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Volumn 216, Issue 1, 2008, Pages 63-70

The relationship between real-time and discrete-generation models of epidemic spread

Author keywords

Chain binomial model; Continuous time process; Epidemic process; Final size; Generations; Reed Frost model

Indexed keywords

CHAIN BINOMIAL MODEL; CONTINUOUS TIME PROCESS; EPIDEMIC PROCESS; FINAL SIZE; GENERATIONS; REED-FROST MODEL;

EID: 54249124424     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2008.08.009     Document Type: Article
Times cited : (31)

References (45)
  • 2
    • 0011481308 scopus 로고    scopus 로고
    • Stochastic epidemic models and their statistical analysis
    • Springer, New York
    • Andersson H., and Britton T. Stochastic epidemic models and their statistical analysis. Lecture Notes in Statistics vol. 151 (2000), Springer, New York
    • (2000) Lecture Notes in Statistics , vol.151
    • Andersson, H.1    Britton, T.2
  • 3
    • 0032593230 scopus 로고    scopus 로고
    • The asymptotic final size distribution of multitype chain-binomial epidemic processes
    • Andersson M. The asymptotic final size distribution of multitype chain-binomial epidemic processes. Adv. Appl. Probab. 31 1 (1999) 220
    • (1999) Adv. Appl. Probab. , vol.31 , Issue.1 , pp. 220
    • Andersson, M.1
  • 4
    • 85043981295 scopus 로고
    • On estimating the latent and infectious periods of measles: I. Families with two susceptibles only
    • Bailey N.T.J. On estimating the latent and infectious periods of measles: I. Families with two susceptibles only. Biometrika 43 1/2 (1956) 15
    • (1956) Biometrika , vol.43 , Issue.1-2 , pp. 15
    • Bailey, N.T.J.1
  • 6
    • 0010707667 scopus 로고
    • A threshold theorem for the Reed-Frost chain-binomial epidemic
    • Ball F. A threshold theorem for the Reed-Frost chain-binomial epidemic. J. Appl. Probab. 20 1 (1983) 153
    • (1983) J. Appl. Probab. , vol.20 , Issue.1 , pp. 153
    • Ball, F.1
  • 7
    • 0000943691 scopus 로고
    • A unified approach to the distribution of total size and total ara under the trajectory of infectives in epidemic models
    • Ball F. A unified approach to the distribution of total size and total ara under the trajectory of infectives in epidemic models. Adv. Appl. Probab. 18 2 (1986) 289
    • (1986) Adv. Appl. Probab. , vol.18 , Issue.2 , pp. 289
    • Ball, F.1
  • 9
    • 0036846225 scopus 로고    scopus 로고
    • A general model for stochastic SIR epidemics with two levels of mixing
    • Ball F., and Neal P. A general model for stochastic SIR epidemics with two levels of mixing. Math. Biosci. 180 (2002) 73
    • (2002) Math. Biosci. , vol.180 , pp. 73
    • Ball, F.1    Neal, P.2
  • 10
    • 0020763656 scopus 로고
    • The threshold behaviour of epidemic models
    • Ball F.G. The threshold behaviour of epidemic models. J. Appl. Probab. 20 2 (1983) 227
    • (1983) J. Appl. Probab. , vol.20 , Issue.2 , pp. 227
    • Ball, F.G.1
  • 11
    • 39549092111 scopus 로고    scopus 로고
    • An epidemic model with infector-dependent severity
    • Ball F.G., and Britton T. An epidemic model with infector-dependent severity. Adv. Appl. Probab. 39 4 (2007) 949
    • (2007) Adv. Appl. Probab. , vol.39 , Issue.4 , pp. 949
    • Ball, F.G.1    Britton, T.2
  • 12
    • 0041405990 scopus 로고    scopus 로고
    • Design issues for studies of infectious diseases
    • Becker N.G., and Britton T. Design issues for studies of infectious diseases. J. Stat. Plan. Infer. 96 1 (2001) 41
    • (2001) J. Stat. Plan. Infer. , vol.96 , Issue.1 , pp. 41
    • Becker, N.G.1    Britton, T.2
  • 13
    • 0029054589 scopus 로고
    • The effect of household distribution on transmission and control of highly infectious diseases
    • Becker N.G., and Dietz K. The effect of household distribution on transmission and control of highly infectious diseases. Math. Biosci. 127 (1995) 207
    • (1995) Math. Biosci. , vol.127 , pp. 207
    • Becker, N.G.1    Dietz, K.2
  • 14
    • 0032886393 scopus 로고    scopus 로고
    • Efficiency of estimating vaccine efficacy for susceptibility and infectiousness: randomization by individual versus household
    • Datta S., Halloran M.E., and Longini Jr. I.M. Efficiency of estimating vaccine efficacy for susceptibility and infectiousness: randomization by individual versus household. Biometrics 55 3 (1999) 792
