메뉴 건너뛰기




Volumn 243, Issue 1, 2013, Pages 99-108

Relations between deterministic and stochastic thresholds for disease extinction in continuous- and discrete-time infectious disease models

Author keywords

Branching process; Difference equation; Differential equation; Infectious diseases; Markov chain

Indexed keywords

BRANCHING PROCESS; CONTINUOUS-TIME; DETERMINISTIC MODELS; INFECTIOUS DISEASE; INFECTIOUS DISEASE MODELS; WEST NILE VIRUS;

EID: 84875803481     PISSN: 00255564     EISSN: 18793134     Source Type: Journal    
DOI: 10.1016/j.mbs.2013.02.006     Document Type: Article
Times cited : (94)

References (40)
  • 1
    • 84868312013 scopus 로고    scopus 로고
    • Extinction thresholds in deterministic and stochastic epidemic models
    • Allen L.J.S., Lahodny G.E. Extinction thresholds in deterministic and stochastic epidemic models. Journal of Biological Dynamics 2012, 6:590.
    • (2012) Journal of Biological Dynamics , vol.6 , pp. 590
    • Allen, L.J.S.1    Lahodny, G.E.2
  • 4
    • 0020763656 scopus 로고
    • The threshold behaviour of epidemic models
    • Ball F. The threshold behaviour of epidemic models. Journal of Applied Probability 1983, 20:227.
    • (1983) Journal of Applied Probability , vol.20 , pp. 227
    • Ball, F.1
  • 5
    • 0026360189 scopus 로고
    • Dynamic population epidemic models
    • Ball F. Dynamic population epidemic models. Mathematical Biosciences 1983, 107:299.
    • (1983) Mathematical Biosciences , vol.107 , pp. 299
    • Ball, F.1
  • 7
    • 0011485892 scopus 로고
    • The relevance of stochastic models for large-scale epidemiological phenomena
    • Bartlett M.S. The relevance of stochastic models for large-scale epidemiological phenomena. Journal of the Royal Statistical Society Series C 1964, 13:2.
    • (1964) Journal of the Royal Statistical Society Series C , vol.13 , pp. 2
    • Bartlett, M.S.1
  • 8
    • 27944465693 scopus 로고    scopus 로고
    • A stochastic SIS infection model incorporating indirect transmission
    • Clancy D. A stochastic SIS infection model incorporating indirect transmission. Journal of Applied Probability 2005, 42:726.
    • (2005) Journal of Applied Probability , vol.42 , pp. 726
    • Clancy, D.1
  • 10
    • 0028683292 scopus 로고
    • The net reproductive value and stability in matrix population models
    • Cushing J.M., Zhou Y. The net reproductive value and stability in matrix population models. Natural Resource Modeling 1994, 8:297.
    • (1994) Natural Resource Modeling , vol.8 , pp. 297
    • Cushing, J.M.1    Zhou, Y.2
  • 13
    • 34250697942 scopus 로고    scopus 로고
    • Epidemiological models with non-exponentially distributed disease stages and applications to disease control
    • Feng Z., Xu D., Zhao H. Epidemiological models with non-exponentially distributed disease stages and applications to disease control. Bulletin of Mathematical Biology 2007, 69:1511.
    • (2007) Bulletin of Mathematical Biology , vol.69 , pp. 1511
    • Feng, Z.1    Xu, D.2    Zhao, H.3
  • 14
    • 0040972073 scopus 로고
    • A bivariate birth-death process which approximates to the spread of a disease involving a vector
    • Griffiths D.A. A bivariate birth-death process which approximates to the spread of a disease involving a vector. Journal of Applied Probability 1972, 9:65.
    • (1972) Journal of Applied Probability , vol.9 , pp. 65
    • Griffiths, D.A.1
  • 15
    • 0007632955 scopus 로고
    • Multivariate birth-and-death processes as approximations to epidemic processes
    • Griffiths D.A. Multivariate birth-and-death processes as approximations to epidemic processes. Journal of Applied Probability 1973, 10:15.
    • (1973) Journal of Applied Probability , vol.10 , pp. 15
    • Griffiths, D.A.1
  • 16
    • 79954677689 scopus 로고    scopus 로고
    • The probability of extinction in a bovine respiratory syncytial virus epidemic model
    • Griffiths M., Greenhalgh D. The probability of extinction in a bovine respiratory syncytial virus epidemic model. Mathematical Biosciences 2011, 231:144.
    • (2011) Mathematical Biosciences , vol.231 , pp. 144
    • Griffiths, M.1    Greenhalgh, D.2
  • 18
    • 33847405628 scopus 로고    scopus 로고
    • The type-reproduction number T in models for infectious disease control
    • Heesterbeek J.A., Roberts M.G. The type-reproduction number T in models for infectious disease control. Mathematical Biosciences 2007, 206:3.
    • (2007) Mathematical Biosciences , vol.206 , pp. 3
    • Heesterbeek, J.A.1    Roberts, M.G.2
  • 19
    • 84864350554 scopus 로고    scopus 로고
    • On a new perspective of the basic reproduction number in heterogeneous environments
    • Inaba H. On a new perspective of the basic reproduction number in heterogeneous environments. Journal of Mathematical Biology 2012, 65:309.
