메뉴 건너뛰기




Volumn 7, Issue 1, 1997, Pages 46-89

Epidemics with two levels of mixing

Author keywords

Asymptotic distribution; Branching processes; Embedding; Epidemic; Estimation; Final outcome; Gontcharoff polynomials; Household; R0; Random graphs; Reed Frost; Threshold parameters; Vaccination

Indexed keywords


EID: 0031285152     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1034625252     Document Type: Article
Times cited : (432)

References (56)
  • 1
    • 0026055447 scopus 로고
    • A generalized stochastic model for the analysis of infectious disease final size data
    • ADDY, C. L., LONGINI, I. M. and HABER, M. (1991). A generalized stochastic model for the analysis of infectious disease final size data. Biometrics 47 961-974.
    • (1991) Biometrics , vol.47 , pp. 961-974
    • Addy, C.L.1    Longini, I.M.2    Haber, M.3
  • 2
    • 0010660708 scopus 로고
    • M.Sc. dissertation, Technical Report 1993:31, Dept. Mathematics, Chalmers Univ. Technology, Göteborg, Sweden
    • ANDERSSON, M. (1993). The final size of a multitype chain-binomial epidemic process. M.Sc. dissertation, Technical Report 1993:31, Dept. Mathematics, Chalmers Univ. Technology, Göteborg, Sweden.
    • (1993) The Final Size of a Multitype Chain-Binomial Epidemic Process
    • Andersson, M.1
  • 4
    • 0010707667 scopus 로고
    • A threshold theorem for the Reed-Frost chain-binomial epidemic
    • BALL, F. G. (1983a). 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.G.1
  • 5
    • 0020763656 scopus 로고
    • The threshold behavior of epidemic models
    • BALL, F. G. (1983b). The threshold behavior of epidemic models. J. Appl. Probab. 20 227-241.
    • (1983) J. Appl. Probab. , vol.20 , pp. 227-241
    • Ball, F.G.1
  • 6
    • 0000943691 scopus 로고
    • A unified approach to the distribution of total size and total area under the trajectory of infectives in epidemic models
    • BALL, F. G. (1986). A unified approach to the distribution of total size and total area under the trajectory of infectives in epidemic models. Adv. in Appl. Probab. 18 289-310.
    • (1986) Adv. in Appl. Probab. , vol.18 , pp. 289-310
    • Ball, F.G.1
  • 7
    • 0001481954 scopus 로고    scopus 로고
    • Threshold behaviour in stochastic epidemics among households
    • Applied Probability 1. Springer, Berlin
    • BALL, F. G. (1996). Threshold behaviour in stochastic epidemics among households. Applied Probability 1. Lecture Notes in Statist. 114 253-266. Springer, Berlin.
    • (1996) Lecture Notes in Statist , vol.114 , pp. 253-266
    • Ball, F.G.1
  • 9
    • 0000504567 scopus 로고
    • The final size and severity of a generalised stochastic multitype epidemic model
    • BALL, F. G. and CLANCY, D. (1993). The final size and severity of a generalised stochastic multitype epidemic model. Adv. in Appl. Probab. 25 721-736.
    • (1993) Adv. in Appl. Probab. , vol.25 , pp. 721-736
    • Ball, F.G.1    Clancy, D.2
  • 10
    • 0001998990 scopus 로고
    • Strong approximations for epidemic models
    • BALL, F. G. and DONNELLY, P. J. (1995). Strong approximations for epidemic models. Stochastic Process Appl. 55 1-21.
    • (1995) Stochastic Process Appl. , vol.55 , pp. 1-21
    • Ball, F.G.1    Donnelly, P.J.2
  • 11
    • 0028037026 scopus 로고
    • The shape of the size distribution of an epidemic in a finite population
    • BALL, F. G. and NÅSELL, I. (1994). The shape of the size distribution of an epidemic in a finite population. Math. Biosci. 123 167-181.
    • (1994) Math. Biosci. , vol.123 , pp. 167-181
    • Ball, F.G.1    Nåsell, I.2
  • 12
    • 0013549755 scopus 로고
    • Epidemics and random graphs
    • Stochastic Processes in Epidemic Theory. Springer, Berlin
