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

Nishiura H - Biomed Eng Online (2011)

Bottom Line: The forecasts of both weekly incidence and final epidemic size greatly improved at and after the epidemic peak with all the observed data points falling within the uncertainty bounds.Real-time forecasting using the discrete time stochastic model with its simple computation of the uncertainty bounds was successful.Because of the simplistic model structure, the proposed model has the potential to additionally account for various types of heterogeneity, time-dependent transmission dynamics and epidemiological details.

View Article: PubMed Central - HTML - PubMed

Affiliation: PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama, Japan. nishiura@hku.hk

ABSTRACT

Background: Real-time forecasting of epidemics, especially those based on a likelihood-based approach, is understudied. This study aimed to develop a simple method that can be used for the real-time epidemic forecasting.

Methods: A discrete time stochastic model, accounting for demographic stochasticity and conditional measurement, was developed and applied as a case study to the weekly incidence of pandemic influenza (H1N1-2009) in Japan. By imposing a branching process approximation and by assuming the linear growth of cases within each reporting interval, the epidemic curve is predicted using only two parameters. The uncertainty bounds of the forecasts are computed using chains of conditional offspring distributions.

Results: The quality of the forecasts made before the epidemic peak appears largely to depend on obtaining valid parameter estimates. The forecasts of both weekly incidence and final epidemic size greatly improved at and after the epidemic peak with all the observed data points falling within the uncertainty bounds.

Conclusions: Real-time forecasting using the discrete time stochastic model with its simple computation of the uncertainty bounds was successful. Because of the simplistic model structure, the proposed model has the potential to additionally account for various types of heterogeneity, time-dependent transmission dynamics and epidemiological details. The impact of such complexities on forecasting should be explored when the data become available as part of the disease surveillance.

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Weekly incidence of influenza cases in Japan from 2009-10. The vertical axis represents the estimated weekly number of cases based on a nationwide sentinel surveillance, covering the period from week 27 (the week ending on 5 July 2009) to week 18 (the week ending on 9 May 2010). The estimates, based on the notified number of cases from a total of 4800 randomly sampled sentinel hospitals, are extrapolated to the total number of medical facilities in Japan. The case represents all influenza-like illness cases that received medical attendance. During the period of interest, influenza A (H1N1-2009) dominated all influenza viruses that were isolated. The four arrows indicate the weeks (weeks 42, 45, 48 and 51 in 2009) that were used for the model predictions in the present study.
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Figure 1: Weekly incidence of influenza cases in Japan from 2009-10. The vertical axis represents the estimated weekly number of cases based on a nationwide sentinel surveillance, covering the period from week 27 (the week ending on 5 July 2009) to week 18 (the week ending on 9 May 2010). The estimates, based on the notified number of cases from a total of 4800 randomly sampled sentinel hospitals, are extrapolated to the total number of medical facilities in Japan. The case represents all influenza-like illness cases that received medical attendance. During the period of interest, influenza A (H1N1-2009) dominated all influenza viruses that were isolated. The four arrows indicate the weeks (weeks 42, 45, 48 and 51 in 2009) that were used for the model predictions in the present study.

Mentions: To clearly explain the motivation in carrying out this study, the empirical data of the pandemic (H1N1-2009) in Japan is first presented. Figure 1 shows the estimated weekly number of influenza cases based on national sentinel surveillance in Japan from week 27 in 2009 (the week ending 5 July) to week 18 in 2010 (the week ending 9 May). The estimates follow an extrapolation of the notified number of cases from a total of 4,800 randomly sampled sentinel hospitals to the total number of medical facilities in Japan. The notified cases represent patients who sought medical attendance and who met the following criteria, (a) acute course of illness (sudden onset), (b) fever higher than 38°C, (c) cough, sputum or breathlessness (symptoms of upper respiratory infection), and (d) general fatigue, or patients who were strongly suspected of having the disease and who undertook laboratory diagnosis (e.g. rapid diagnostic testing). Although the estimates of sentinel surveillance data have various epidemiological biases and errors, these issues have been ignored in the present study. For instance, by examining the information for test negative individuals, an unbiased estimate of true incidence of influenza (an estimate that excludes influenza-like illnesses due to other causes) could potentially be made [24]. However, no comprehensive data set is available and so the issue of misclassification is disregarded for now. During the period of interest, influenza A (H1N1-2009) substantially dominated all other isolated influenza viruses. The dynamics of confirmed cases during the very early epidemic phases have been reported elsewhere [25,26].


