Real-time forecasting of an epidemic using a discrete time stochastic model: A case study of pandemic influenza (H1N1-2009)

BioMedical Engineering Online

Volumn 10, Issue , 2011, Pages

  Nishiura, Hiroshi ^a,b,c  

^a JAPAN SCIENCE AND TECHNOLOGY AGENCY   (Japan)

^b UTRECHT UNIVERSITY   (Netherlands)

^c UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

BRANCHING PROCESS; CONDITIONAL MEASUREMENTS; DEMOGRAPHIC STOCHASTICITY; DISCRETE TIME; DISEASE SURVEILLANCE; EPIDEMIC CURVE; LINEAR GROWTH; OBSERVED DATA; PANDEMIC INFLUENZA; PARAMETER ESTIMATE; REAL-TIME FORECASTING; SIMPLE METHOD; TIME-DEPENDENT; TRANSMISSION DYNAMICS; TWO PARAMETER; UNCERTAINTY BOUNDS;

EPIDEMIOLOGY; FORECASTING; STOCHASTIC SYSTEMS; UNCERTAINTY ANALYSIS;

STOCHASTIC MODELS;

ARTICLE; DISEASE PREDISPOSITION; DISEASE TRANSMISSION; FORECASTING; HUMAN; INFLUENZA; INFLUENZA VIRUS A H1N1; METHODOLOGY; PANDEMIC; PHYSIOLOGY; STATISTICS; TIME; VIROLOGY;

DISEASE SUSCEPTIBILITY; FORECASTING; HUMANS; INFLUENZA A VIRUS, H1N1 SUBTYPE; INFLUENZA, HUMAN; PANDEMICS; STOCHASTIC PROCESSES; TIME FACTORS;

EID: 79951557043     PISSN: 1475925X     EISSN: 1475925X     Source Type: Journal    
DOI: 10.1186/1475-925X-10-15     Document Type: Article

References (52)

