Skip to main content
Top
Published in: Emerging Themes in Epidemiology 1/2007

Open Access 01-12-2007 | Analytic perspective

Early efforts in modeling the incubation period of infectious diseases with an acute course of illness

Author: Hiroshi Nishiura

Published in: Emerging Themes in Epidemiology | Issue 1/2007

Login to get access

Abstract

The incubation period of infectious diseases, the time from infection with a microorganism to onset of disease, is directly relevant to prevention and control. Since explicit models of the incubation period enhance our understanding of the spread of disease, previous classic studies were revisited, focusing on the modeling methods employed and paying particular attention to relatively unknown historical efforts. The earliest study on the incubation period of pandemic influenza was published in 1919, providing estimates of the incubation period of Spanish flu using the daily incidence on ships departing from several ports in Australia. Although the study explicitly dealt with an unknown time of exposure, the assumed periods of exposure, which had an equal probability of infection, were too long, and thus, likely resulted in slight underestimates of the incubation period.
After the suggestion that the incubation period follows lognormal distribution, Japanese epidemiologists extended this assumption to estimates of the time of exposure during a point source outbreak. Although the reason why the incubation period of acute infectious diseases tends to reveal a right-skewed distribution has been explored several times, the validity of the lognormal assumption is yet to be fully clarified. At present, various different distributions are assumed, and the lack of validity in assuming lognormal distribution is particularly apparent in the case of slowly progressing diseases. The present paper indicates that (1) analysis using well-defined short periods of exposure with appropriate statistical methods is critical when the exact time of exposure is unknown, and (2) when assuming a specific distribution for the incubation period, comparisons using different distributions are needed in addition to estimations using different datasets, analyses of the determinants of incubation period, and an understanding of the underlying disease mechanisms.
Appendix
Available only for authorised users
Literature
1.
go back to reference Brookmeyer R: Incubation period of infectious diseases. In Encyclopedia of Biostatistics Edited by: Armitage P, Colton T. New York: Wiley; 1998:2011-2016. Brookmeyer R: Incubation period of infectious diseases. In Encyclopedia of Biostatistics Edited by: Armitage P, Colton T. New York: Wiley; 1998:2011-2016.
2.
go back to reference Armenian HK, Lilienfeld AM: Incubation period of disease. Epidemiol Rev. 1983, 5: 1-15.PubMed Armenian HK, Lilienfeld AM: Incubation period of disease. Epidemiol Rev. 1983, 5: 1-15.PubMed
3.
go back to reference Fracastorii H: De sympathia et antipathia rervm liber vnvs. De contagione et contagiosis morbis et eorum curatione, Libri III. Venetiis: apud heredes Lucaeantonij Iuntae Florentini; 1546 (in Latin. Translation and notes by Wright WC: On Contagion, Contagious Diseases and Their Cure) New York: GP Putnam and Sons; 1930. Fracastorii H: De sympathia et antipathia rervm liber vnvs. De contagione et contagiosis morbis et eorum curatione, Libri III. Venetiis: apud heredes Lucaeantonij Iuntae Florentini; 1546 (in Latin. Translation and notes by Wright WC: On Contagion, Contagious Diseases and Their Cure) New York: GP Putnam and Sons; 1930.
4.
go back to reference Anderson RM, May RM: Infectious Diseases of Humans: Dynamics and Control Oxford: Oxford University Press;; 1991. Anderson RM, May RM: Infectious Diseases of Humans: Dynamics and Control Oxford: Oxford University Press;; 1991.
5.
go back to reference Mandell GL, Bennett JE, Dolin R: Principles and Practice of Infectious Diseases 6th edition. Philadelphia, PA: Elsevier Churchill Livingstone; 2004. Mandell GL, Bennett JE, Dolin R: Principles and Practice of Infectious Diseases 6th edition. Philadelphia, PA: Elsevier Churchill Livingstone; 2004.
6.
go back to reference Tateno I: Incubation period and the initial symptoms of tetanus: A clinical assessment of the problem of the passage of tetanus toxin to the central nervous system. Jpn J Exp Med. 1963, 33: 149-158.PubMed Tateno I: Incubation period and the initial symptoms of tetanus: A clinical assessment of the problem of the passage of tetanus toxin to the central nervous system. Jpn J Exp Med. 1963, 33: 149-158.PubMed
7.
go back to reference Nishiura H: Incubation period as a clinical predictor of botulism: analysis of previous izushi-borne outbreaks in Hokkaido, Japan, from 1951 to 1965. Epidemiol Infect. 2007, 135: 126-130. 10.1017/S0950268806006169PubMedCentralPubMed Nishiura H: Incubation period as a clinical predictor of botulism: analysis of previous izushi-borne outbreaks in Hokkaido, Japan, from 1951 to 1965. Epidemiol Infect. 2007, 135: 126-130. 10.1017/S0950268806006169PubMedCentralPubMed
8.
go back to reference Glynn JR, Bradley DJ: The relationship between infecting dose and severity of disease in reported outbreaks of Salmonella infections. Epidemiol Infect. 1992, 109: 371-388.PubMedCentralPubMed Glynn JR, Bradley DJ: The relationship between infecting dose and severity of disease in reported outbreaks of Salmonella infections. Epidemiol Infect. 1992, 109: 371-388.PubMedCentralPubMed
9.
go back to reference Nishiura H, Halstead SB: Natural history of dengue virus (DENV)-1 and DENV-4 infections: reanalysis of classic studies. J Infect Dis. 2007, 195: 1007-1013. 10.1086/511825PubMed Nishiura H, Halstead SB: Natural history of dengue virus (DENV)-1 and DENV-4 infections: reanalysis of classic studies. J Infect Dis. 2007, 195: 1007-1013. 10.1086/511825PubMed
10.