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

Nishiura H - Biomed Eng Online (2011)

Weekly incidence of influenza cases in Japan from 2009-10. The vertical axis represents the estimated weekly number of cases based on a nationwide sentinel surveillance, covering the period from week 27 (the week ending on 5 July 2009) to week 18 (the week ending on 9 May 2010). The estimates, based on the notified number of cases from a total of 4800 randomly sampled sentinel hospitals, are extrapolated to the total number of medical facilities in Japan. The case represents all influenza-like illness cases that received medical attendance. During the period of interest, influenza A (H1N1-2009) dominated all influenza viruses that were isolated. The four arrows indicate the weeks (weeks 42, 45, 48 and 51 in 2009) that were used for the model predictions in the present study.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3045989&req=5

Figure 1: Weekly incidence of influenza cases in Japan from 2009-10. The vertical axis represents the estimated weekly number of cases based on a nationwide sentinel surveillance, covering the period from week 27 (the week ending on 5 July 2009) to week 18 (the week ending on 9 May 2010). The estimates, based on the notified number of cases from a total of 4800 randomly sampled sentinel hospitals, are extrapolated to the total number of medical facilities in Japan. The case represents all influenza-like illness cases that received medical attendance. During the period of interest, influenza A (H1N1-2009) dominated all influenza viruses that were isolated. The four arrows indicate the weeks (weeks 42, 45, 48 and 51 in 2009) that were used for the model predictions in the present study.
Mentions: To clearly explain the motivation in carrying out this study, the empirical data of the pandemic (H1N1-2009) in Japan is first presented. Figure 1 shows the estimated weekly number of influenza cases based on national sentinel surveillance in Japan from week 27 in 2009 (the week ending 5 July) to week 18 in 2010 (the week ending 9 May). The estimates follow an extrapolation of the notified number of cases from a total of 4,800 randomly sampled sentinel hospitals to the total number of medical facilities in Japan. The notified cases represent patients who sought medical attendance and who met the following criteria, (a) acute course of illness (sudden onset), (b) fever higher than 38°C, (c) cough, sputum or breathlessness (symptoms of upper respiratory infection), and (d) general fatigue, or patients who were strongly suspected of having the disease and who undertook laboratory diagnosis (e.g. rapid diagnostic testing). Although the estimates of sentinel surveillance data have various epidemiological biases and errors, these issues have been ignored in the present study. For instance, by examining the information for test negative individuals, an unbiased estimate of true incidence of influenza (an estimate that excludes influenza-like illnesses due to other causes) could potentially be made [24]. However, no comprehensive data set is available and so the issue of misclassification is disregarded for now. During the period of interest, influenza A (H1N1-2009) substantially dominated all other isolated influenza viruses. The dynamics of confirmed cases during the very early epidemic phases have been reported elsewhere [25,26].

Bottom Line: The forecasts of both weekly incidence and final epidemic size greatly improved at and after the epidemic peak with all the observed data points falling within the uncertainty bounds.Real-time forecasting using the discrete time stochastic model with its simple computation of the uncertainty bounds was successful.Because of the simplistic model structure, the proposed model has the potential to additionally account for various types of heterogeneity, time-dependent transmission dynamics and epidemiological details.

View Article: PubMed Central - HTML - PubMed

Affiliation: PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama, Japan. nishiura@hku.hk

ABSTRACT

Background: Real-time forecasting of epidemics, especially those based on a likelihood-based approach, is understudied. This study aimed to develop a simple method that can be used for the real-time epidemic forecasting.

Methods: A discrete time stochastic model, accounting for demographic stochasticity and conditional measurement, was developed and applied as a case study to the weekly incidence of pandemic influenza (H1N1-2009) in Japan. By imposing a branching process approximation and by assuming the linear growth of cases within each reporting interval, the epidemic curve is predicted using only two parameters. The uncertainty bounds of the forecasts are computed using chains of conditional offspring distributions.

Results: The quality of the forecasts made before the epidemic peak appears largely to depend on obtaining valid parameter estimates. The forecasts of both weekly incidence and final epidemic size greatly improved at and after the epidemic peak with all the observed data points falling within the uncertainty bounds.

Conclusions: Real-time forecasting using the discrete time stochastic model with its simple computation of the uncertainty bounds was successful. Because of the simplistic model structure, the proposed model has the potential to additionally account for various types of heterogeneity, time-dependent transmission dynamics and epidemiological details. The impact of such complexities on forecasting should be explored when the data become available as part of the disease surveillance.

Show MeSH
Related in: MedlinePlus