1. Murray JD. Mathematical Biology: I. An Introduction (Interdisciplinary Applied Mathematics) 2007, New York: Springer, 3.
2. Boutayab A, Chetouani A. A critical review of mathematical models and data used in diabetology. Biomed Eng Online 2006, 5:43.
3. Brauer F, Castillo-Chavez C. Mathematical Models in Population Biology and Epidemiology 2001, New York: Springer.
4. Keeling MJ, Rohani P. Modelling Infectious Diseases in Humans & Animals 2007, Princeton: Princeton University Press.
5. Derouich M, Boutayab A, Twizell EH. A model of dengue fever. Biomed Eng Online 2003, 2:4.
6. Anderson RM, May RM. Infectious Diseases of Humans: Dynamics and Control 1992, New York: Oxford University Press.
7. Anonymous Mathematical modelling of the pandemic H1N1 2009. Wkly Epidemiol Rec 2009, 84:341-348. Anonymous.
8. Massad E, Burattini MN, Lopez LF, Coutinho FA. Forecasting versus projection models in epidemiology: the case of the SARS epidemics. Med Hypotheses 2005, 65:17-22.
9. Cox DR, Davison AC. Prediction for small subgroups. Philos Trans R Soc Lond B Biol Sci 1989, 325:185-187.
10. Solomon PJ, Wilson SR. Prediction of new cases of disease or infection for small subgroups. Biomet J 1993, 3:333-341.
11. Banks HT, Davidan M, Samuels JR, Sutton KL. An inverse problem statistical methodology summary. Mathematical and Statistical Estimation Approaches in Epidemiology 2009, 249-302. New York: Springer, Chowell G, Hyman JM, Bettencourt LMA, Castillo-Chavez C.
12. Chowell G, Fenimore PW, Castillo-Garsow MA, Castillo-Chavez C. SARS outbreaks in Ontario, Hong Kong and Singapore: the role of diagnosis and isolation as a control mechanism. J Theor Biol 2003, 224:1-8.
13. Keyfitz N. On future population. J Am Stat Assoc 1972, 67:347-363.
14. Ferguson NM, Cummings DA, Fraser C, Cajka JC, Cooley PC, Burke DS. Strategies for mitigating an influenza pandemic. Nature 2006, 442:448-452.
15. Longini IM, Halloran ME, Nizam A, Yang Y. Containing pandemic influenza with antiviral agents. Am J Epidemiol 2004, 159:623-633.
16. Farrington CP, Andrews N. Outbreak Detection: Application to Infectious Disease Surveillance. Monitoring the Health of Populations: Statistical Principles and Methods for Public Health Surveillance 2003, 203-231. New York: Oxford University Press, Brookmeyer R, Stroup DF.
17. Cauchemez S, Boelle PY, Donnelly CA, Ferguson NM, Thomas G, Leung GM, Hedley AJ, Anderson RM, Valleron AJ. Real-time estimates in early detection of SARS. Emerg Infect Dis 2006, 12:110-113.
18. Hsieh YH, Cheng YS. Real-time forecast of multiphase outbreak. Emerg Infect Dis 2006, 12:122-127.
19. Hsieh YH. Pandemic influenza A (H1N1) during winter influenza season in the southern hemisphere. Influenza Other Respi Viruses 2010, 4:187-197.
20. Diekmann O, Heesterbeek JAP. Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation (Wiley Series in Mathematical & Computational Biology) 2000, New York: Wiley.
21. Omori R, Nishiura H. Theoretical basis to measure the impact of short-lasting control of an infectious disease on the epidemic peak. Theor Biol Med Model 2011, 8:2.
22. Hall IM, Gani R, Hughes HE, Leach S. Real-time epidemic forecasting for pandemic influenza. Epidemiol Infect 2007, 135:372-385.
23. Ong JB, Chen MI, Cook AR, Lee HC, Lee VJ, Lin RT, Tambyah PA, Goh LG. Real-time epidemic monitoring and forecasting of H1N1-2009 using influenza-like illness from general practice and family doctor clinics in Singapore. PLoS One 2010, 5:e10036.
24. Nishiura H. Joint quantification of transmission dynamics and diagnostic accuracy applied to influenza. Math Biosci Eng 2011, 8:49-64.
25. Nishiura H, Castillo-Chavez C, Safan M, Chowell G. Transmission potential of the new influenza A(H1N1) virus and its age-specificity in Japan. Euro Surveill 2009, 14. pii=19227.
26. Nishiura H, Chowell G, Safan M, Castillo-Chavez C. Pros and cons of estimating the reproduction number from early epidemic growth rate of influenza A (H1N1) 2009. Theor Biol Med Model 2010, 7:1.
27. van den Broek J, Nishiura H. Using epidemic prevalence data to jointly estimate reproduction and removal. Ann Appl Stat 2009, 3:1505-1520.
28. Andersson H, Britton T. Stochastic Epidemic Models and Their Statistical Analysis 2000, New York: Springer.