go back to reference Farewell VT, Herzberg AM, James KW, Ho LM, Leung GM: SARS incubation and quarantine times: when is an exposed individual known to be disease free?. Stat Med. 2005, 24: 3431-3445. 10.1002/sim.2206PubMed Farewell VT, Herzberg AM, James KW, Ho LM, Leung GM: SARS incubation and quarantine times: when is an exposed individual known to be disease free?. Stat Med. 2005, 24: 3431-3445. 10.1002/sim.2206PubMed
11.
go back to reference Fraser C, Riley S, Anderson RM, Ferguson NM: Factors that make an infectious disease outbreak controllable. Proc Natl Acad Sci USA. 2004, 101: 6146-6151. 10.1073/pnas.0307506101PubMedCentralPubMed Fraser C, Riley S, Anderson RM, Ferguson NM: Factors that make an infectious disease outbreak controllable. Proc Natl Acad Sci USA. 2004, 101: 6146-6151. 10.1073/pnas.0307506101PubMedCentralPubMed
12.
go back to reference Sartwell PE: The distribution of incubation periods of infectious diseases. Am J Hyg 1950, 51:310-318. (reprinted in Am J Epidemiol 1995, 141: 386–394)PubMed Sartwell PE: The distribution of incubation periods of infectious diseases. Am J Hyg 1950, 51:310-318. (reprinted in Am J Epidemiol 1995, 141: 386–394)PubMed
13.
go back to reference Brookmeyer R, You X: A hypothesis test for the end of a common source outbreak. Biometrics. 2006, 62: 61-65. 10.1111/j.1541-0420.2005.00421.xPubMed Brookmeyer R, You X: A hypothesis test for the end of a common source outbreak. Biometrics. 2006, 62: 61-65. 10.1111/j.1541-0420.2005.00421.xPubMed
14.
go back to reference Brookmeyer R, Gail MH: A method for obtaining short-term projections and lower bounds on the size of the AIDS epidemic. J Am Stat Assoc. 1988, 83: 301-308. 10.2307/2288844. 10.2307/2288844 Brookmeyer R, Gail MH: A method for obtaining short-term projections and lower bounds on the size of the AIDS epidemic. J Am Stat Assoc. 1988, 83: 301-308. 10.2307/2288844. 10.2307/2288844
15.
go back to reference Brookmeyer R, Gail MH: AIDS Epidemiology: A Quantitative Approach (Monographs in Epidemiology and Biostatistics) New York: Oxford University Press; 1994. Brookmeyer R, Gail MH: AIDS Epidemiology: A Quantitative Approach (Monographs in Epidemiology and Biostatistics) New York: Oxford University Press; 1994.
16.
go back to reference Anderson RM, Donnelly CA, Ferguson NM, Woolhouse ME, Watt CJ, Udy HJ, MaWhinney S, Dunstan SP, Southwood TR, Wilesmith JW, Ryan JB, Hoinville LJ, Hillerton JE, Austin AR, Wells GA: Transmission dynamics and epidemiology of BSE in British cattle. Nature. 1996, 382: 779-788. 10.1038/382779a0PubMed Anderson RM, Donnelly CA, Ferguson NM, Woolhouse ME, Watt CJ, Udy HJ, MaWhinney S, Dunstan SP, Southwood TR, Wilesmith JW, Ryan JB, Hoinville LJ, Hillerton JE, Austin AR, Wells GA: Transmission dynamics and epidemiology of BSE in British cattle. Nature. 1996, 382: 779-788. 10.1038/382779a0PubMed
17.
go back to reference Donnelly CA, Ferguson NM, Ghani AC, Anderson RM: Extending backcalculation to analyse BSE data. Stat Methods Med Res. 2003, 12: 177-190. 10.1191/0962280203sm337raPubMed Donnelly CA, Ferguson NM, Ghani AC, Anderson RM: Extending backcalculation to analyse BSE data. Stat Methods Med Res. 2003, 12: 177-190. 10.1191/0962280203sm337raPubMed
18.
go back to reference Cousens SN, Vynnycky E, Zeidler M, Will RG, Smith PG: Predicting the CJD epidemic in humans. Nature. 1997, 385: 197-198. 10.1038/385197a0PubMed Cousens SN, Vynnycky E, Zeidler M, Will RG, Smith PG: Predicting the CJD epidemic in humans. Nature. 1997, 385: 197-198. 10.1038/385197a0PubMed
19.
go back to reference Valleron AJ, Boelle PY, Will R, Cesbron JY: Estimation of epidemic size and incubation time based on age characteristics of vCJD in the United Kingdom. Science. 2001, 294: 1726-1728. 10.1126/science.1066838PubMed Valleron AJ, Boelle PY, Will R, Cesbron JY: Estimation of epidemic size and incubation time based on age characteristics of vCJD in the United Kingdom. Science. 2001, 294: 1726-1728. 10.1126/science.1066838PubMed
20.
go back to reference Huillard d'Aignaux JN, Cousens SN, Smith PG: The predictability of the epidemic of variant Creutzfeldt-Jakob disease by back-calculation methods. Stat Methods Med Res. 2003, 12: 203-220. 10.1191/0962280203sm328raPubMed Huillard d'Aignaux JN, Cousens SN, Smith PG: The predictability of the epidemic of variant Creutzfeldt-Jakob disease by back-calculation methods. Stat Methods Med Res. 2003, 12: 203-220. 10.1191/0962280203sm328raPubMed
21.
go back to reference Ghani AC, Ferguson NM, Donnelly CA, Anderson RM: Predicted vCJD mortality in Great Britain. Nature. 2000, 406: 583-584. 10.1038/35020688PubMed Ghani AC, Ferguson NM, Donnelly CA, Anderson RM: Predicted vCJD mortality in Great Britain. Nature. 2000, 406: 583-584. 10.1038/35020688PubMed
22.