    • (1999) Biometrics , vol.55 , Issue.3 , pp. 792
    • Datta, S.1    Halloran, M.E.2    Longini Jr., I.M.3
  • 15
    • 28044449928 scopus 로고    scopus 로고
    • Bayesian inference for stochastic multitype epidemics in structured populations via random graphs
    • Demiris N., and O'Neill P.D. Bayesian inference for stochastic multitype epidemics in structured populations via random graphs. J. Roy. Stat. Soc. 67 (2005) 731
    • (2005) J. Roy. Stat. Soc. , vol.67 , pp. 731
    • Demiris, N.1    O'Neill, P.D.2
  • 17
  • 18
    • 0001369140 scopus 로고
    • Epidemics and rumours: a survey
    • Dietz K. Epidemics and rumours: a survey. J. Roy. Stat. Soc. 130 4 (1967) 505
    • (1967) J. Roy. Stat. Soc. , vol.130 , Issue.4 , pp. 505
    • Dietz, K.1
  • 20
    • 0035843902 scopus 로고    scopus 로고
    • The foot-and-mouth epidemic in great Britain: pattern of spread and impact of interventions
    • Ferguson N.M., Donnelly C.A., and Anderson R.M. The foot-and-mouth epidemic in great Britain: pattern of spread and impact of interventions. Science 292 5519 (2001) 1155
    • (2001) Science , vol.292 , Issue.5519 , pp. 1155
    • Ferguson, N.M.1    Donnelly, C.A.2    Anderson, R.M.3
  • 23
    • 0037364857 scopus 로고    scopus 로고
    • Estimating vaccine efficacy from secondary attack rates
    • Halloran M.E. Estimating vaccine efficacy from secondary attack rates. J. Am. Stat. Assoc. 98 461 (2003) 38
    • (2003) J. Am. Stat. Assoc. , vol.98 , Issue.461 , pp. 38
    • Halloran, M.E.1
  • 24
    • 33846199646 scopus 로고    scopus 로고
    • Antiviral effects on influenza viral transmission and pathogenicity: observations from household-based trials
    • Halloran M.E., Hayden F.G., Yang Y., Longini I.M., and Monto A.S. Antiviral effects on influenza viral transmission and pathogenicity: observations from household-based trials. Am. J. Epidemiol. 165 2 (2007) 212
    • (2007) Am. J. Epidemiol. , vol.165 , Issue.2 , pp. 212
    • Halloran, M.E.1    Hayden, F.G.2    Yang, Y.3    Longini, I.M.4    Monto, A.S.5
  • 25
    • 0034486891 scopus 로고    scopus 로고
    • The mathematics of infectious diseases
    • Hethcote H.W. The mathematics of infectious diseases. SIAM Rev. 42 4 (2000) 599
    • (2000) SIAM Rev. , vol.42 , Issue.4 , pp. 599
    • Hethcote, H.W.1
  • 26
    • 0018856876 scopus 로고
    • Integral equation models for endemic infectious diseases
    • Hethcote H.W., and Tudor D.W. Integral equation models for endemic infectious diseases. J. Math. Biol. 9 1 (1980) 37
    • (1980) J. Math. Biol. , vol.9 , Issue.1 , pp. 37
    • Hethcote, H.W.1    Tudor, D.W.2
  • 27
    • 50449118725 scopus 로고
    • Does influenza spread within the household?
    • Hope Simpson R.E., and Sutherland I. Does influenza spread within the household?. Lancet 266 6814 (1954) 721
    • (1954) Lancet , vol.266 , Issue.6814 , pp. 721
    • Hope Simpson, R.E.1    Sutherland, I.2
  • 28
    • 0000581927 scopus 로고
    • Epidemics in competition. II. The general epidemic
    • Kendall W.S., and Saunders I.W. Epidemics in competition. II. The general epidemic. J. Roy. Stat. Soc. Ser. B 45 2 (1983) 238
    • (1983) J. Roy. Stat. Soc. Ser. B , vol.45 , Issue.2 , pp. 238
    • Kendall, W.S.1    Saunders, I.W.2
  • 30
    • 0001107279 scopus 로고
    • Poisson approximation for the final state of a generalized epidemic process
    • Lefevre C., and Utev S. Poisson approximation for the final state of a generalized epidemic process. Ann. Probab. 23 3 (1995) 1139
    • (1995) Ann. Probab. , vol.23 , Issue.3 , pp. 1139
    • Lefevre, C.1    Utev, S.2
  • 31
    • 4544248681 scopus 로고    scopus 로고
    • Branching approximation for the collective epidemic model
    • Lefevre C., and Utev S. Branching approximation for the collective epidemic model. Method. Comput. Appl. Probab. 1 2 (1999) 211
    • (1999) Method. Comput. Appl. Probab. , vol.1 , Issue.2 , pp. 211
    • Lefevre, C.1    Utev, S.2
  • 32
    • 0019899273 scopus 로고
    • Household and community transmission parameters from final distributions of infections in households
    • Longini I.M., and Koopman J.S. Household and community transmission parameters from final distributions of infections in households. Biometrics 38 1 (1982) 115
    • (1982) Biometrics , vol.38 , Issue.1 , pp. 115
    • Longini, I.M.1    Koopman, J.S.2
  • 33
    • 0019948714 scopus 로고