    • BARBOUR, A. D. and MOLLISON, D. (1989). Epidemics and random graphs. In Stochastic Processes in Epidemic Theory. Lecture Notes in Biomath. 86 86-89. Springer, Berlin.
    • (1989) Lecture Notes in Biomath. , vol.86 , pp. 86-89
    • Barbour, A.D.1    Mollison, D.2
  • 13
    • 0003188315 scopus 로고
    • Measles periodicity and community size
    • BARTLETT, M. S. (1957). Measles periodicity and community size. J. Roy. Statist. Soc. Ser. A 120 48-70.
    • (1957) J. Roy. Statist. Soc. Ser. A , vol.120 , pp. 48-70
    • Bartlett, M.S.1
  • 14
  • 16
    • 0029054589 scopus 로고
    • The effect of the household distribution on transmission and control of highly infectious diseases
    • BECKER, N. G. and DIETZ, K. (1995). The effect of the household distribution on transmission and control of highly infectious diseases. Math. Biosci. 127 207-219.
    • (1995) Math. Biosci. , vol.127 , pp. 207-219
    • Becker, N.G.1    Dietz, K.2
  • 17
    • 0030059502 scopus 로고    scopus 로고
    • Immunization levels for preventing epidemics in a community of households made up of individuals of different types
    • BECKER, N. G. and HALL, R. (1996). Immunization levels for preventing epidemics in a community of households made up of individuals of different types. Math. Biosci. 132 205-216.
    • (1996) Math. Biosci. , vol.132 , pp. 205-216
    • Becker, N.G.1    Hall, R.2
  • 21
    • 0010750282 scopus 로고
    • A deterministic general epidemic model in a stratified population
    • F. P. Kelly, ed. Wiley, Chichester
    • DALEY, D. J. and GANI, J. (1994). A deterministic general epidemic model in a stratified population. In Probability, Statistics and Optimisation (F. P. Kelly, ed.) 117-132. Wiley, Chichester.
    • (1994) Probability, Statistics and Optimisation , pp. 117-132
    • Daley, D.J.1    Gani, J.2
  • 22
    • 0010707455 scopus 로고
    • Collapsing supercritical branching processes
    • DALY, F. (1979). Collapsing supercritical branching processes. J. Appl. Probab. 16 732-739.
    • (1979) J. Appl. Probab. , vol.16 , pp. 732-739
    • Daly, F.1
  • 25
    • 0027736832 scopus 로고
    • The estimation of the basic reproduction number for infectious diseases
    • DIETZ, K. (1993). The estimation of the basic reproduction number for infectious diseases. Statistical Methods in Medical Research 2 23-41.
    • (1993) Statistical Methods in Medical Research , vol.2 , pp. 23-41
    • Dietz, K.1
  • 26
    • 0000740198 scopus 로고
    • A correction to "The area under the infectives trajectory of the general stochastic epidemic"
    • DOWNTON, F. (1972). A correction to "The area under the infectives trajectory of the general stochastic epidemic." J. Appl. Probab. 9 873-876.
    • (1972) J. Appl. Probab. , vol.9 , pp. 873-876
    • Downton, F.1
  • 27
    • 0010711933 scopus 로고
    • An extension of Raikov's theorem derivable from a result in epidemic theory
    • GANI, J. and SHANBHAG, D. N. (1974). An extension of Raikov's theorem derivable from a result in epidemic theory. Z. Wahrsch. Verw. Gebiete 29 33-37.
    • (1974) Z. Wahrsch. Verw. Gebiete , vol.29 , pp. 33-37
    • Gani, J.1    Shanbhag, D.N.2
  • 28
    • 0002706835 scopus 로고
    • Epidemic process on a random graph: Some preliminary results
    • GERTSBAKH, I. B. (1977). Epidemic process on a random graph: some preliminary results. J. Appl. Probab. 14 427-438.
    • (1977) J. Appl. Probab. , vol.14 , pp. 427-438
    • Gertsbakh, I.B.1
  • 30
    • 0023824351 scopus 로고
    • Models for the statistical analysis of infectious disease data
    • HABER, M., LONGINI, I. M. and COTSONIS, G. A. (1988). Models for the statistical analysis of infectious disease data. Biometrics 44 163-173.
    • (1988) Biometrics , vol.44 , pp. 163-173
    • Haber, M.1    Longini, I.M.2    Cotsonis, G.A.3
  • 31
    • 0026273197 scopus 로고
