Real-time quantification of the next-generation matrix and age-dependent forecasting of pandemic influenza H1N1 2009 in Japan

Abstract

Purpose: To quantify the age-dependent next-generation matrix (NGM) for the 2009 H1N1 influenza pandemic and forecast the age-stratified cumulative incidence in Japan.

Methods: Using a renewal equation model that describes the time evolution of the 2009 H1N1 influenza pandemic, we derive the likelihood function to estimate parameters of the NGM and reporting coverage. Comparing the Akaike Information Criterion of models using empirically observed data from the 2009 pandemic in Gifu, Japan, we excluded redundant parameters and identified the three best models that were parameterized in different ways.

Results: The initial proportions of susceptible populations were suggested as redundant information to be inferred. The three models selected successfully captured the order of the age-dependent cumulative incidence. We found that the time required for reliable estimation of age-dependent cumulative incidence was at least 180 days.

Conclusions: To forecast the age-dependent cumulative incidence reliably following the estimation of the NGM and reporting coverage, we need empirically observed data for more than 5 months from the start of the epidemic, which is likely to be after the peak. To increase the practical efficacy in forecasting the cumulative incidence, additional data and approaches are required.

Keywords: Epidemiologic studies; Forecasting; H1N1 subtype; Influenza A virus; Models; Statistical estimation; Theoretical.