메뉴 건너뛰기




Volumn 210, Issue 2, 2007, Pages 647-658

Growth rate and basic reproduction number for population models with a simple periodic factor

Author keywords

Continued fractions; Epidemic threshold; Periodic contact rate

Indexed keywords

MATHEMATICAL MODELS; PARAMETER ESTIMATION; POPULATION DYNAMICS;

EID: 36148974693     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2007.07.005     Document Type: Article
Times cited : (81)

References (24)
  • 2
    • 77956980711 scopus 로고
    • On the use of matrices in certain population mathematics
    • Leslie P.H. On the use of matrices in certain population mathematics. Biometrika 33 (1945) 213
    • (1945) Biometrika , vol.33 , pp. 213
    • Leslie, P.H.1
  • 3
    • 36149000662 scopus 로고    scopus 로고
    • L. Euler, Recherches générales sur la mortalité et la multiplication du genre humain, Histoire de l'Académie royale des sciences et belles-lettres de Berlin (1767, année 1760) pp. 144-164. http://bibliothek.bbaw.de.
  • 5
    • 0021523081 scopus 로고
    • Renewal theorems for linear periodic Volterra integral equations
    • Thieme H.R. Renewal theorems for linear periodic Volterra integral equations. J. Integr. Equ. 7 (1984) 253
    • (1984) J. Integr. Equ. , vol.7 , pp. 253
    • Thieme, H.R.1
  • 6
    • 0040825727 scopus 로고
    • Branching processes in periodically varying environment
    • Jagers P., and Nerman O. Branching processes in periodically varying environment. Ann. Prob. 13 (1985) 254
    • (1985) Ann. Prob. , vol.13 , pp. 254
    • Jagers, P.1    Nerman, O.2
  • 7
    • 33748152440 scopus 로고    scopus 로고
    • The epidemic threshold of vector-borne diseases with seasonality
    • Bacaër N., and Guernaoui S. The epidemic threshold of vector-borne diseases with seasonality. J. Math. Biol. 53 (2006) 421
    • (2006) J. Math. Biol. , vol.53 , pp. 421
    • Bacaër, N.1    Guernaoui, S.2
  • 8
    • 33947541669 scopus 로고    scopus 로고
    • 0 for vector-borne diseases with a periodic vector population
    • 0 for vector-borne diseases with a periodic vector population. Bull. Math. Biol. 69 (2007) 1067
    • (2007) Bull. Math. Biol. , vol.69 , pp. 1067
    • Bacaër, N.1
  • 10
    • 0345848728 scopus 로고    scopus 로고
    • On the eigenvalue spectrum for time-delayed Floquet problems
    • Just W. On the eigenvalue spectrum for time-delayed Floquet problems. Physica D 142 (2000) 153
    • (2000) Physica D , vol.142 , pp. 153
    • Just, W.1
  • 11
    • 0030825041 scopus 로고    scopus 로고
    • Infectious disease persistence when transmission varies seasonally
    • Williams B.G., and Dye C. Infectious disease persistence when transmission varies seasonally. Math. Biosci. 145 (1997) 77
    • (1997) Math. Biosci. , vol.145 , pp. 77
    • Williams, B.G.1    Dye, C.2
  • 12
    • 0021051389 scopus 로고
    • Infinite subharmonic bifurcation in an SEIR epidemic model
    • Schwartz I.B., and Smith H.L. Infinite subharmonic bifurcation in an SEIR epidemic model. J. Math. Biol. 18 (1983) 233
    • (1983) J. Math. Biol. , vol.18 , pp. 233
    • Schwartz, I.B.1    Smith, H.L.2
  • 13
    • 0021690803 scopus 로고
    • Seasonality and period-doubling bifurcations in an epidemic model
    • Aron J.L., and Schwartz I.B. Seasonality and period-doubling bifurcations in an epidemic model. J. Theor. Biol. 110 (1984) 665
    • (1984) J. Theor. Biol. , vol.110 , pp. 665
    • Aron, J.L.1    Schwartz, I.B.2
  • 14
    • 0027978417 scopus 로고
    • Bifurcation analysis of periodic SEIR and SIR epidemic models