    • Metapopulation dynamics: Brief history and conceptual domain
    • HANSKI, I. and GILPIN, M. (1991). Metapopulation dynamics: brief history and conceptual domain. Biology Journal of the Linnean Society 42 3-16.
    • (1991) Biology Journal of the Linnean Society , vol.42 , pp. 3-16
    • Hanski, I.1    Gilpin, M.2
  • 32
    • 0018247773 scopus 로고
    • An immunization model for a heterogeneous population
    • HETHCOTE, H. W. (1978). An immunization model for a heterogeneous population. Theoret. Population Biol. 14 338-349.
    • (1978) Theoret. Population Biol. , vol.14 , pp. 338-349
    • Hethcote, H.W.1
  • 33
    • 0023177943 scopus 로고
    • Epidemiological models for heterogeneous populations: Proportionate mixing, parameter estimation and immunization programs
    • HETHCOTE, H. W. and VAN ARK, J. W. (1986). Epidemiological models for heterogeneous populations: proportionate mixing, parameter estimation and immunization programs. Math. Biosci. 84 84-118.
    • (1986) Math. Biosci. , vol.84 , pp. 84-118
    • Hethcote, H.W.1    Van Ark, J.W.2
  • 34
    • 0029871031 scopus 로고    scopus 로고
    • A random graph model for the finalsize distribution of household infections
    • ISLAM, M. N., O'SHAUGHNESSY, C. D. and SMITH, B. (1996). A random graph model for the finalsize distribution of household infections. Statistics in Medicine 15 837-843.
    • (1996) Statistics in Medicine , vol.15 , pp. 837-843
    • Islam, M.N.1    O'Shaughnessy, C.D.2    Smith, B.3
  • 36
    • 0025526270 scopus 로고
    • Population dynamics in spatially complex environments: Theory and data
    • KAREIVA, P. (1990). Population dynamics in spatially complex environments: theory and data. Philos. Trans. Roy. Soc. London Ser. B 330 175-190.
    • (1990) Philos. Trans. Roy. Soc. London Ser. B , vol.330 , pp. 175-190
    • Kareiva, P.1
  • 38
    • 0001249058 scopus 로고
    • Limit theorems for sequences of jump Markov processes approximating ordinary differential processes
    • KURTZ, T. G. (1970). Limit theorems for sequences of jump Markov processes approximating ordinary differential processes. J. Appl. Probab. 8 344-356.
    • (1970) J. Appl. Probab. , vol.8 , pp. 344-356
    • Kurtz, T.G.1
  • 40
    • 0002708819 scopus 로고
    • A non-standard family of polynomials and the final size distribution of Reed-Frost epidemic processes
    • LEFÈVRE, C. and PICARD, PH. (1990). A non-standard family of polynomials and the final size distribution of Reed-Frost epidemic processes. Adv. in Appl. Probab. 22 25-48.
    • (1990) Adv. in Appl. Probab. , vol.22 , pp. 25-48
    • Lefèvre, C.1    Picard, Ph.2
  • 41
    • 0019899273 scopus 로고
    • Household and community transmission parameters from final distributions of infections in households
    • LONGINI, I. M. and KOOPMAN, J. S. (1982). Household and community transmission parameters from final distributions of infections in households. Biometrics 38 115-126.
    • (1982) Biometrics , vol.38 , pp. 115-126
    • Longini, I.M.1    Koopman, J.S.2
  • 42
    • 0021529194 scopus 로고
    • Spatial heterogeneity and the design of immunization programs
    • MAY, R. M. and ANDERSON, R. M. (1984). Spatial heterogeneity and the design of immunization programs. Math. Biosci. 72 83-111.
    • (1984) Math. Biosci. , vol.72 , pp. 83-111
    • May, R.M.1    Anderson, R.M.2
  • 43
    • 0001707002 scopus 로고
    • The rate of propagation of simple epidemics
    • Univ. California Press, Berkeley
    • MOLLISON, D. (1972). The rate of propagation of simple epidemics. Proc. Sixth Berkeley Symp. Math. Statist. Probab. 3 579-614. Univ. California Press, Berkeley.
    • (1972) Proc. Sixth Berkeley Symp. Math. Statist. Probab. , vol.3 , pp. 579-614
    • Mollison, D.1
  • 44
  • 45