go back to reference Ghani AC, Ferguson NM, Donnelly CA, Anderson RM: Short-term projections for variant Creutzfeldt-Jakob disease onsets. Stat Methods Med Res. 2003, 12: 191-201. 10.1191/0962280203sm327raPubMed Ghani AC, Ferguson NM, Donnelly CA, Anderson RM: Short-term projections for variant Creutzfeldt-Jakob disease onsets. Stat Methods Med Res. 2003, 12: 191-201. 10.1191/0962280203sm327raPubMed
23.
go back to reference Huillard d'Aignaux JN, Cousens SN, Maccario J, Costagliola D, Alpers MP, Smith PG, Alperovitch A: The incubation period of kuru. Epidemiology. 2002, 13: 402-408. 10.1097/00001648-200207000-00007PubMed Huillard d'Aignaux JN, Cousens SN, Maccario J, Costagliola D, Alpers MP, Smith PG, Alperovitch A: The incubation period of kuru. Epidemiology. 2002, 13: 402-408. 10.1097/00001648-200207000-00007PubMed
24.
go back to reference Eichner M, Dietz K: Transmission potential of smallpox: estimates based on detailed data from an outbreak. Am J Epidemiol. 2003, 158: 110-117. 10.1093/aje/kwg103PubMed Eichner M, Dietz K: Transmission potential of smallpox: estimates based on detailed data from an outbreak. Am J Epidemiol. 2003, 158: 110-117. 10.1093/aje/kwg103PubMed
25.
go back to reference Nishiura H, Eichner M: Infectiousness of smallpox relative to disease age: Estimates based on transmission network and incubation period. Epidemiol Infect 2007 in press. (doi: 10.1017/ S0950268806007618) Nishiura H, Eichner M: Infectiousness of smallpox relative to disease age: Estimates based on transmission network and incubation period. Epidemiol Infect 2007 in press. (doi: 10.1017/ S0950268806007618)
26.
go back to reference Nishiura H, Lee HW, Cho SH, Lee WG, In TS, Moon SU, Chung GT, Kim TS: Estimates of short and long incubation periods of Plasmodium vivax malaria in the Republic of Korea. Trans R Soc Trop Med Hyg. 2007, 101: 338-343. 10.1016/j.trstmh.2006.11.002PubMed Nishiura H, Lee HW, Cho SH, Lee WG, In TS, Moon SU, Chung GT, Kim TS: Estimates of short and long incubation periods of Plasmodium vivax malaria in the Republic of Korea. Trans R Soc Trop Med Hyg. 2007, 101: 338-343. 10.1016/j.trstmh.2006.11.002PubMed
27.
go back to reference Tiburskaja NA, Sergiev PG, Vrublevskaja OS: Dates of onset of relapses and the duration of infection in induced tertian malaria with short and long incubation periods. Bull World Health Organ. 1968, 38: 447-457.PubMedCentralPubMed Tiburskaja NA, Sergiev PG, Vrublevskaja OS: Dates of onset of relapses and the duration of infection in induced tertian malaria with short and long incubation periods. Bull World Health Organ. 1968, 38: 447-457.PubMedCentralPubMed
28.
go back to reference Brookmeyer R: AIDS, epidemics, and statistics. Biometrics. 1996, 52: 781-796. 10.2307/2533042PubMed Brookmeyer R: AIDS, epidemics, and statistics. Biometrics. 1996, 52: 781-796. 10.2307/2533042PubMed
29.
go back to reference Little RJA, Rubin DB: Statistical analysis with missing data 2nd edition. New York: John Wiley and Sons; 2002. Little RJA, Rubin DB: Statistical analysis with missing data 2nd edition. New York: John Wiley and Sons; 2002.
30.
go back to reference Donnelly CA, Ghani AC, Leung GM, Hedley AJ, Fraser C, Riley S, Abu-Raddad LJ, Ho LM, Thach TQ, Chau P, Chan KP, Lam TH, Tse LY, Tsang T, Liu SH, Kong JH, Lau EM, Ferguson NM, Anderson RM: Epidemiological determinants of spread of causal agent of severe acute respiratory syndrome in Hong Kong. Lancet. 2003, 361: 1761-1766. 10.1016/S0140-6736(03)13410-1PubMed Donnelly CA, Ghani AC, Leung GM, Hedley AJ, Fraser C, Riley S, Abu-Raddad LJ, Ho LM, Thach TQ, Chau P, Chan KP, Lam TH, Tse LY, Tsang T, Liu SH, Kong JH, Lau EM, Ferguson NM, Anderson RM: Epidemiological determinants of spread of causal agent of severe acute respiratory syndrome in Hong Kong. Lancet. 2003, 361: 1761-1766. 10.1016/S0140-6736(03)13410-1PubMed
31.
go back to reference Donnelly CA, Fisher MC, Fraser C, Ghani AC, Riley S, Ferguson NM, Anderson RM: Epidemiological and genetic analysis of severe acute respiratory syndrome. Lancet Infect Dis. 2004, 4: 672-683. 10.1016/S1473-3099(04)01173-9PubMed Donnelly CA, Fisher MC, Fraser C, Ghani AC, Riley S, Ferguson NM, Anderson RM: Epidemiological and genetic analysis of severe acute respiratory syndrome. Lancet Infect Dis. 2004, 4: 672-683. 10.1016/S1473-3099(04)01173-9PubMed
32.
go back to reference Elveback LR, Fox JP, Ackerman E, Langworthy A, Boyd M, Gatewood L: An influenza simulation model for immunization studies. Am J Epidemiol. 1976, 103: 152-165.PubMed Elveback LR, Fox JP, Ackerman E, Langworthy A, Boyd M, Gatewood L: An influenza simulation model for immunization studies. Am J Epidemiol. 1976, 103: 152-165.PubMed
33.