    • (2012) Journal of Mathematical Biology , vol.65 , pp. 309
    • Inaba, H.1
  • 20
    • 0026360185 scopus 로고
    • Reproduction number and thresholds in stochastic epidemic models I. Homogeneous populations
    • Jacquez J.A., O'Neill P. Reproduction number and thresholds in stochastic epidemic models I. Homogeneous populations. Mathematical Biosciences 1991, 107:161.
    • (1991) Mathematical Biosciences , vol.107 , pp. 161
    • Jacquez, J.A.1    O'Neill, P.2
  • 23
    • 0032518718 scopus 로고    scopus 로고
    • Effect of variability in infection period on the persistence and spatial spread of infectious diseases
    • Keeling M.J., Grenfell B.T. Effect of variability in infection period on the persistence and spatial spread of infectious diseases. Mathematical Biosciences 1998, 147:207.
    • (1998) Mathematical Biosciences , vol.147 , pp. 207
    • Keeling, M.J.1    Grenfell, B.T.2
  • 25
    • 0002232633 scopus 로고
    • Solutions of ordinary differential equations as limits of pure jump Markov processes
    • Kurtz T.G. Solutions of ordinary differential equations as limits of pure jump Markov processes. Journal of Applied Probability 1970, 7:49.
    • (1970) Journal of Applied Probability , vol.7 , pp. 49
    • Kurtz, T.G.1
  • 26
    • 0001249058 scopus 로고
    • Limit theorems for sequences of jump Markov processes approximating ordinary differential processes
    • Kurtz T.G. Limit theorems for sequences of jump Markov processes approximating ordinary differential processes. Journal of Applied Probability 1971, 8:344.
    • (1971) Journal of Applied Probability , vol.8 , pp. 344
    • Kurtz, T.G.1
  • 27
    • 0001455869 scopus 로고
    • The relationship between stochastic and deterministic models for chemical reactions
    • Kurtz T.G. The relationship between stochastic and deterministic models for chemical reactions. Journal of Chemical Physics 1972, 57:2976.
    • (1972) Journal of Chemical Physics , vol.57 , pp. 2976
    • Kurtz, T.G.1
  • 29
    • 0036581212 scopus 로고    scopus 로고
    • Applications of Perron-Frobenius theory to population dynamics
    • Li C.-K., Schneider H. Applications of Perron-Frobenius theory to population dynamics. Journal of Mathematical Biology 2002, 44:450.
    • (2002) Journal of Mathematical Biology , vol.44 , pp. 450
    • Li, C.-K.1    Schneider, H.2
  • 30
    • 0034799244 scopus 로고    scopus 로고
    • Realistic distributions of infectious periods in epidemic models: changing patterns of persistence and dynamics
    • Lloyd A.L. Realistic distributions of infectious periods in epidemic models: changing patterns of persistence and dynamics. Theoretical Population Biology 2001, 60:59.
    • (2001) Theoretical Population Biology , vol.60 , pp. 59
    • Lloyd, A.L.1
  • 32
    • 84857795612 scopus 로고    scopus 로고
    • The basic reproduction number and the probability of extinction for a dynamic epidemic model
    • Neal P. The basic reproduction number and the probability of extinction for a dynamic epidemic model. Mathematical Biosciences 2012, 236:31.
    • (2012) Mathematical Biosciences , vol.236 , pp. 31
    • Neal, P.1
  • 36
    • 0036845274 scopus 로고    scopus 로고
    • Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
    • van den Driessche P., Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences 2002, 180:29.
    • (2002) Mathematical Biosciences , vol.180 , pp. 29
    • van den Driessche, P.1    Watmough, J.2
  • 37
    • 42249085379 scopus 로고    scopus 로고
    • Further notes on the basic reproduction number
    • Springer, Berlin, F. Brauer, P. van den Driessche, J. Wu (Eds.) Mathematical Epidemiology
    • van den Driessche P., Watmough J. Further notes on the basic reproduction number. Lecture Notes in Mathematics 2008, vol. 1945:159-178. Springer, Berlin. F. Brauer, P. van den Driessche, J. Wu (Eds.).
    • (2008) Lecture Notes in Mathematics , vol.1945 , pp. 159-178
    • van den Driessche, P.1    Watmough, J.2
  • 38
    • 77949699515 scopus 로고    scopus 로고
    • Impact of the infection period distribution on the epidemic spread in a metapopulation model
    • Vergu E., Busson H., Ezanno P. Impact of the infection period distribution on the epidemic spread in a metapopulation model. PLoS One 2010, 5:e9371.
    • (2010) PLoS One , vol.5
    • Vergu, E.1    Busson, H.2    Ezanno, P.3
  • 39
    • 0001236565 scopus 로고
    • The outcome of a stochastic epidemic: a note on Bailey's paper
    • Whittle P. The outcome of a stochastic epidemic: a note on Bailey's paper. Biometrika 1955, 42:116.
    • (1955) Biometrika , vol.42 , pp. 116
    • Whittle, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.