29. Becker NG. Analysis of Infectious Disease Data 1989, London: Chapman & Hall.
30. Nishiura H, Kakehashi M, Inaba H. Two critical issues in quantitative modeling of communicable diseases: Inference of unobservables and dependent happening. Mathematical and Statistical Estimation Approaches in Epidemiology 2009, 53-87. New York: Springer, Chowell G, Hyman JM, Bettencourt LMA, Castillo-Chavez C.
31. Daley DJ, Gani J. Epidemic Modelling: An Introduction (Cambridge Studies in Mathematical Biology) 2001, Cambridge: Cambridge University Press.
32. Abbey H. An examination of the Reed Frost theory of epidemics. Hum Biol 1952, 24:201-233.
33. Fine PEM. A commentary on the mechanical analogue to the Reed-Frost epidemic model. Am J Epidemiol 1977, 106:87-100.
34. Ferrari MJ, Bjørnstad ON, Dobson AP. Estimation and inference of R0 of an infectious pathogen by a removal method. Math Biosci 2005, 198:14-26.
35. Ball F, O'Neill P. The distribution of general final state random variables for stochastic epidemic models. J Appl Prob 1999, 36:473-491.
36. Sellke T. On the asymptotic distribution of the size of a stochastic epidemic. J Appl Prob 1983, 20:390-394.
37. Barbour AD, Utev S. Approximating the Reed-Frost epidemic process. Stochastic Process Appl 2004, 113:173-197.
38. Nishiura H. Time variations in the generation time of an infectious disease: Implications for sampling to appropriately quantify transmission potential. Math Biosci Eng 2010, 7:851-869.
39. Hahné S, Donker T, Meijer A, Timen A, van Steenbergen J, Osterhaus A, van der Sande M, Koopmans M, Wallinga J, Coutinho R, . Dutch New Influenza A(H1N1)v Investigation Team Epidemiology and control of influenza A(H1N1)v in the Netherlands: the first 115 cases. Euro Surveill 2009, 14. pii=19267, Dutch New Influenza A(H1N1)v Investigation Team.
40. Nishiura H, Chowell G, Heesterbeek H, Wallinga J. The ideal reporting interval for an epidemic to objectively interpret the epidemiological time course. J R Soc Interface 2010, 7:297-307.
41. Nishiura H, Chowell G. The effective reproduction number as a prelude to statistical estimation of time-dependent epidemic trends. Mathematical and Statistical Estimation Approaches in Epidemiology 2009, 103-121. New York: Springer, Chowell G, Hyman JM, Bettencourt LMA, Castillo-Chavez C.
42. Nishiura H, Omori R. An epidemiological analysis of the foot-and-mouth disease epidemic in Miyazaki, Japan, 2010. Transbound Emerg Dis 2010, 57:396-403.
43. Wallinga J, Lipsitch M. How generation intervals shape the relationship between growth rates and reproductive numbers. Proc R Soc Lond Ser B 2007, 274:599-604.
44. Lindsey JK. Nonlinear Models in Medical Statistics (Oxford Statistical Science Series 24) 2001, Oxford: Oxford University Press.
45. Ma J, Earn DJ. Generality of the final size formula for an epidemic of a newly invading infectious disease. Bull Math Biol 2006, 68:679-702.
46. Sanchez MA, Blower SM. Uncertainty and sensitivity analysis of the basic reproductive rate. Tuberculosis as an example. Am J Epidemiol 1997, 145:1127-1137.
47. Lloyd-Smith JO, Schreiber SJ, Kopp PE, Getz WM. Superspreading and the effect of individual variation on disease emergence. Nature 2005, 438:355-359.
48. Armstrong JS. Evaluating forecasting methods. Principles of Forecasting: A Handbook for Researchers and Practitioners 2001, 443-472. Boston: Kluwer Academic Publishers, Armstrong JS.
49. Miller E, Hoschler K, Hardelid P, Stanford E, Andrews N, Zambon M. Incidence of 2009 pandemic influenza A H1N1 infection in England: a cross-sectional serological study. Lancet 2010, 375:1100-1108.
50. Chatfield C. Prediction Intervals for Time-Series Forecasting. Principles of Forecasting: A Handbook for Researchers and Practitioners 2001, 475-494. Boston: Kluwer Academic Publishers, Armstrong JS.
51. Ball F, Clancy D. The final size and severity of a generalised stochastic multitype epidemic model. Adv Appl Prob 1993, 25:721-736.
52. Balcan D, Hu H, Goncalves B, Bajardi P, Poletto C, Ramasco JJ, Paolotti D, Perra N, Tizzoni M, Van den Broeck W, Colizza V, Vespignani A. Seasonal transmission potential and activity peaks of the new influenza A(H1N1): a Monte Carlo likelihood analysis based on human mobility. BMC Med 2009, 7:45.