go back to reference Rvachev LA, Longini IM: A mathematical model for the global spread of influenza. Math Biosci. 1985, 75: 3-22. 10.1016/0025-5564(85)90064-1. 10.1016/0025-5564(85)90064-1 Rvachev LA, Longini IM: A mathematical model for the global spread of influenza. Math Biosci. 1985, 75: 3-22. 10.1016/0025-5564(85)90064-1. 10.1016/0025-5564(85)90064-1
34.
go back to reference Moser MR, Bender TR, Margolis HS, Noble GR, Kendal AP, Ritter DG: An outbreak of influenza aboard a commercial airliner. Am J Epidemiol. 1979, 110: 1-6.PubMed Moser MR, Bender TR, Margolis HS, Noble GR, Kendal AP, Ritter DG: An outbreak of influenza aboard a commercial airliner. Am J Epidemiol. 1979, 110: 1-6.PubMed
35.
go back to reference Ferguson NM, Cummings DA, Cauchemez S, Fraser C, Riley S, Meeyai A, Iamsirithaworn S, Burke DS: Strategies for containing an emerging influenza pandemic in Southeast Asia. Nature. 2005, 437: 209-214. 10.1038/nature04017PubMed Ferguson NM, Cummings DA, Cauchemez S, Fraser C, Riley S, Meeyai A, Iamsirithaworn S, Burke DS: Strategies for containing an emerging influenza pandemic in Southeast Asia. Nature. 2005, 437: 209-214. 10.1038/nature04017PubMed
36.
go back to reference McKendrick AG, Morison J: The determination of incubation periods from maritime statistics, with particular reference to the incubation period of influenza. Indian J Med Res 1919, 7:364-371. McKendrick AG, Morison J: The determination of incubation periods from maritime statistics, with particular reference to the incubation period of influenza. Indian J Med Res 1919, 7:364-371.
37.
go back to reference McKendrick AG, Morison J: The determination of incubation periods from maritime statistics, with particular reference to the incubation period of influenza. Indian J Med Res 1919, 7:364-371. McKendrick AG, Morison J: The determination of incubation periods from maritime statistics, with particular reference to the incubation period of influenza. Indian J Med Res 1919, 7:364-371.
38.
go back to reference Dietz K: Introduction to McKendrick (1926). Application of mathematics to medical problems. In Breakthroughs in Statistics: Volume III Edited by: Kotz S, Johnson NL. New York: Springer; 1997:17-26. Dietz K: Introduction to McKendrick (1926). Application of mathematics to medical problems. In Breakthroughs in Statistics: Volume III Edited by: Kotz S, Johnson NL. New York: Springer; 1997:17-26.
39.
go back to reference Gani J: Anderson Gray McKendrick. In Statisticians of the Centuries Edited by: Heyde CC, Seneta E. New York: Springer; 2001:323-327. Gani J: Anderson Gray McKendrick. In Statisticians of the Centuries Edited by: Heyde CC, Seneta E. New York: Springer; 2001:323-327.
40.
go back to reference Kermack WO, McKendrick AG: A contribution to the mathematical theory of epidemics. Proc R Soc Lond Ser A 1927, 115:700-721. (Reprinted in Bull Math Biol 1991, 53: 33–55) Kermack WO, McKendrick AG: A contribution to the mathematical theory of epidemics. Proc R Soc Lond Ser A 1927, 115:700-721. (Reprinted in Bull Math Biol 1991, 53: 33–55)
41.
go back to reference Anderson RM: Discussion: the Kermack-McKendrick epidemic threshold theorem. Bull Math Biol. 1991, 53: 3-32. 10.1016/S0092-8240(05)80039-4PubMed Anderson RM: Discussion: the Kermack-McKendrick epidemic threshold theorem. Bull Math Biol. 1991, 53: 3-32. 10.1016/S0092-8240(05)80039-4PubMed
42.
go back to reference Cumpston JHL: Service Publication No. 18. Influenza and maritime quarantine in Australia Melbourne: Commonwealth of Australia, Quarantine Service; 1919. Cumpston JHL: Service Publication No. 18. Influenza and maritime quarantine in Australia Melbourne: Commonwealth of Australia, Quarantine Service; 1919.
45.
go back to reference Cai QC, Xu QF, Xu JM, Guo Q, Cheng X, Zhao GM, Sun QW, Lu J, Jiang QW: Refined estimate of the incubation period of severe acute respiratory syndrome and related influencing factors. Am J Epidemiol. 2006, 163: 211-216. 10.1093/aje/kwj034PubMed Cai QC, Xu QF, Xu JM, Guo Q, Cheng X, Zhao GM, Sun QW, Lu J, Jiang QW: Refined estimate of the incubation period of severe acute respiratory syndrome and related influencing factors. Am J Epidemiol. 2006, 163: 211-216. 10.1093/aje/kwj034PubMed
46.
go back to reference Miner JR: The incubation period of typhoid fever. J Infect Dis. 1922, 31: 296-301. Miner JR: The incubation period of typhoid fever. J Infect Dis. 1922, 31: 296-301.
47.
go back to reference Elderton WP: Frequency Curves and Correlation 4th edition. Washington DC: Harren Press; 1953. Elderton WP: Frequency Curves and Correlation 4th edition. Washington DC: Harren Press; 1953.
48.
go back to reference Fine PE: The interval between successive cases of an infectious disease. Am J Epidemiol. 2003, 158: 1039-1047. 10.1093/aje/kwg251PubMed Fine PE: The interval between successive cases of an infectious disease. Am J Epidemiol. 2003, 158: 1039-1047. 10.1093/aje/kwg251PubMed
49.
go back to reference Greenwood M: The infectiousness of measles. Biometrika. 1949, 36: 1-8. Greenwood M: The infectiousness of measles. Biometrika. 1949, 36: 1-8.