    • 0000586087 scopus 로고
    • Spatial dynamics of parasitism
    • B. T. Grenfell and A. Dobson, eds. Cambridge Univ. Press
    • MOLLISON, D. and LEVIN, S. A. (1995). Spatial dynamics of parasitism. In Ecology of Infectious Diseases in Natural Populations (B. T. Grenfell and A. Dobson, eds.) 384-398. Cambridge Univ. Press.
    • (1995) Ecology of Infectious Diseases in Natural Populations , pp. 384-398
    • Mollison, D.1    Levin, S.A.2
  • 46
    • 0002242439 scopus 로고
    • The threshold concept in stochastic epidemic and endemic models
    • D. Mollison, ed. Cambridge Univ. Press
    • NÅSELL, I. (1995). The threshold concept in stochastic epidemic and endemic models. In Epidemic Models: Their Structure and Relation to Data (D. Mollison, ed.) 71-83. Cambridge Univ. Press.
    • (1995) Epidemic Models: Their Structure and Relation to Data , pp. 71-83
    • Nåsell, I.1
  • 47
    • 0000729953 scopus 로고
    • A unified analysis of the final size and severity distribution in collective Reed-Frost epidemic processes
    • PICARD, PH. and LEFÈVRE, C. (1990). A unified analysis of the final size and severity distribution in collective Reed-Frost epidemic processes. Adv. in Appl. Probab. 22 269-294.
    • (1990) Adv. in Appl. Probab. , vol.22 , pp. 269-294
    • Picard, Ph.1    Lefèvre, C.2
  • 48
    • 0020735310 scopus 로고
    • Endemic disease in environments with spatially heterogeneous host populations
    • POST, W. M., DEANGELIS, D. L. and TRAVIS, C. C. (1983). Endemic disease in environments with spatially heterogeneous host populations. Math. Biosci. 63 289-302.
    • (1983) Math. Biosci. , vol.63 , pp. 289-302
    • Post, W.M.1    Deangelis, D.L.2    Travis, C.C.3
  • 49
    • 0001552196 scopus 로고
    • The deterministic model of a simple epidemic for more than one community
    • RUSHTON, S. and MAUTNER, A. J. (1955). The deterministic model of a simple epidemic for more than one community. Biometrika 42 126-132.
    • (1955) Biometrika , vol.42 , pp. 126-132
    • Rushton, S.1    Mautner, A.J.2
  • 50
    • 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
  • 51
    • 0001088291 scopus 로고
    • On the asymptotic final size distribution of epidemics in heterogeneous populations
    • Stochastic Processes in Epidemic Theory. Springer, Berlin
    • SCALIA-TOMBA, G. (1990). On the asymptotic final size distribution of epidemics in heterogeneous populations. In Stochastic Processes in Epidemic Theory. Lecture Notes in Biomath. 86 189-196. Springer, Berlin.
    • (1990) Lecture Notes in Biomath. , vol.86 , pp. 189-196
    • Scalia-Tomba, G.1
  • 52
    • 0000045988 scopus 로고
    • On the asymptotic distribution of the size of a stochastic epidemic
    • SELLKE, T. (1983). On the asymptotic distribution of the size of a stochastic epidemic. J. Appl. Probab. 20 390-394.
    • (1983) J. Appl. Probab. , vol.20 , pp. 390-394
    • Sellke, T.1
  • 53
    • 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
  • 54
    • 0000042146 scopus 로고
    • On an epidemic in a stratified population
    • WATSON, R. K. (1972). On an epidemic in a stratified population. J. Appl. Probab. 9 659-666.
    • (1972) J. Appl. Probab. , vol.9 , pp. 659-666
    • Watson, R.K.1
  • 55
    • 0000161729 scopus 로고
    • Conditioned Markov processes
    • WAUGH, W. A. O'N. (1958). Conditioned Markov processes. Biometrika 45 241-249.
    • (1958) Biometrika , vol.45 , pp. 241-249
    • Waugh, W.A.O'N.1
  • 56
    • 0001236565 scopus 로고
    • The outcome of a stochastic epidemic - A note on Bailey's paper
    • WHITTLE, P. (1955). The outcome of a stochastic epidemic - a note on Bailey's paper. Biometrika 42 116-122.
    • (1955) Biometrika , vol.42 , pp. 116-122
    • Whittle, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.