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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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Related in: MedlinePlus

Approximation of an epidemic curve. The solid line represents the epidemic curve with assumed exponential growth within each reporting interval. The vertical dashed lines separate each reporting interval (week-wise). Growth rate in week k is assumed to be rk, and the area under the curve of week k (the cumulative incidence in each week) corresponds to the reported weekly incidence Ck. Susceptible individuals in week k, Sk, represent the number of susceptible individuals at the end of week k. The horizontal dotted line indicates the initial value of incidence, ik and represents the number of new cases at the beginning of week k.
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Figure 2: Approximation of an epidemic curve. The solid line represents the epidemic curve with assumed exponential growth within each reporting interval. The vertical dashed lines separate each reporting interval (week-wise). Growth rate in week k is assumed to be rk, and the area under the curve of week k (the cumulative incidence in each week) corresponds to the reported weekly incidence Ck. Susceptible individuals in week k, Sk, represent the number of susceptible individuals at the end of week k. The horizontal dotted line indicates the initial value of incidence, ik and represents the number of new cases at the beginning of week k.

Mentions: Figure 2 illustrates the proposed approximation strategy. Because no information regarding the dynamics within each week is available, exponential growth in each week k with a growth rate rk is assumed. The area under the epidemic curve in week k (the cumulative incidence in week k) corresponds to the reported weekly incidence Ck. Supposing that the initial value of incidence in week k is ik, then


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)

Approximation of an epidemic curve. The solid line represents the epidemic curve with assumed exponential growth within each reporting interval. The vertical dashed lines separate each reporting interval (week-wise). Growth rate in week k is assumed to be rk, and the area under the curve of week k (the cumulative incidence in each week) corresponds to the reported weekly incidence Ck. Susceptible individuals in week k, Sk, represent the number of susceptible individuals at the end of week k. The horizontal dotted line indicates the initial value of incidence, ik and represents the number of new cases at the beginning of week k.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 2: Approximation of an epidemic curve. The solid line represents the epidemic curve with assumed exponential growth within each reporting interval. The vertical dashed lines separate each reporting interval (week-wise). Growth rate in week k is assumed to be rk, and the area under the curve of week k (the cumulative incidence in each week) corresponds to the reported weekly incidence Ck. Susceptible individuals in week k, Sk, represent the number of susceptible individuals at the end of week k. The horizontal dotted line indicates the initial value of incidence, ik and represents the number of new cases at the beginning of week k.
Mentions: Figure 2 illustrates the proposed approximation strategy. Because no information regarding the dynamics within each week is available, exponential growth in each week k with a growth rate rk is assumed. The area under the epidemic curve in week k (the cumulative incidence in week k) corresponds to the reported weekly incidence Ck. Supposing that the initial value of incidence in week k is ik, then

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