50.
go back to reference The Editors: In Memoriam: Philip E. Sartwell (1908–1999). Am J Epidemiol. 2000, 151: 439 The Editors: In Memoriam: Philip E. Sartwell (1908–1999). Am J Epidemiol. 2000, 151: 439
51.
go back to reference Sartwell PE: The incubation period of poliomyelitis. Am J Public Health. 1952, 42: 1403-1408. Sartwell PE: The incubation period of poliomyelitis. Am J Public Health. 1952, 42: 1403-1408.
52.
go back to reference Sartwell PE: The incubation period and the dynamics of infectious diseases. Am J Epidemiol. 1966, 83: 204-216.PubMed Sartwell PE: The incubation period and the dynamics of infectious diseases. Am J Epidemiol. 1966, 83: 204-216.PubMed
53.
go back to reference Johnson NL, Kotz S: Continuous univariate distributions Volume 1. Boston: Houghton Mifflin Co.;; 1970. Johnson NL, Kotz S: Continuous univariate distributions Volume 1. Boston: Houghton Mifflin Co.;; 1970.
55.
go back to reference Casey AE: The incubation period in epidemic poliomyelitis. J Am Med Assoc. 1942, 120: 805-807. Casey AE: The incubation period in epidemic poliomyelitis. J Am Med Assoc. 1942, 120: 805-807.
56.
go back to reference Brookmeyer R, Blades N, Hugh-Jones M, Henderson DA: The statistical analysis of truncated data: application to the Sverdlovsk anthrax outbreak. Biostatistics. 2001, 2: 233-247. 10.1093/biostatistics/2.2.233PubMed Brookmeyer R, Blades N, Hugh-Jones M, Henderson DA: The statistical analysis of truncated data: application to the Sverdlovsk anthrax outbreak. Biostatistics. 2001, 2: 233-247. 10.1093/biostatistics/2.2.233PubMed
57.
go back to reference Brookmeyer R, Johnson E, Barry S: Modelling the incubation period of anthrax. Stat Med. 2005, 24: 531-542. 10.1002/sim.2033PubMed Brookmeyer R, Johnson E, Barry S: Modelling the incubation period of anthrax. Stat Med. 2005, 24: 531-542. 10.1002/sim.2033PubMed
58.
go back to reference Armenian HK: Invited commentary on "The distribution of incubation periods of infectious disease". Am J Epidemiol. 1995, 141: 385 Armenian HK: Invited commentary on "The distribution of incubation periods of infectious disease". Am J Epidemiol. 1995, 141: 385
59.
go back to reference Hirayama T: Epidemiology (Ekigaku) Tokyo: Sekibundo Press; 1958. (in Japanese) Hirayama T: Epidemiology (Ekigaku) Tokyo: Sekibundo Press; 1958. (in Japanese)
60.
go back to reference Kanamitsu M, Okada H, Kohno R, Shigematsu I, Hirayama T: Epidemiology and its application (Ekigaku To Sono-ouyou) Tokyo: Nanzando; 1966. (in Japanese) Kanamitsu M, Okada H, Kohno R, Shigematsu I, Hirayama T: Epidemiology and its application (Ekigaku To Sono-ouyou) Tokyo: Nanzando; 1966. (in Japanese)
61.
go back to reference Majkowski J: Strategies for rapid response to emerging foodborne microbial hazards. Emerg Infect Dis. 1997, 3: 551-554.PubMedCentralPubMed Majkowski J: Strategies for rapid response to emerging foodborne microbial hazards. Emerg Infect Dis. 1997, 3: 551-554.PubMedCentralPubMed
62.
go back to reference Armenian HK, Lilienfeld AM: The distribution of incubation periods of neoplastic diseases. Am J Epidemiol. 1974, 99: 92-100.PubMed Armenian HK, Lilienfeld AM: The distribution of incubation periods of neoplastic diseases. Am J Epidemiol. 1974, 99: 92-100.PubMed
63.
go back to reference Horner RD, Samsa G: Criteria for the use of Sartwell's incubation period model to study chronic diseases with uncertain etiology. J Clin Epidemiol. 1992, 45: 1071-1080. 10.1016/0895-4356(92)90147-FPubMed Horner RD, Samsa G: Criteria for the use of Sartwell's incubation period model to study chronic diseases with uncertain etiology. J Clin Epidemiol. 1992, 45: 1071-1080. 10.1016/0895-4356(92)90147-FPubMed
64.
go back to reference Horiuchi K, Nakai S, Ueshima S, Sugiyama H: Theoretical epidemiologic study on the estimation of the time of exposure (Part 1). Jpn J Public Health (Nippon Koshu Eisei Zasshi) 1956, 3:184-186. (in Japanese) Horiuchi K, Nakai S, Ueshima S, Sugiyama H: Theoretical epidemiologic study on the estimation of the time of exposure (Part 1). Jpn J Public Health (Nippon Koshu Eisei Zasshi) 1956, 3:184-186. (in Japanese)
65.
go back to reference Horiuchi K, Oki Y, Sugiyama H: Statistical study of the incubation period of acute communicable diseases. Theoretical Epidemiology (Riron Ekigaku). 1959, 6: 5-17. Horiuchi K, Oki Y, Sugiyama H: Statistical study of the incubation period of acute communicable diseases. Theoretical Epidemiology (Riron Ekigaku). 1959, 6: 5-17.
