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Volumn 19, Issue 4, 2014, Pages 1155-1170

Persistence in some periodic epidemic models with infection age or constant periods of infection

Author keywords

Delay differential equation; Epidemiological models; Persistence; Seasonality

Indexed keywords


EID: 84902189465     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2014.19.1155     Document Type: Article
Times cited : (14)

References (28)
  • 1
    • 0003921124 scopus 로고    scopus 로고
    • Mathematical Modelling: Theory and Applications, Kluwer Academic Publishers, Dordrecht
    • S. Anita, Analysis and Control of Age-Dependent Population Dynamics, Mathematical Modelling: Theory and Applications, 11, Kluwer Academic Publishers, Dordrecht, 2000.
    • (2000) Analysis and Control of Age-Dependent Population Dynamics , vol.11
    • Anita, S.1
  • 2
    • 33947541669 scopus 로고    scopus 로고
    • 0 for vector-borne diseases with a periodic vector population
    • DOI 10.1007/s11538-006-9166-9
    • N. Bacäer, Approximation of the basic reproduction number R0 for vector-borne diseases with a periodic vector population, Bull. Math. Biol., 69 (2007), 1067-1091. (Pubitemid 46466311)
    • (2007) Bulletin of Mathematical Biology , vol.69 , Issue.3 , pp. 1067-1091
    • Bacaer, N.1
  • 3
    • 79953038195 scopus 로고    scopus 로고
    • Genealogy with seasonality, the basic reproduction number, and the influenza pandemic
    • N. Bacäer and E. Ait Dads, Genealogy with seasonality, the basic reproduction number, and the influenza pandemic, J. Math. Biol., 62 (2011), 741-762.
    • (2011) J. Math. Biol , vol.62 , pp. 741-762
    • Bacäer, N.1    Ait Dads, E.2
  • 4
    • 33748152440 scopus 로고    scopus 로고
    • The epidemic threshold of vector-borne diseases with seasonality
    • N. Bacäer and S. Guernaoui, The epidemic threshold of vector-borne diseases with seasonality, J. Math. Biol., 53 (2006), 421-436.
    • (2006) J. Math. Biol , vol.53 , pp. 421-436
    • Bacäer, N.1    Guernaoui, S.2
  • 5
    • 36148974693 scopus 로고    scopus 로고
    • Growth rate and basic reproduction number for population models with a simple periodic factor
    • DOI 10.1016/j.mbs.2007.07.005, PII S0025556407001526
    • N. Bacäer and R. Ouifki, Growth rate and basic reproduction number for population models with a simple periodic factor, Math. Biosci., 210 (2007), 647-658. (Pubitemid 350116910)
    • (2007) Mathematical Biosciences , vol.210 , Issue.2 , pp. 647-658
    • Bacaer, N.1    Ouifki, R.2
  • 6
    • 0027678367 scopus 로고
    • How may infection-age dependent infectivity affect the dynamics of hiv/aids?
    • H. R. Thieme and C. Castillo-Chavez, How may infection-age dependent infectivity affect the dynamics of HIV/AIDS?, SIAM J. Appl. Math., 53 (1993), 1447-1479.
    • (1993) SIAM J. Appl. Math , vol.53 , pp. 1447-1479
    • Thieme, H.R.1    Castillo-Chavez, C.2
  • 7
    • 0017104702 scopus 로고
    • A periodicity threshold theorem for epidemics and population growth
    • K. Cooke and J. L. Kaplan, A periodicity threshold theorem for epidemics and population growth, Math. Biosci., 31 (1976), 87-104.
    • (1976) Math. Biosci , vol.31 , pp. 87-104
    • Cooke, K.1    Kaplan, J.L.2
  • 8
    • 34548815639 scopus 로고    scopus 로고
    • An overview of semi-continuity results on the spectral radius and positivity
    • G. Degla, An overview of semi-continuity results on the spectral radius and positivity, J. Math. Anal. Appl., 338 (2008), 101-110.
    • (2008) J. Math. Anal. Appl , vol.338 , pp. 101-110
    • Degla, G.1
  • 9
    • 84986244874 scopus 로고    scopus 로고
    • Bounds for the spectral radius of positive operators
    • R. Drnovšek, Bounds for the spectral radius of positive operators, Comment. Math. Univ. Carolinae, 41 (2000), 459-467.
    • (2000) Comment. Math. Univ. Carolinae , vol.41 , pp. 459-467
    • Drnovšek, R.1
  • 10
    • 84968495017 scopus 로고
    • Uniformly persistent semidynamical systems
