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Volumn 41, Issue 4, 1996, Pages 730-740

On the distribution of the size of an epidemic in a non-Markovian model

Author keywords

Distribution of the size of an epidemic; Limit theorems; Non Markovian models; Order statistics

Indexed keywords


EID: 0039333695     PISSN: 0040585X     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0040585X97975721     Document Type: Article
Times cited : (10)

References (20)
  • 2
    • 0001591406 scopus 로고
    • On the spread of epidemics by carriers
    • G. WEIS, On the spread of epidemics by carriers, Biometrics, 21 (1965), pp. 481-490.
    • (1965) Biometrics , vol.21 , pp. 481-490
    • Weis, G.1
  • 4
    • 0013826540 scopus 로고
    • On the partial differential equation of epidemic theory. I
    • J. GANI, On the partial differential equation of epidemic theory. I. Biornetrika, 52 (1965), pp. 617-622.
    • (1965) Biornetrika , vol.52 , pp. 617-622
    • Gani, J.1
  • 5
    • 0013839597 scopus 로고
    • Solution of the general stochastic epidemic
    • V. SISKIND, Solution of the general stochastic epidemic, Biometrika, 52 (1965), pp. 613-616.
    • (1965) Biometrika , vol.52 , pp. 613-616
    • Siskind, V.1
  • 6
    • 0039421176 scopus 로고
    • First-passage times for the partial sums of a sequence of geometric distributions
    • A. J. WOODS, First-passage times for the partial sums of a sequence of geometric distributions, J. Appl. Probab., 19 (1982), pp. 430-432.
    • (1982) J. Appl. Probab. , vol.19 , pp. 430-432
    • Woods, A.J.1
  • 7
    • 0040013540 scopus 로고
    • On the distribution of the absorption moment for a class of two-dimensional Markov random walks
    • in Russian
    • A. N. STARTSEV, On the distribution of the absorption moment for a class of two-dimensional Markov random walks, Uzbek. Matem. J., 4 (1994), pp. 80-88 (in Russian).
    • (1994) Uzbek. Matem. J. , vol.4 , pp. 80-88
    • Startsev, A.N.1
  • 8
    • 85050710259 scopus 로고
    • Some problems in the statistical analysis of epidemic data
    • N. T. J. BAILEY, Some problems in the statistical analysis of epidemic data, J. Roy. Statist. Soc., Ser. B, 17 (1955), pp. 35-38.
    • (1955) J. Roy. Statist. Soc., Ser. B , vol.17 , pp. 35-38
    • Bailey, N.T.J.1
  • 9
    • 0001236565 scopus 로고
    • The outcome of a stochastic epidemic
    • P. WHITTLE, The outcome of a stochastic epidemic, Biometrika, 42 (1955), pp. 116-122.
    • (1955) Biometrika , vol.42 , pp. 116-122
    • Whittle, P.1
  • 10
    • 0002647627 scopus 로고
    • The asymptotic analysis of a stochastic model of an epidemic
    • A. V. NAGAEV AND A. N. STARTSEV, The asymptotic analysis of a stochastic model of an epidemic, Theory Probab. Appl., XV (1970), pp. 98-107.
    • (1970) Theory Probab. Appl. , vol.15 , pp. 98-107
    • Nagaev, A.V.1    Startsev, A.N.2
  • 11
    • 0002373491 scopus 로고
    • Limit theorems for the epidemic size in a generalized probabilistic model
    • Fan, Tashkent, in Russian
    • A. N. STARTSEV AND Z. S. CHAI, Limit theorems for the epidemic size in a generalized probabilistic model, in Probabilistic Models and Mathematical Statistics, Fan, Tashkent, 1971, pp. 92-105 (in Russian).
    • (1971) Probabilistic Models and Mathematical Statistics , pp. 92-105
    • Startsev, A.N.1    Chai, Z.S.2
  • 12
    • 0007169539 scopus 로고
    • Limit theorems for the epidemic size in a general probabilistic model
    • Fan, Tashkent, in Russian
    • A. N. STARTSEV, Limit theorems for the epidemic size in a general probabilistic model, in Stochastic Processes and Statistical Inferences, Fan, Tashkent, 1971, pp. 60-73 (in Russian).
    • (1971) Stochastic Processes and Statistical Inferences , pp. 60-73
    • Startsev, A.N.1
  • 13
    • 0000045988 scopus 로고
    • On the asymptotic distribution of the size of a stochastic epidemic
    • T. SELLKE, On the asymptotic distribution of the size of a stochastic epidemic, J. Appl. Probab., 20 (1983), pp. 390-394.
    • (1983) J. Appl. Probab. , vol.20 , pp. 390-394
    • Sellke, T.1
  • 14
    • 0000943691 scopus 로고
    • A unified approach to the distribution of total size and total area under the trajectory of infectives in epidemic models
    • F. BALL, A unified approach to the distribution of total size and total area under the trajectory of infectives in epidemic models, Adv. Appl. Probab., 18 (1986), pp. 281-310.
    • (1986) Adv. Appl. Probab. , vol.18 , pp. 281-310
    • Ball, F.1
  • 16
    • 0000005110 scopus 로고
    • Sur la distribution limite du terme maximum d'une série aléatoire
    • B. V. GNEDENKO, Sur la distribution limite du terme maximum d'une série aléatoire, Ann. Math., 44 (1943), pp. 423-453.
    • (1943) Ann. Math. , vol.44 , pp. 423-453
    • Gnedenko, B.V.1
  • 18
    • 65649089673 scopus 로고
    • Some remarks on the limit laws for order statistics
    • N. V. SMIRNOV, Some remarks on the limit laws for order statistics, Theory Probab. Appl., 12 (1967), pp. 391-392.
    • (1967) Theory Probab. Appl. , vol.12 , pp. 391-392
    • Smirnov, N.V.1
  • 20
    • 0010883030 scopus 로고
    • Limit distributions for order statistics. II
    • A. A. BALKEMA AND L. DE HAAN, Limit distributions for order statistics. II, Theory Probab. Appl., 23 (1978), pp. 341-358.
    • (1978) Theory Probab. Appl. , vol.23 , pp. 341-358
    • Balkema, A.A.1    De Haan, L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.