66.
go back to reference Yamamoto K, Oki Y, Ueshima I, Ueki T: A theoretical, epidemiological estimation of the time of exposure to the source of infection: Application of an estimation method to mass incidence caused by food poisoning. J Osaka City Med Center (Osaka Shiritsu Daigaku Igaku Zasshi) 1958, 7:1040-1043. (in Japanese with English abstract) Yamamoto K, Oki Y, Ueshima I, Ueki T: A theoretical, epidemiological estimation of the time of exposure to the source of infection: Application of an estimation method to mass incidence caused by food poisoning. J Osaka City Med Center (Osaka Shiritsu Daigaku Igaku Zasshi) 1958, 7:1040-1043. (in Japanese with English abstract)
67.
go back to reference Yoshida K, Matsui Y, Kimura K: Some questions concerning the practical application to the graphical method of estimating the time of exposure to the source of infection. Jpn J Public Health (Nippon Koshu Eisei Zasshi) 1960, 7:967-973. (in Japanese with English abstract) Yoshida K, Matsui Y, Kimura K: Some questions concerning the practical application to the graphical method of estimating the time of exposure to the source of infection. Jpn J Public Health (Nippon Koshu Eisei Zasshi) 1960, 7:967-973. (in Japanese with English abstract)
68.
go back to reference Oki Y: Studies on the incubation period of acute infectious diseases from the view point of theoretical epidemiology. J Osaka City Med Center (Osaka Shiritsu Daigaku Igaku Zasshi) 1960, 9:2341-2368. (in Japanese with English abstract) Oki Y: Studies on the incubation period of acute infectious diseases from the view point of theoretical epidemiology. J Osaka City Med Center (Osaka Shiritsu Daigaku Igaku Zasshi) 1960, 9:2341-2368. (in Japanese with English abstract)
69.
go back to reference Kondo K: Exposure analysis -Estimating the time of exposure from case onset information. J Clin Exp Med (Igaku No Ayumi) 1972, 82:576. (in Japanese) Kondo K: Exposure analysis -Estimating the time of exposure from case onset information. J Clin Exp Med (Igaku No Ayumi) 1972, 82:576. (in Japanese)
70.
go back to reference Sakamoto K: Incubation period distribution of communicable disease. In Epidemiology and epidemiological model (Ekigaku To Ekigaku Model) Kyoto: Kinpodo; 1985:290-298. (in Japanese) Sakamoto K: Incubation period distribution of communicable disease. In Epidemiology and epidemiological model (Ekigaku To Ekigaku Model) Kyoto: Kinpodo; 1985:290-298. (in Japanese)
71.
go back to reference Horiuchi K: Theoretical epidemiologic study on the estimation of the time of exposure (Part 2). Theoretical Epidemiology (Riron Ekigaku) 1956, 3:35-42. (in Japanese) Horiuchi K: Theoretical epidemiologic study on the estimation of the time of exposure (Part 2). Theoretical Epidemiology (Riron Ekigaku) 1956, 3:35-42. (in Japanese)
72.
go back to reference Horiuchi K: Speculation on the incubation period. Theoretical Epidemiology (Riron Ekigaku) 1957, 4:9-16. (in Japanese) Horiuchi K: Speculation on the incubation period. Theoretical Epidemiology (Riron Ekigaku) 1957, 4:9-16. (in Japanese)
73.
go back to reference Mizuno H, Ito A, Hotta I, Morita J: An experimental study on applicable limits of the estimating-method for the exposed point of infection. Jpn J Public Health (Nippon Koshu Eisei Zasshi) 1960, 7:391-394. (in Japanese with English abstract) Mizuno H, Ito A, Hotta I, Morita J: An experimental study on applicable limits of the estimating-method for the exposed point of infection. Jpn J Public Health (Nippon Koshu Eisei Zasshi) 1960, 7:391-394. (in Japanese with English abstract)
74.
go back to reference Kato H: Epidemiological studies on the incubation periods of infectious diseases. II. Influence of the biological factors upon the incubation periods. Sapporo Med J (Sapporo Igaku Zasshi) 1955, 7:260-266. (in Japanese with English abstract) Kato H: Epidemiological studies on the incubation periods of infectious diseases. II. Influence of the biological factors upon the incubation periods. Sapporo Med J (Sapporo Igaku Zasshi) 1955, 7:260-266. (in Japanese with English abstract)
75.
go back to reference Kimura K: On the variability in the distribution of incubation periods in the case of mass occurrence of dysentery. Mie Med J. 1960, 10: 87-102. Kimura K: On the variability in the distribution of incubation periods in the case of mass occurrence of dysentery. Mie Med J. 1960, 10: 87-102.
76.
go back to reference Meynell GG: Interpretation of distributions of individual response times in microbial infections. Nature. 1963, 198: 970-973. 10.1038/198970b0PubMed Meynell GG: Interpretation of distributions of individual response times in microbial infections. Nature. 1963, 198: 970-973. 10.1038/198970b0PubMed
77.
go back to reference Tango T: Maximum likelihood estimation of date of infection in an outbreak of diarrhea due to contaminated foods assuming lognormal distribution for the incubation period. Nippon Koshu Eisei Zasshi 1998, 45:129-141. (in Japanese with English abstract)PubMed Tango T: Maximum likelihood estimation of date of infection in an outbreak of diarrhea due to contaminated foods assuming lognormal distribution for the incubation period. Nippon Koshu Eisei Zasshi 1998, 45:129-141. (in Japanese with English abstract)PubMed
78.
go back to reference Giesbrecht F, Kempthorne O: Maximum likelihood estimation in three-parameter lognormal distribution. J R Stat Soc Ser B. 1976, 38: 257-264. Giesbrecht F, Kempthorne O: Maximum likelihood estimation in three-parameter lognormal distribution. J R Stat Soc Ser B. 1976, 38: 257-264.
