Pros and cons of estimating the reproduction number from early epidemic growth rate of influenza A (H1N1) 2009

<p>Abstract</p> <p>Background</p> <p>In many parts of the world, the exponential growth rate of infections during the initial epidemic phase has been used to make statistical inferences on the reproduction number, <it>R</it>, a summary measure of the transmission potential for the novel influenza A (H1N1) 2009. The growth rate at the initial stage of the epidemic in Japan led to estimates for <it>R </it>in the range 2.0 to 2.6, capturing the intensity of the initial outbreak among school-age children in May 2009.</p> <p>Methods</p> <p>An updated estimate of <it>R </it>that takes into account the epidemic data from 29 May to 14 July is provided. An age-structured renewal process is employed to capture the age-dependent transmission dynamics, jointly estimating the reproduction number, the age-dependent susceptibility and the relative contribution of imported cases to secondary transmission. Pitfalls in estimating epidemic growth rates are identified and used for scrutinizing and re-assessing the results of our earlier estimate of <it>R</it>.</p> <p>Results</p> <p>Maximum likelihood estimates of <it>R </it>using the data from 29 May to 14 July ranged from 1.21 to 1.35. The next-generation matrix, based on our age-structured model, predicts that only 17.5% of the population will experience infection by the end of the first pandemic wave. Our earlier estimate of <it>R </it>did not fully capture the population-wide epidemic in quantifying the next-generation matrix from the estimated growth rate during the initial stage of the pandemic in Japan.</p> <p>Conclusions</p> <p>In order to quantify <it>R </it>from the growth rate of cases, it is essential that the selected model captures the underlying transmission dynamics embedded in the data. Exploring additional epidemiological information will be useful for assessing the temporal dynamics. Although the simple concept of <it>R </it>is more easily grasped by the general public than that of the next-generation matrix, the matrix incorporating detailed information (e.g., age-specificity) is essential for reducing the levels of uncertainty in predictions and for assisting public health policymaking. Model-based prediction and policymaking are best described by sharing fundamental notions of heterogeneous risks of infection and death with non-experts to avoid potential confusion and/or possible misuse of modelling results.</p

Theoretical basis to measure the impact of short-lasting control of an infectious disease on the epidemic peak

Background. While many pandemic preparedness plans have promoted disease control effort to lower and delay an epidemic peak, analytical methods for determining the required control effort and making statistical inferences have yet to be sought. As a first step to address this issue, we present a theoretical basis on which to assess the impact of an early intervention on the epidemic peak, employing a simple epidemic model. Methods. We focus on estimating the impact of an early control effort (e.g. unsuccessful containment), assuming that the transmission rate abruptly increases when control is discontinued. We provide analytical expressions for magnitude and time of the epidemic peak, employing approximate logistic and logarithmic-form solutions for the latter. Empirical influenza data (H1N1-2009) in Japan are analyzed to estimate the effect of the summer holiday period in lowering and delaying the peak in 2009. Results. Our model estimates that the epidemic peak of the 2009 pandemic was delayed for 21 days due to summer holiday. Decline in peak appears to be a nonlinear function of control-associated reduction in the reproduction number. Peak delay is shown to critically depend on the fraction of initially immune individuals. Conclusions. The proposed modeling approaches offer methodological avenues to assess empirical data and to objectively estimate required control effort to lower and delay an epidemic peak. Analytical findings support a critical need to conduct population-wide serological survey as a prior requirement for estimating the time of peak. © 2011 Omori and Nishiura; licensee BioMed Central Ltd.published_or_final_versio

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

<p>Abstract</p> <p>Background</p> <p>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.</p> <p>Methods</p> <p>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.</p> <p>Results</p> <p>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.</p> <p>Conclusions</p> <p>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.</p

Impact of School Closures on an Influenza Pandemic: Scientific Evidence Base Review

School closure has been recommended as a potential component of a mitigation strategy during an influenza pandemic, and schools were closed in the UK and elsewhere during the 2009 pandemic. This report aims to inform the development of options for policy in influenza pandemics by collating and updating the evidence base concerning the effects of school closure on influenza transmission

Epidemiological and transmissibility analysis of influenza A(H1N1)v in a southern hemisphere setting: Peru

We present a preliminary analysis of 1,771 confirmed cases of influenza A(H1N1)v reported in Peru by 17 July including the frequency of the clinical characteristics, the spatial and age distribution of the cases and the estimate of the transmission potential. Age-specific frequency of cases was highest among school age children and young adults, with the lowest frequency of cases among seniors, a pattern that is consistent with reports from other countries. Estimates of the reproduction number lie in the range of 1.2 to 1.7, which is broadly consistent with previous estimates for this pandemic in other regions. Validation of these estimates will be possible as additional data become available

Did Modeling Overestimate the Transmission Potential of Pandemic (H1N1-2009)? Sample Size Estimation for Post-Epidemic Seroepidemiological Studies

abstract: Background Seroepidemiological studies before and after the epidemic wave of H1N1-2009 are useful for estimating population attack rates with a potential to validate early estimates of the reproduction number, R, in modeling studies. Methodology/Principal Findings Since the final epidemic size, the proportion of individuals in a population who become infected during an epidemic, is not the result of a binomial sampling process because infection events are not independent of each other, we propose the use of an asymptotic distribution of the final size to compute approximate 95% confidence intervals of the observed final size. This allows the comparison of the observed final sizes against predictions based on the modeling study (R = 1.15, 1.40 and 1.90), which also yields simple formulae for determining sample sizes for future seroepidemiological studies. We examine a total of eleven published seroepidemiological studies of H1N1-2009 that took place after observing the peak incidence in a number of countries. Observed seropositive proportions in six studies appear to be smaller than that predicted from R = 1.40; four of the six studies sampled serum less than one month after the reported peak incidence. The comparison of the observed final sizes against R = 1.15 and 1.90 reveals that all eleven studies appear not to be significantly deviating from the prediction with R = 1.15, but final sizes in nine studies indicate overestimation if the value R = 1.90 is used. Conclusions Sample sizes of published seroepidemiological studies were too small to assess the validity of model predictions except when R = 1.90 was used. We recommend the use of the proposed approach in determining the sample size of post-epidemic seroepidemiological studies, calculating the 95% confidence interval of observed final size, and conducting relevant hypothesis testing instead of the use of methods that rely on a binomial proportion.The article is published at http://journals.plos.org/plosone/article?id=10.1371/journal.pone.001790

Open Access

Cost-effective length and timing of school closure during an influenza pandemic depend on the severit