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Volumn 8, Issue 4, 1998, Pages 1331-1349

Limit theorems for a random graph epidemic model

Author keywords

Branching process; Degree sequence; Epidemic model; Random graph

Indexed keywords


EID: 0032264732     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1028903384     Document Type: Article
Times cited : (87)

References (23)
  • 1
    • 0031082134 scopus 로고    scopus 로고
    • Epidemics in a population with social structures
    • ANDERSSON, H. (1997). Epidemics in a population with social structures. Math. Biosci. 140 79-84.
    • (1997) Math. Biosci. , vol.140 , pp. 79-84
    • Andersson, H.1
  • 2
    • 0032264092 scopus 로고    scopus 로고
    • Heterogeneity in epidemic models and its effect on the spread of infection
    • To appear
    • ANDERSSON, H. and BRITTON, T. (1998). Heterogeneity in epidemic models and its effect on the spread of infection. J. Appl. Probab. To appear.
    • (1998) J. Appl. Probab.
    • Andersson, H.1    Britton, T.2
  • 3
    • 0001000365 scopus 로고
    • Threshold limit theorems for some epidemic processes
    • VON BAHR, B. and MARTIN-LÖF, A. (1980). Threshold limit theorems for some epidemic processes. Adv. in Appl. Probab. 12 319-349.
    • (1980) Adv. in Appl. Probab. , vol.12 , pp. 319-349
    • Von Bahr, B.1    Martin-Löf, A.2
  • 5
    • 0010707667 scopus 로고
    • A threshold theorem for the Reed-Frost chain-binomial epidemic
    • BALL, F. (1983). A threshold theorem for the Reed-Frost chain-binomial epidemic. J. Appl. Probab. 20 153-157.
    • (1983) J. Appl. Probab. , vol.20 , pp. 153-157
    • Ball, F.1
  • 6
    • 0020763656 scopus 로고
    • The threshold behavior of epidemic models
    • BALL, F. (1983). The threshold behavior of epidemic models. J. Appl. Probab. 20 227-241.
    • (1983) J. Appl. Probab. , vol.20 , pp. 227-241
    • Ball, F.1
  • 7
    • 0001998990 scopus 로고
    • Strong approximations for epidemic models
    • BALL, F. and DONNELLY, P. (1995). Strong approximations for epidemic models. Stochastic Process. Appl. 55 1-21.
    • (1995) Stochastic Process. Appl. , vol.55 , pp. 1-21
    • Ball, F.1    Donnelly, P.2
  • 11
    • 0000664045 scopus 로고
    • The asymptotic number of labelled graphs with given degree sequences
    • BENDER, E. A. and CANFIELD, E. R. (1978). The asymptotic number of labelled graphs with given degree sequences. J. Combin. Theory Ser. A 24 296-307.
    • (1978) J. Combin. Theory Ser. A , vol.24 , pp. 296-307
    • Bender, E.A.1    Canfield, E.R.2
  • 14
    • 0032392720 scopus 로고    scopus 로고
    • A deterministic epidemic model taking account of repeated contacts between the same individuals
    • DIEKMANN, O., DE JONG, M. C. M. and METZ, J. A. J. (1998). A deterministic epidemic model taking account of repeated contacts between the same individuals. J. Appl. Probab. 35 462-468.
    • (1998) J. Appl. Probab. , vol.35 , pp. 462-468
    • Diekmann, O.1    De Jong, M.C.M.2    Metz, J.A.J.3
  • 15
    • 0028552640 scopus 로고
    • Stochastic spatial models: A user's guide to ecological applications
    • DURRETT, R. and LEVIN, S. A. (1994). Stochastic spatial models: a user's guide to ecological applications. Philos. Trans. Roy. Soc. London Ser. B 343 329-350.
    • (1994) Philos. Trans. Roy. Soc. London Ser. B , vol.343 , pp. 329-350
    • Durrett, R.1    Levin, S.A.2
  • 18
    • 0000585349 scopus 로고
    • Deterministic and stochastic epidemics in closed populations
    • Univ. California Press, Berkeley
    • KENDALL, D. G. (1956). Deterministic and stochastic epidemics in closed populations. Proc. Third Berkeley Symp. Math. Statist. Probab. 4 149-165. Univ. California Press, Berkeley.
    • (1956) Proc. Third Berkeley Symp. Math. Statist. Probab. , vol.4 , pp. 149-165
    • Kendall, D.G.1
  • 19
    • 0000618154 scopus 로고
    • Symmetric sampling procedures, general epidemic processes and their threshold limit theorems
    • MARTIN-LÖF, A. (1986). Symmetric sampling procedures, general epidemic processes and their threshold limit theorems. J. Appl. Probab. 23 265-282.
    • (1986) J. Appl. Probab. , vol.23 , pp. 265-282
    • Martin-Löf, A.1
  • 20
    • 0002767066 scopus 로고
    • Asymptotics for symmetric 0-1 matrices with prescribed row sums
    • MCKAY, B. D. (1985). Asymptotics for symmetric 0-1 matrices with prescribed row sums. Ars Combin. 19A 15-25.
    • (1985) Ars Combin. , vol.19 A , pp. 15-25
    • Mckay, B.D.1
  • 21
    • 84990671447 scopus 로고
    • A critical point for random graphs with a given degree sequence
    • MOLLOY, M. and REED, B. (1995). A critical point for random graphs with a given degree sequence. Random Structures Algorithms 6 161-179.
    • (1995) Random Structures Algorithms , vol.6 , pp. 161-179
    • Molloy, M.1    Reed, B.2
  • 22
    • 0038960071 scopus 로고    scopus 로고
    • Correlation equations and pair approximations for spatial ecologies
    • J. McGlade, ed.. Blackwell, Malden, Massachusetts
    • RAND, D. (1997). Correlation equations and pair approximations for spatial ecologies. In Theoretical Ecology 2 (J. McGlade, ed.). Blackwell, Malden, Massachusetts.
    • (1997) Theoretical Ecology , vol.2
    • Rand, D.1
  • 23
    • 0001694893 scopus 로고
    • Asymptotic final size distribution for some chain-binomial processes
    • SCALIA-TOMBA, G. (1985). Asymptotic final size distribution for some chain-binomial processes. Adv. in Appl. Probab. 17 477-495.
    • (1985) Adv. in Appl. Probab. , vol.17 , pp. 477-495
    • Scalia-Tomba, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.