79.
go back to reference Cohen AC, Whitten BT: Estimation in the three-parameter lognormal distribution. J Am Stat Assoc. 1980, 75: 399-404. 10.2307/2287466. 10.2307/2287466 Cohen AC, Whitten BT: Estimation in the three-parameter lognormal distribution. J Am Stat Assoc. 1980, 75: 399-404. 10.2307/2287466. 10.2307/2287466
80.
go back to reference Hill BM: The three-parameter lognormal distribution and Bayesian analysis of a point-source epidemic. J Am Stat Assoc. 1963, 58: 72-84. 10.2307/2282955. 10.2307/2282955 Hill BM: The three-parameter lognormal distribution and Bayesian analysis of a point-source epidemic. J Am Stat Assoc. 1963, 58: 72-84. 10.2307/2282955. 10.2307/2282955
81.
go back to reference Tango T: Topics II: Food-borne outbreak caused by Esherichia coli O-157. In Introduction to Statistical Model (Tokei Model) Tokyo: Asakura Publishing Co; 2000:6-17. (in Japanese) Tango T: Topics II: Food-borne outbreak caused by Esherichia coli O-157. In Introduction to Statistical Model (Tokei Model) Tokyo: Asakura Publishing Co; 2000:6-17. (in Japanese)
82.
go back to reference Cohen AC: Three-parameter estimation. In Lognormal Distribution- Theory and Applications Edited by: Crow EL, Shimizu K. New York: Marcel Dekker; 1988:113-137. Cohen AC: Three-parameter estimation. In Lognormal Distribution- Theory and Applications Edited by: Crow EL, Shimizu K. New York: Marcel Dekker; 1988:113-137.
83.
go back to reference Fenner F: The pathogenesis of the acute exanthems. An interpretation based upon experimental investigation with mouse-pox (infectious ectromelia of mice). Lancet. 1948, ii: 915-920. 10.1016/S0140-6736(48)91599-2. 10.1016/S0140-6736(48)91599-2 Fenner F: The pathogenesis of the acute exanthems. An interpretation based upon experimental investigation with mouse-pox (infectious ectromelia of mice). Lancet. 1948, ii: 915-920. 10.1016/S0140-6736(48)91599-2. 10.1016/S0140-6736(48)91599-2
84.
go back to reference Meynell GG, Meynell EW: The growth of micro-organisms in vivo with particular reference to the relation between dose and latent period. J Hyg (Lond). 1958, 56: 323-346. Meynell GG, Meynell EW: The growth of micro-organisms in vivo with particular reference to the relation between dose and latent period. J Hyg (Lond). 1958, 56: 323-346.
85.
go back to reference Gart JJ: Some stochastic models relating time and dosage in response curves. Biometrics. 1965, 21: 583-599. 10.2307/2528543PubMed Gart JJ: Some stochastic models relating time and dosage in response curves. Biometrics. 1965, 21: 583-599. 10.2307/2528543PubMed
86.
go back to reference Williams T: The distribution of response times in a birth-death process. Biometrika. 1965, 52: 581-585.PubMed Williams T: The distribution of response times in a birth-death process. Biometrika. 1965, 52: 581-585.PubMed
87.
go back to reference Williams T: The basic birth-death model for microbial infection. J R Stat Soc Ser B. 1965, 27: 338-360. Williams T: The basic birth-death model for microbial infection. J R Stat Soc Ser B. 1965, 27: 338-360.
88.
go back to reference Armitage P, Meynell GG, Williams T: Birth-death and other models for microbial infection. Nature. 1965, 207: 570-572. 10.1038/207570a0PubMed Armitage P, Meynell GG, Williams T: Birth-death and other models for microbial infection. Nature. 1965, 207: 570-572. 10.1038/207570a0PubMed
89.
go back to reference Puri PS: A class of stochastic models of response after infection in the absence of defense mechanism. In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability (June 21-July 18, 1965 and December 27, 1965-January 7, 1966) Edited by: le Cam LM, Neyman J. Los Angeles: University of California Press; 1967:511-535. Puri PS: A class of stochastic models of response after infection in the absence of defense mechanism. In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability (June 21-July 18, 1965 and December 27, 1965-January 7, 1966) Edited by: le Cam LM, Neyman J. Los Angeles: University of California Press; 1967:511-535.
90.
go back to reference Kondo K: The lognormal distribution of the incubation time of exogenous diseases. Genetic interpretations and a computer simulation. Jinrui Idengaku Zasshi. 1977, 21: 217-237.PubMed Kondo K: The lognormal distribution of the incubation time of exogenous diseases. Genetic interpretations and a computer simulation. Jinrui Idengaku Zasshi. 1977, 21: 217-237.PubMed
91.
go back to reference Lawrence RJ: The lognormal as event-time distribution. In Lognormal Distribution- Theory and Applications Edited by: Crow EL, Shimizu K. New York: Marcel Dekker; 1988:211-228. Lawrence RJ: The lognormal as event-time distribution. In Lognormal Distribution- Theory and Applications Edited by: Crow EL, Shimizu K. New York: Marcel Dekker; 1988:211-228.
92.
go back to reference Netea MG, Kullberg BJ, Van der Meer JW: Circulating cytokines as mediators of fever. Clin Infect Dis. 2000, 31: S178-S184. 10.1086/317513PubMed Netea MG, Kullberg BJ, Van der Meer JW: Circulating cytokines as mediators of fever. Clin Infect Dis. 2000, 31: S178-S184. 10.1086/317513PubMed
93.
go back to reference Kuk AY, Ma S: The estimation of SARS incubation distribution from serial interval data using a convolution likelihood. Stat Med. 2005, 24: 2525-2537. 10.1002/sim.2123PubMed Kuk AY, Ma S: The estimation of SARS incubation distribution from serial interval data using a convolution likelihood. Stat Med. 2005, 24: 2525-2537. 10.1002/sim.2123PubMed
94.
