonic bifurcations 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
  • 308
    • 0002072428 scopus 로고
    • Coexistence of cycles of a continuous map of a line into itself
    • Sharkovskii, A. N., 1964, Coexistence of cycles of a continuous map of a line into itself, Ukrainian Math. J. 16, 61-71.
    • (1964) Ukrainian Math. J , vol.16 , pp. 61-71
    • Sharkovskii, A.N.1
  • 309
    • 0000577267 scopus 로고
    • A problem in age-distribution
    • Sharpe, F. R., and Lotka, A. J., 1911, A problem in age-distribution, Phil. Mag. (6) 21, 435-438.
    • (1911) Phil. Mag , vol.21 , Issue.6 , pp. 435-438
    • Sharpe, F.R.1    Lotka, A.J.2
  • 310
    • 0004288501 scopus 로고
    • Oxford University Press (hard cover), Penguin (paperback)
    • Sigmund, K., 1993, Games of life, Oxford University Press (hard cover), Penguin (paperback).
    • (1993) Games of life
    • Sigmund, K.1
  • 311
    • 0026846319 scopus 로고
    • Reproduction numbers and the stability of equilibria of SI models for heterogeneous populations
    • Simon, C. P., and Jacquez, J. A., 1992, Reproduction numbers and the stability of equilibria of SI models for heterogeneous populations, SIAM J. Appl. Math. 22, 541-576.
    • (1992) SIAM J. Appl. Math , vol.22 , pp. 541-576
    • Simon, C.P.1    Jacquez, J.A.2
  • 314
    • 0000228519 scopus 로고
    • Population dynamics in Daphnia magna and a new model for population growth
    • Smith, F. E., 1963, Population dynamics in Daphnia magna and a new model for population growth, Ecology 44, 651-663.
    • (1963) Ecology , vol.44 , pp. 651-663
    • Smith, F.E.1
  • 315
    • 0020963836 scopus 로고
    • Subharmonic bifurcation in an SIR epidemic model
    • Smith, H. L., 1983a, Subharmonic bifurcation in an SIR epidemic model, J. Math. Biol. 17, 163-177.
    • (1983) J. Math. Biol , vol.17 , pp. 163-177
    • Smith, H.L.1
  • 316
    • 0020956406 scopus 로고
    • Multiple stable subharmonics for a periodic epidemic model
    • Smith, H. L., 1983b, 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
  • 319
    • 0019382844 scopus 로고
    • Stability in a class of cyclic epidemic models with delay
    • Stech, H. W., and Williams, M., 1981, Stability in a class of cyclic epidemic models with delay, J. Math. Biol. 11, 95-103.
    • (1981) J. Math. Biol , vol.11 , pp. 95-103
    • Stech, H.W.1    Williams, M.2
  • 320
    • 31344474159 scopus 로고
    • Attack rate and incubation period of measles
    • Stillerman, M., and Thalhimer, W., 1944, Attack rate and incubation period of measles, Am. J. Dis. Child. 67, 15.
    • (1944) Am. J. Dis. Child , vol.67 , pp. 15
    • Stillerman, M.1    Thalhimer, W.2
  • 321
    • 0030174748 scopus 로고    scopus 로고
    • Convergence in the part metric for discrete dynamical systems in ordered topological cones
    • Takáč, P., 1996, Convergence in the part metric for discrete dynamical systems in ordered topological cones, Nonlinear Analysis TMA 26, 1753-1777.
    • (1996) Nonlinear Analysis TMA , vol.26 , pp. 1753-1777
    • Takáč, P.1
  • 324
    • 0029690373 scopus 로고    scopus 로고
    • Permanence in Kolmogorov-type systems of nonautonomous functional differential equations
    • Tang, B., and Kuang, Y., 1996, Permanence in Kolmogorov-type systems of nonautonomous functional differential equations, JMAA 197, 427-447.
    • (1996) JMAA , vol.197 , pp. 427-447
    • Tang, B.1    Kuang, Y.2
  • 325
    • 0031091133 scopus 로고    scopus 로고
    • Population dynamics and competition in chemostat models with adaptive nutrient uptake
    • Tang, B., Sitomer, A., and Jackson, T., 1997, Population dynamics and competition in chemostat models with adaptive nutrient uptake, J. Math. Biol. 35, 453-479.