    • Estimating household and community transmission parameters for influenza
    • Longini I.M., Koopman J.S., Monto A.S., and Fox J.P. Estimating household and community transmission parameters for influenza. Am. J. Epidemiol. 115 5 (1982) 736
    • (1982) Am. J. Epidemiol. , vol.115 , Issue.5 , pp. 736
    • Longini, I.M.1    Koopman, J.S.2    Monto, A.S.3    Fox, J.P.4
  • 35
    • 0007166942 scopus 로고
    • Stochastic Population Theories
    • Springer, Berlin
    • Ludwig D. Stochastic Population Theories. Lecture Notes in Biomathematics vol. 3 (1974), Springer, Berlin
    • (1974) Lecture Notes in Biomathematics , vol.3
    • Ludwig, D.1
  • 36
    • 0016636706 scopus 로고
    • Final size distributions for epidemics
    • Ludwig D. Final size distributions for epidemics. Math. Biosci. 23 (1975) 33
    • (1975) Math. Biosci. , vol.23 , pp. 33
    • Ludwig, D.1
  • 37
    • 33750503157 scopus 로고    scopus 로고
    • Multitype randomized Reed-Frost epidemics and epidemics upon random graphs
    • Neal P. Multitype randomized Reed-Frost epidemics and epidemics upon random graphs. Ann. Appl. Probab. 16 3 (2006) 1166
    • (2006) Ann. Appl. Probab. , vol.16 , Issue.3 , pp. 1166
    • Neal, P.1
  • 38
    • 0000729953 scopus 로고
    • A unified analysis of the final size and severity distribution in collective Reed-Frost epidemic processes
    • Picard P., and Lefevre C. A unified analysis of the final size and severity distribution in collective Reed-Frost epidemic processes. Adv. Appl. Probab. 22 2 (1990) 269
    • (1990) Adv. Appl. Probab. , vol.22 , Issue.2 , pp. 269
    • Picard, P.1    Lefevre, C.2
  • 39
    • 0001694893 scopus 로고
    • Asymptotic final-size distribution for some chain-binomial processes
    • Scalia-Tomba G. Asymptotic final-size distribution for some chain-binomial processes. J. Appl. Probab. 17 3 (1985) 477
    • (1985) J. Appl. Probab. , vol.17 , Issue.3 , pp. 477
    • Scalia-Tomba, G.1
  • 40
    • 0344713455 scopus 로고
    • Asymptotic final size distribution of the multitype Reed-Frost process
    • Scalia-Tomba G. Asymptotic final size distribution of the multitype Reed-Frost process. J. Appl. Probab. 23 3 (1986) 563
    • (1986) J. Appl. Probab. , vol.23 , Issue.3 , pp. 563
    • Scalia-Tomba, G.1
  • 41
    • 0001088291 scopus 로고
    • On the asymptotic final size distribution of epidemics on heterogeneous populations
    • Stochastic Processes in Epidemic Theory. Gabriel J.-P., Lefvre C., and Picard P. (Eds), Luminy
    • Scalia-Tomba G. On the asymptotic final size distribution of epidemics on heterogeneous populations. In: Gabriel J.-P., Lefvre C., and Picard P. (Eds). Stochastic Processes in Epidemic Theory. Lecture Notes in Biomathematics vol. 86 (1988), Luminy 189
    • (1988) Lecture Notes in Biomathematics , vol.86 , pp. 189
    • Scalia-Tomba, G.1
  • 42
    • 0000045988 scopus 로고
    • On the asymptotic distribution of the size of a stochastic epidemic
    • Sellke T. On the asymptotic distribution of the size of a stochastic epidemic. J. Appl. Probab. 20 2 (1983) 390
    • (1983) J. Appl. Probab. , vol.20 , Issue.2 , pp. 390
    • Sellke, T.1
  • 43
    • 54249163791 scopus 로고    scopus 로고
    • Å. Svensson, G. Scalia-Tomba, Competing epidemics in closed populations, Research Report/Mathematical Statistics, Stockholm University, 2001. p. 8. Math. Stat., SU, Stockholm, 2001.
    • Å. Svensson, G. Scalia-Tomba, Competing epidemics in closed populations, Research Report/Mathematical Statistics, Stockholm University, 2001. p. 8. Math. Stat., SU, Stockholm, 2001.
  • 44
    • 0000042146 scopus 로고
    • On an epidemic in a stratified population
    • Watson R.K. On an epidemic in a stratified population. J. Appl. Probab. 9 3 (1972) 659
    • (1972) J. Appl. Probab. , vol.9 , Issue.3 , pp. 659
    • Watson, R.K.1
  • 45
    • 33645676327 scopus 로고    scopus 로고
    • Design and evaluation of prophylactic interventions using infectious disease incidence data from close contact groups
    • Yang Y., Longini Jr. I.M., and Halloran M.E. Design and evaluation of prophylactic interventions using infectious disease incidence data from close contact groups. Appl. Stat. 55 3 (2006) 317
    • (2006) Appl. Stat. , vol.55 , Issue.3 , pp. 317
    • Yang, Y.1    Longini Jr., I.M.2    Halloran, M.E.3


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