    • Kuznetsov Yu.A., and Piccardi C. Bifurcation analysis of periodic SEIR and SIR epidemic models. J. Math. Biol. 32 (1994) 109
    • (1994) J. Math. Biol. , vol.32 , pp. 109
    • Kuznetsov, Yu.A.1    Piccardi, C.2
  • 15
    • 33847663496 scopus 로고    scopus 로고
    • Use of a periodic vaccination strategy to control the spread of epidemics with seasonally varying contact rate
    • Moneim I.A., and Greenhalgh D. Use of a periodic vaccination strategy to control the spread of epidemics with seasonally varying contact rate. Math. Biosci. Eng. 2 (2005) 591
    • (2005) Math. Biosci. Eng. , vol.2 , pp. 591
    • Moneim, I.A.1    Greenhalgh, D.2
  • 16
    • 33748131158 scopus 로고    scopus 로고
    • Epidemic threshold conditions for seasonally forced SEIR models
    • Ma J., and Ma Z. Epidemic threshold conditions for seasonally forced SEIR models. Math. Biosci. Eng. 3 (2006) 161
    • (2006) Math. Biosci. Eng. , vol.3 , pp. 161
    • Ma, J.1    Ma, Z.2
  • 17
    • 0034723248 scopus 로고    scopus 로고
    • A simple model for complex dynamical transitions in epidemics
    • Earn D.J.D., Rohani P., Bolker B.M., and Grenfell B.T. A simple model for complex dynamical transitions in epidemics. Science 287 (2000) 667
    • (2000) Science , vol.287 , pp. 667
    • Earn, D.J.D.1    Rohani, P.2    Bolker, B.M.3    Grenfell, B.T.4
  • 18
    • 0034657863 scopus 로고    scopus 로고
    • Estimation of the contact rate in a seasonal SEIR model: application to chickenpox incidence in France
    • Deguen S., Thomas G., and Chau N.P. Estimation of the contact rate in a seasonal SEIR model: application to chickenpox incidence in France. Statist. Med. 19 (2000) 1207
    • (2000) Statist. Med. , vol.19 , pp. 1207
    • Deguen, S.1    Thomas, G.2    Chau, N.P.3
  • 20
    • 33748982385 scopus 로고    scopus 로고
    • Seasonal infectious disease epidemiology
    • Grassly N.C., and Fraser C. Seasonal infectious disease epidemiology. Proc. R. Soc. B 273 (2006) 2541
    • (2006) Proc. R. Soc. , vol.B 273 , pp. 2541
    • Grassly, N.C.1    Fraser, C.2
  • 21
    • 0017104702 scopus 로고
    • A periodicity threshold theorem for epidemics and population growth
    • Cooke K.L., and Kaplan J.L. A periodicity threshold theorem for epidemics and population growth. Math. Biosci. 31 (1976) 87
    • (1976) Math. Biosci. , vol.31 , pp. 87
    • Cooke, K.L.1    Kaplan, J.L.2
  • 22
    • 0017328061 scopus 로고
    • On periodic solutions of a delay integral equation modelling epidemics
    • Smith H.L. On periodic solutions of a delay integral equation modelling epidemics. J. Math. Biol. 4 (1977) 69
    • (1977) J. Math. Biol. , vol.4 , pp. 69
    • Smith, H.L.1
  • 23
    • 0011508129 scopus 로고
    • Periodic solutions of some integral equations from the theory of epidemics
    • Lakshmikantham V. (Ed), Academic Press, New York
    • Nussbaum R.D. Periodic solutions of some integral equations from the theory of epidemics. In: Lakshmikantham V. (Ed). Nonlinear Systems and Applications (1977), Academic Press, New York 235
    • (1977) Nonlinear Systems and Applications , pp. 235
    • Nussbaum, R.D.1
  • 24
    • 0000954935 scopus 로고
    • A periodicity threshold theorem for some nonlinear integral equations
    • Nussbaum R.D. A periodicity threshold theorem for some nonlinear integral equations. SIAM J. Math. Anal. 9 (1978) 356
    • (1978) SIAM J. Math. Anal. , vol.9 , pp. 356
    • Nussbaum, R.D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.