    • (1997) J. Math. Biol , vol.35 , pp. 453-479
    • Tang, B.1    Sitomer, A.2    Jackson, T.3
  • 326
    • 0344419318 scopus 로고
    • Local stability in epidemic models for heterogeneous populations
    • (ed.V. Capasso, E. Grosso, S. L. Paveri-Fontana), Lecture Notes in Biomathematics, Springer, Berlin
    • Thieme, H. R., 1983, Local stability in epidemic models for heterogeneous populations, Mathematics in biology and medicine (ed.V. Capasso, E. Grosso, S. L. Paveri-Fontana), pp. 185-189, Lecture Notes in Biomathematics, vol. 57, Springer, Berlin.
    • (1983) Mathematics in biology and medicine , vol.57 , pp. 185-189
    • Thieme, H.R.1
  • 327
    • 0343579606 scopus 로고
    • Renewal theorems for some mathematical models in epidemiology
    • Thieme, H. R., 1985, Renewal theorems for some mathematical models in epidemiology, J. Integ. Eqns 8, 185-216.
    • (1985) J. Integ. Eqns , vol.8 , pp. 185-216
    • Thieme, H.R.1
  • 328
    • 0013081169 scopus 로고
    • Asymptotic proportionality (weak ergodicity) and conditional asymptotic equality of solutions to time-heterogeneous sublinear difference and differential equations
    • Thieme, H. R., 1988a, Asymptotic proportionality (weak ergodicity) and conditional asymptotic equality of solutions to time-heterogeneous sublinear difference and differential equations, J. Diff. Eqns 73, 237-268.
    • (1988) J. Diff. Eqns , vol.73 , pp. 237-268
    • Thieme, H.R.1
  • 329
    • 0000340781 scopus 로고
    • Well-posedness of physiologically structured population models for Daphnia magna
    • Thieme, H. R., 1988b, Well-posedness of physiologically structured population models for Daphnia magna, J. Math. Biol. 26, 299-317.
    • (1988) J. Math. Biol , vol.26 , pp. 299-317
    • Thieme, H.R.1
  • 330
    • 0001511664 scopus 로고
    • Stability change of the endemic equilibrium in age-structured models for the spread of S-I-R type infectious diseases
    • (ed. S. Busenberg, M. Martelli), Lecture Notes in Biomathematics, Springer, Berlin
    • Thieme, H. R., 1991, Stability change of the endemic equilibrium in age-structured models for the spread of S-I-R type infectious diseases, Differential equations models in biology, epidemiology and ecology (ed. S. Busenberg, M. Martelli), pp. 139-158, Lecture Notes in Biomathematics, vol. 92, Springer, Berlin.
    • (1991) Differential equations models in biology, epidemiology and ecology , vol.92 , pp. 139-158
    • Thieme, H.R.1
  • 331
    • 77952672921 scopus 로고
    • Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations
    • Thieme, H. R., 1992, Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations, J. Math. Biol. 30, 755-763.
    • (1992) J. Math. Biol , vol.30 , pp. 755-763
    • Thieme, H.R.1
  • 332
    • 0039591930 scopus 로고
    • Persistence under relaxed point-dissipativity (with applications to an epidemic model)
    • Thieme, H. R., 1993, Persistence under relaxed point-dissipativity (with applications to an epidemic model), SIAM J. Math. Analysis 24, 407-435.
    • (1993) SIAM J. Math. Analysis , vol.24 , pp. 407-435
    • Thieme, H.R.1
  • 333
    • 84881166951 scopus 로고
    • Asymptotically autonomous differential equations in the plane
    • Thieme, H. R., 1994a, Asymptotically autonomous differential equations in the plane, Rocky Mountain J. Math. 24, 351-380.
    • (1994) Rocky Mountain J. Math , vol.24 , pp. 351-380
    • Thieme, H.R.1
  • 334
    • 33746945861 scopus 로고
    • Asymptotically autonomous differential equations in the plane, II, Stricter Poincaré-Bendixson type results
    • Thieme, H. R., 1994b, Asymptotically autonomous differential equations in the plane, II, Stricter Poincaré-Bendixson type results, Diff. Integral Eqns 7, 1625-1640.
    • (1994) Diff. Integral Eqns , vol.7 , pp. 1625-1640
    • Thieme, H.R.1
  • 335
    • 0004460872 scopus 로고    scopus 로고
    • Positive perturbations of dual and integrated semigroups
    • Thieme, H. R., 1996, Positive perturbations of dual and integrated semigroups, Adv. Math. Sci. Appl. 6, 445-507.