    • A. Fonda, Uniformly persistent semidynamical systems, Proc. Amer. Math. Soc., 104 (1988), 111-116.
    • (1988) Proc. Amer. Math. Soc , vol.104 , pp. 111-116
    • Fonda, A.1
  • 11
    • 33749332732 scopus 로고    scopus 로고
    • Dissipation and compact attractors
    • DOI 10.1007/s10884-006-9021-6
    • J. Hale, Dissipation and compact attractors, J. Dynam. Differ. Equat., 18 (2006), 485-523. (Pubitemid 44494955)
    • (2006) Journal of Dynamics and Differential Equations , vol.18 , Issue.3 , pp. 485-523
    • Hale, J.K.1
  • 13
    • 0001862504 scopus 로고
    • A unified approach to persistence
    • J. Hofbauer, A unified approach to persistence, Acta Applicandae Math., 14 (1989), 11-22.
    • (1989) Acta Applicandae Math , vol.14 , pp. 11-22
    • Hofbauer, J.1
  • 14
    • 84966222841 scopus 로고
    • Uniform persistence and repellors for maps
    • J. Hofbauer and J. W. H. So, Uniform persistence and repellors for maps, Proc. Amer. Math. Soc., 107 (1989), 1137-1142.
    • (1989) Proc. Amer. Math. Soc , vol.107 , pp. 1137-1142
    • Hofbauer, J.1    So, J.W.H.2
  • 16
    • 24944547503 scopus 로고    scopus 로고
    • Compact attractors for time-periodic age-structured population models
    • P. Magal, Compact attractors for time-periodic age-structured population models, Electron. J. Differ. Equat., 65 (2001), 1-35.
    • (2001) Electron. J. Differ. Equat , vol.65 , pp. 1-35
    • Magal, P.1
  • 17
    • 77953948341 scopus 로고    scopus 로고
    • Lyapunov functional and global asymptotic stability for an infectious-age model
    • P. Magal, C. C. McCluskey and G. F. Webb, Lyapunov functional and global asymptotic stability for an infectious-age model, Applic. Anal., 89 (2010), 1109-1140.
    • (2010) Applic. Anal , vol.89 , pp. 1109-1140
    • Magal, P.1    McCluskey, C.C.2    Webb, G.F.3
  • 19
    • 0000954935 scopus 로고
    • A periodicity threshold theorem for some nonlinear integral equations
    • R. D. Nussbaum, A periodicity threshold theorem for some nonlinear integral equations, SIAM J. Math. Anal., 9 (1978), 356-376.
    • (1978) SIAM J. Math. Anal , vol.9 , pp. 356-376
    • Nussbaum, R.D.1
  • 20
    • 84859635780 scopus 로고    scopus 로고
    • Persistence in seasonally forced epidemiological models
    • C. Rebelo, A. Margheri and N. Bacäer, Persistence in seasonally forced epidemiological models, J. Math. Biol., 64 (2012), 933-949.
    • (2012) J. Math. Biol , vol.64 , pp. 933-949
    • Rebelo, C.1    Margheri, A.2    Bacäer, N.3
  • 21
    • 0017328061 scopus 로고
    • On periodic solutions of a delay integral equation modelling epidemics
    • H. L. Smith, On periodic solutions of a delay integral equation modelling epidemics, J. Math. Biol., 4 (1977), 69-80. (Pubitemid 8045498)
    • (1977) Journal of Mathematical Biology , vol.4 , Issue.1 , pp. 69-80
    • Smith, H.L.1
  • 24
    • 67649378819 scopus 로고    scopus 로고
    • Spectral bound and reproduction number for infinite-dimensional population structure and time heterogeneity
    • H. R. Thieme, Spectral bound and reproduction number for infinite-dimensional population structure and time heterogeneity, SIAM J. Appl. Math., 70 (2009), 188-211.
    • (2009) SIAM J. Appl. Math , vol.70 , pp. 188-211
    • Thieme, H.R.1
  • 25
    • 0021523081 scopus 로고
    • Renewal theorems for linear periodic volterra integral equations
    • H. R. Thieme, Renewal theorems for linear periodic Volterra integral equations, J. Integral Equat., 7 (1984), 253-277.
    • (1984) J. Integral Equat , vol.7 , pp. 253-277
    • Thieme, H.R.1
  • 28
    • 33750325602 scopus 로고    scopus 로고
    • A periodic epidemic model in a patchy environment
    • DOI 10.1016/j.jmaa.2006.01.085, PII S0022247X06000989
    • F. Zhang and X. Q. Zhao, A periodic epidemic model in a patchy environment, J. Math. Anal. Appl., 325 (2007), 496-516. (Pubitemid 44615349)
    • (2007) Journal of Mathematical Analysis and Applications , vol.325 , Issue.1 , pp. 496-516
    • Zhang, F.1    Zhao, X.-Q.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.