go back to reference Cowling BJ, Muller MP, Wong IO, Ho LM, Louie M, McGeer A, Leung GM: Alternative methods of estimating an incubation distribution: Examples from severe acute respiratory syndrome. Epidemiology. 2007, 18: 253-259. 10.1097/01.ede.0000254660.07942.fbPubMed Cowling BJ, Muller MP, Wong IO, Ho LM, Louie M, McGeer A, Leung GM: Alternative methods of estimating an incubation distribution: Examples from severe acute respiratory syndrome. Epidemiology. 2007, 18: 253-259. 10.1097/01.ede.0000254660.07942.fbPubMed
95.
go back to reference Riley S, Ferguson NM: Smallpox transmission and control: spatial dynamics in Great Britain. Proc Natl Acad Sci USA. 2006, 103: 12637-12642. 10.1073/pnas.0510873103PubMedCentralPubMed Riley S, Ferguson NM: Smallpox transmission and control: spatial dynamics in Great Britain. Proc Natl Acad Sci USA. 2006, 103: 12637-12642. 10.1073/pnas.0510873103PubMedCentralPubMed
96.
go back to reference Nishiura H, Eichner M: Interpreting the epidemiology of postexposure vaccination against smallpox. Int J Hyg Environ Health 2007 in press. (doi:10.1016/j.ijheh.2007.01.029) Nishiura H, Eichner M: Interpreting the epidemiology of postexposure vaccination against smallpox. Int J Hyg Environ Health 2007 in press. (doi:10.1016/j.ijheh.2007.01.029)
97.
go back to reference Ferguson NM, Donnelly CA, Woolhouse ME, Anderson RM: The epidemiology of BSE in cattle herds in Great Britain. II. Model construction and analysis of transmission dynamics. Philos Trans R Soc Lond B Biol Sci. 1997, 352: 803-808. 10.1098/rstb.1997.0063PubMedCentralPubMed Ferguson NM, Donnelly CA, Woolhouse ME, Anderson RM: The epidemiology of BSE in cattle herds in Great Britain. II. Model construction and analysis of transmission dynamics. Philos Trans R Soc Lond B Biol Sci. 1997, 352: 803-808. 10.1098/rstb.1997.0063PubMedCentralPubMed
98.
go back to reference Nowak MA, Krakauer DC, Klug A, May RM: Prion infection dynamics. Integr Biol. 1998, 1: 3-15. 10.1002/(SICI)1520-6602(1998)1:1<3::AID-INBI2>3.0.CO;2-9. 10.1002/(SICI)1520-6602(1998)1:1<3::AID-INBI2>3.0.CO;2-9 Nowak MA, Krakauer DC, Klug A, May RM: Prion infection dynamics. Integr Biol. 1998, 1: 3-15. 10.1002/(SICI)1520-6602(1998)1:1<3::AID-INBI2>3.0.CO;2-9. 10.1002/(SICI)1520-6602(1998)1:1<3::AID-INBI2>3.0.CO;2-9
99.
go back to reference Masel J, Jansen VA, Nowak MA: Quantifying the kinetic parameters of prion replication. Biophys Chem. 1999, 77: 139-152. 10.1016/S0301-4622(99)00016-2PubMed Masel J, Jansen VA, Nowak MA: Quantifying the kinetic parameters of prion replication. Biophys Chem. 1999, 77: 139-152. 10.1016/S0301-4622(99)00016-2PubMed
100.
go back to reference Dietz K: Epidemics and rumors: A survey. J R Stat Soc Ser A. 1967, 130: 505-528. 10.2307/2982521. 10.2307/2982521 Dietz K: Epidemics and rumors: A survey. J R Stat Soc Ser A. 1967, 130: 505-528. 10.2307/2982521. 10.2307/2982521
101.
go back to reference Morgan BJT, Watts SA: On modelling microbial infections. Biometrics. 1980, 36: 317-321. 10.2307/2529985PubMed Morgan BJT, Watts SA: On modelling microbial infections. Biometrics. 1980, 36: 317-321. 10.2307/2529985PubMed
102.
go back to reference Nowak MA, May RM: Virus Dynamics Mathematical Principles of Immunology and Virology New York: Oxford University Press; 2000 Nowak MA, May RM: Virus Dynamics Mathematical Principles of Immunology and Virology New York: Oxford University Press; 2000
103.
go back to reference Bailey NTJ: A statistical method of estimating the periods of incubation and infection of an infectious diseases. Nature. 1954, 174: 139-140. 10.1038/174139a0PubMed Bailey NTJ: A statistical method of estimating the periods of incubation and infection of an infectious diseases. Nature. 1954, 174: 139-140. 10.1038/174139a0PubMed
104.
go back to reference Bailey NTJ: The mathematical theory of infectious diseases and its applications 2nd edition. London: Griffin; 1975. Bailey NTJ: The mathematical theory of infectious diseases and its applications 2nd edition. London: Griffin; 1975.
105.
go back to reference Nishiura H: Epidemiology of a primary pneumonic plague in Kantoshu, Manchuria, from 1910 to 1911: statistical analysis of individual records collected by the Japanese Empire. Int J Epidemiol. 2006, 35: 1059-1065. 10.1093/ije/dyl091PubMed Nishiura H: Epidemiology of a primary pneumonic plague in Kantoshu, Manchuria, from 1910 to 1911: statistical analysis of individual records collected by the Japanese Empire. Int J Epidemiol. 2006, 35: 1059-1065. 10.1093/ije/dyl091PubMed
Metadata
Title
Early efforts in modeling the incubation period of infectious diseases with an acute course of illness
Author
Hiroshi Nishiura
Publication date
01-12-2007
Publisher
BioMed Central
Published in
Emerging Themes in Epidemiology / Issue 1/2007
Electronic ISSN: 1742-7622
DOI
https://doi.org/10.1186/1742-7622-4-2

Other articles of this Issue 1/2007

Emerging Themes in Epidemiology 1/2007 Go to the issue