    • (1996) Adv. Math. Sci. Appl , vol.6 , pp. 445-507
    • Thieme, H.R.1
  • 336
    • 0032365243 scopus 로고    scopus 로고
    • Positive perturbation of operator semigroups: Growth bounds, essential compactness, and asynchronous exponential growth
    • Thieme, H. R., 1998, Positive perturbation of operator semigroups: growth bounds, essential compactness, and asynchronous exponential growth, Discr. Cont. Dyn. Syst. 4, 735-764.
    • (1998) Discr. Cont. Dyn. Syst , vol.4 , pp. 735-764
    • Thieme, H.R.1
  • 337
    • 0033841964 scopus 로고    scopus 로고
    • Uniform persistence and permanence for non-autonomous semiflows in population biology
    • Thieme, H. R., 2000, Uniform persistence and permanence for non-autonomous semiflows in population biology, Math. Biosci. 166, 173-201.
    • (2000) Math. Biosci , vol.166 , pp. 173-201
    • Thieme, H.R.1
  • 338
    • 0011356168 scopus 로고    scopus 로고
    • The transition through stages with arbitrary length distributions, and applications in epidemics
    • (ed. C. Castillo-Chavez, S. Blower, P. van den Driessche, D. Kirschner, A.-A.Yakubu), Springer, NewYork
    • Thieme, H. R., 2002, The transition through stages with arbitrary length distributions, and applications in epidemics, Mathematical approaches for emerging and reemerging infectious diseases: models, methods and theory (ed. C. Castillo-Chavez, S. Blower, P. van den Driessche, D. Kirschner, A.-A.Yakubu), pp. 45-84, Springer, NewYork.
    • (2002) Mathematical approaches for emerging and reemerging infectious diseases: Models, methods and theory , pp. 45-84
    • Thieme, H.R.1
  • 339
    • 44549085866 scopus 로고    scopus 로고
    • A Stieltjes type convolution for integrated semigroups of strong bounded variation and Lp solutions to the abstract Cauchy problem
    • Thieme, H. R., and Voßeler, H., 2002, A Stieltjes type convolution for integrated semigroups of strong bounded variation and Lp solutions to the abstract Cauchy problem, J. Diff. Integ. Eqns 15, 1171-1218.
    • (2002) J. Diff. Integ. Eqns , vol.15 , pp. 1171-1218
    • Thieme, H.R.1    Voßeler, H.2
  • 340
    • 3142756609 scopus 로고    scopus 로고
    • On the complex formation approach in modeling predator prey relations, mating and sexual disease transmission, Proceedings of Nonlinear Differential Equations, University of Miami
    • ed. R. S. Cantrell, C. Cosner
    • Thieme, H. R., and Yang, J., 2000, On the complex formation approach in modeling predator prey relations, mating and sexual disease transmission, Proceedings of Nonlinear Differential Equations, University of Miami (ed. R. S. Cantrell, C. Cosner), Electron. J. Diff. Eqns Conf. 05, 255-283.
    • (2000) Electron. J. Diff. Eqns Conf , vol.5 , pp. 255-283
    • Thieme, H.R.1    Yang, J.2
  • 341
    • 0029911718 scopus 로고    scopus 로고
    • A control problem in a polluted environment
    • Thomas, D. M., Snell, T. W., and Jaffar, S. M., 1996, A control problem in a polluted environment, Math. Biosci. 133, 139-163.
    • (1996) Math. Biosci , vol.133 , pp. 139-163
    • Thomas, D.M.1    Snell, T.W.2    Jaffar, S.M.3
  • 345
    • 77957179365 scopus 로고
    • Interactions between egg-eating predator and prey: The effect of the functional response and of age structure
    • van den Bosch, F., and Diekmann, O., 1986, Interactions between egg-eating predator and prey: the effect of the functional response and of age structure, IMA J. Math. Appl. Med. Biol. 3, 53-69.
    • (1986) IMA J. Math. Appl. Med. Biol , vol.3 , pp. 53-69
    • van den Bosch, F.1    Diekmann, O.2
  • 346
    • 0036845274 scopus 로고    scopus 로고
    • Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
    • van den Driessche, P., and Watmough, J., 2002, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180, 29-48.
