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PLOS ONE  2009 

Predicting the Herd Immunity Threshold during an Outbreak: A Recursive Approach

DOI: 10.1371/journal.pone.0004168

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Abstract:

Background The objective was to develop a novel algorithm that can predict, based on field survey data, the minimum vaccination coverage required to reduce the mean number of infections per infectious individual to less than one (the Outbreak Response Immunization Threshold or ORIT) from up to six days in the advance. Methodology/Principal Findings First, the relationship between the rate of immunization and the ORIT was analyzed to establish a link. This relationship served as the basis for the development of a recursive algorithm that predicts the ORIT using survey data from two consecutive days. The algorithm was tested using data from two actual measles outbreaks. The prediction day difference (PDD) was defined as the number of days between the second day of data input and the day of the prediction. The effects of different PDDs on the prediction error were analyzed, and it was found that a PDD of 5 minimized the error in the prediction. In addition, I developed a model demonstrating the relationship between changes in the vaccination coverage and changes in the individual reproduction number. Conclusions/Significance The predictive algorithm for the ORIT generates a viable prediction of the minimum number of vaccines required to stop an outbreak in real time. With this knowledge, the outbreak control agency may plan to expend the lowest amount of funds required stop an outbreak, allowing the diversion of the funds saved to other areas of medical need.

References

[1]  Sniadack D, Moscoso B, Aguilar R, Heath J, Bellini W, et al. (1999) Measles epidemiology and outbreak response immunization in a rural community in Peru. B World Health Organ 77(7): 545–552.
[2]  Grais R, Conlan A, Ferrari M, Djibo A, Le Menach A, et al. (2007) Time is of the essence: exploring a measles outbreak response vaccination in Niamey, Niger. J R Soc Interface 5(18): 67–74.
[3]  White C, Koplan J, Orenstein W (1985) Benefits, Risks, and Costs of Immunization for Measles, Mumps, and Rubella. Am J Public Health 75(7): 739–744.
[4]  Farrington C, Whitaker H (2003) Estimation of effective reproduction numbers for infectious diseases using serological survey data. Biostatistics 4(4): 621–632.
[5]  Fine PE (1993) Herd Immunity: History, Theory, Practice. Epidemiol Rev 15(2): 265–302.
[6]  John T, Samuel R (2000) Herd immunity and herd effect: new insights and definitions. Eur J Epidemiol 16(7): 601–606.
[7]  World Health Organization (2007) Measles Fact Sheet.
[8]  Robertson S, Markowitz L, Berry D, Dini E, Orenstein W (1992) A Million Dollar Measles Outbreak: Epidemiology, Risk Factors, and a Selective Revaccination Strategy. Public Health Rep 107(1): 24–31.
[9]  Centers for Disease Control and Prevention (2003) Vaccine Management: Handling and Storage Details for Vaccines.
[10]  Anderson R, May R (1991) Infectious Diseases of Humans: Dynamics and Control. Oxford: Oxford Science Publications.
[11]  Diekmann O, Heesterbeek J, Metz J (1998) On the definition and computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. J Math Biol 28(4): 365–382.
[12]  Fraser C (2007) Estimating Individual and Household Reproduction Numbers in an Emerging Epidemic. PLoS ONE 2(8): e758. doi:10.1371/journal.pone.0000758.
[13]  Bettencourt LMA, Ribeiro RM (2008) Real Time Bayesian Estimation of the Epidemic Potential of Emerging Infectious Diseases. PLoS ONE 3(5): e2185. doi:10.1371/journal.pone.0002185.
[14]  Wallinga J, Lipsitch M (2007) How generation intervals shape the relationship between growth rates and reproductive numbers. Proc R Soc Ser B-Bio 274(1609): 599–604.
[15]  Cauchemez S, Bo?lle P, Thomas G, Valleron A (2006) Estimating in real time the efficacy of measures to control emerging communicable diseases. Am J Epidemiol 164(6): 591–597.
[16]  Hartnell B (1995) Firefighter! An Application of Domination, presentation, Twentieth Conference on Numerical Mathematics and Computing, University of Manitoba in Winnipeg, Canada.
[17]  Develin M, Hartke SG (2007) Fire Containment in Grids of Dimension Three and Higher. Discrete Applied Mathematics 155(17): 2257–2268.
[18]  Ng KL, Raff P (2008) A generalization of the firefighter problem on z x z. Discrete Applied Mathematics 156(5): 730–745.
[19]  Georgette N (2007) The Quantification Of The Effects Of Changes In Population Parameters On The Herd Immunity Threshold. Internet J Epidemiol 5(1).
[20]  Hyde T, Dayan G, Langidrik J, Nandy R, Edwards R, et al. (2006) Measles outbreak in the Republic of the Marshall Islands, 2003. Int J Epidemiol 35(2): 299–306.
[21]  Samuela S, Tuiketei T, Duncan R, Kubo T, Kool J, et al. (2006) Measles Outbreak and Response—Fiji, February–May 2006. MMWR 55(35): 963–966.

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