    • (2002) Math. Biosci , vol.180 , pp. 29-48
    • van den Driessche, P.1    Watmough, J.2
  • 348
    • 34347158770 scopus 로고
    • Untersuchungen über die Gesetzlichkeit desWachstums, Teil I, Allgemeine Grundlagen der Theorie: Mathematische und physiologische Gesetzlichkeiten desWachstums beiWassertieren
    • von Bertalanffy, L., 1934, Untersuchungen über die Gesetzlichkeit desWachstums, Teil I, Allgemeine Grundlagen der Theorie: mathematische und physiologische Gesetzlichkeiten desWachstums beiWassertieren, Arch. Entwicklungsmech. Org. 131, 613-652.
    • (1934) Arch. Entwicklungsmech. Org , vol.131 , pp. 613-652
    • von Bertalanffy, L.1
  • 349
    • 0002701187 scopus 로고
    • Some remarks on changing populations
    • (ed. F. Stohlman), Grune and Strutton, NewYork
    • VonFoerster, H., 1959, Some remarks on changing populations, The kinetics of cellular proliferation (ed. F. Stohlman), Grune and Strutton, NewYork.
    • (1959) The kinetics of cellular proliferation
    • VonFoerster, H.1
  • 351
    • 0002231761 scopus 로고
    • Abrief survey of persistence in dynamical systems
    • (ed. S. Busenberg, M. Martelli), Lecture Notes in Mathematics, Springer
    • Waltman, P., 1991, Abrief survey of persistence in dynamical systems, Delay differential equations and dynamical systems (ed. S. Busenberg, M. Martelli), pp. 31-40, Lecture Notes in Mathematics, vol. 1475, Springer.
    • (1991) Delay differential equations and dynamical systems , vol.1475 , pp. 31-40
    • Waltman, P.1
  • 352
    • 0001920546 scopus 로고
    • Asemigroup proof of the Sharpe-Lotka theorem
    • (ed. F. Kappel, W. Schappacher), Lecture Notes in Mathematics, Springer, Berlin
    • Webb, G. F., 1984, Asemigroup proof of the Sharpe-Lotka theorem, Infinite dimensional systems (ed. F. Kappel, W. Schappacher), pp. 254-268, Lecture Notes in Mathematics, vol. 1076, Springer, Berlin.
    • (1984) Infinite dimensional systems , vol.1076 , pp. 254-268
    • Webb, G.F.1
  • 356
    • 0242449336 scopus 로고
    • Ecological aspects of amphibian metamorphosis
    • Wilbur, H. M., and Collins, J. P., 1973, Ecological aspects of amphibian metamorphosis, Science 182, 1305-1314.
    • (1973) Science , vol.182 , pp. 1305-1314
    • Wilbur, H.M.1    Collins, J.P.2
  • 358
    • 0034693545 scopus 로고    scopus 로고
    • Homoclinic bifurcation in an SIQR model for childhood diseases
    • Wu, L.-I., and Feng, Z., 2000, Homoclinic bifurcation in an SIQR model for childhood diseases, J. Diff. Eqns 168, 150-167.
    • (2000) J. Diff. Eqns , vol.168 , pp. 150-167
    • Wu, L.-I.1    Feng, Z.2
  • 361
    • 0000313693 scopus 로고
    • Uniform persistence and periodic coexistence states in infinitedimensional periodic semiflows with applications
    • Zhao, X.-Q., 1995, Uniform persistence and periodic coexistence states in infinitedimensional periodic semiflows with applications, Canad. Appl. Math. Quart. 3, 473-495.
    • (1995) Canad. Appl. Math. Quart , vol.3 , pp. 473-495
    • Zhao, X.-Q.1
  • 362
    • 0013126266 scopus 로고    scopus 로고
    • Uniform persistence in processes with application to nonautonomous competitive models
    • Zhao, X.-Q., 2001, Uniform persistence in processes with application to nonautonomous competitive models, J. Math. Analysis Appl. 258, 87-101.
    • (2001) J. Math. Analysis Appl , vol.258 , pp. 87-101
    • Zhao, X.-Q.1
  • 364
    • 0000888730 scopus 로고
    • Stable periodic orbits for a class of three dimensional competitive systems
    • Zhu, Hsiu-Rong, and Smith, H. L., 1994, Stable periodic orbits for a class of three dimensional competitive systems, J. Diff. Eqns 110, 143-156
    • (1994) J. Diff. Eqns , vol.110 , pp. 143-156
    • Zhu, H.-R.1    Smith, H.L.2


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