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The effective reproduction number of pandemic influenza: prospective estimation.

ABSTRACT: Timely estimation of the transmissibility of a novel pandemic influenza virus was a public health priority in 2009.We extended methods for prospective estimation of the effective reproduction number (Rt) over time in an emerging epidemic to allow for reporting delays and repeated importations. We estimated Rt based on case notifications and hospitalizations associated with laboratory-confirmed pandemic (H1N1) 2009 virus infections in Hong Kong from June through October 2009.Rt declined from around 1.4-1.5 at the start of the local epidemic to around 1.1-1.2 later in the summer, suggesting changes in transmissibility perhaps related to school vacations or seasonality. Estimates of Rt based on hospitalizations of confirmed H1N1 cases closely matched estimates based on case notifications.Real-time monitoring of the effective reproduction number is feasible and can provide useful information to public health authorities for situational awareness and calibration of mitigation strategies.

SUBMITTER: Cowling BJ

PROVIDER: S-EPMC3084966 | biostudies-literature | 2010 Nov

REPOSITORIES: biostudies-literature

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The effective reproduction number of pandemic influenza: prospective estimation.

Cowling Benjamin J BJ Lau Max S Y MS Ho Lai-Ming LM Chuang Shuk-Kwan SK Tsang Thomas T Liu Shao-Haei SH Leung Pak-Yin PY Lo Su-Vui SV Lau Eric H Y EH

Epidemiology (Cambridge, Mass.) 20101101 6

<h4>Background</h4>Timely estimation of the transmissibility of a novel pandemic influenza virus was a public health priority in 2009.<h4>Methods</h4>We extended methods for prospective estimation of the effective reproduction number (Rt) over time in an emerging epidemic to allow for reporting delays and repeated importations. We estimated Rt based on case notifications and hospitalizations associated with laboratory-confirmed pandemic (H1N1) 2009 virus infections in Hong Kong from June through ...[more]

PMID: 20805752

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Project description:The reproduction number, R, defined as the average number of secondary cases generated by a primary case, is a crucial quantity for identifying the intensity of interventions required to control an epidemic. Current estimates of the reproduction number for seasonal influenza show wide variation and, in particular, uncertainty bounds for R for the pandemic strain from 1918 to 1919 have been obtained only in a few recent studies and are yet to be fully clarified. Here, we estimate R using daily case notifications during the autumn wave of the influenza pandemic (Spanish flu) in the city of San Francisco, California, from 1918 to 1919. In order to elucidate the effects from adopting different estimation approaches, four different methods are used: estimation of R using the early exponential-growth rate (Method 1), a simple susceptible-exposed-infectious-recovered (SEIR) model (Method 2), a more complex SEIR-type model that accounts for asymptomatic and hospitalized cases (Method 3), and a stochastic susceptible-infectious-removed (SIR) with Bayesian estimation (Method 4) that determines the effective reproduction number Rt at a given time t. The first three methods fit the initial exponential-growth phase of the epidemic, which was explicitly determined by the goodness-of-fit test. Moreover, Method 3 was also fitted to the whole epidemic curve. Whereas the values of R obtained using the first three methods based on the initial growth phase were estimated to be 2.98 (95% confidence interval (CI): 2.73, 3.25), 2.38 (2.16, 2.60) and 2.20 (1.55, 2.84), the third method with the entire epidemic curve yielded a value of 3.53 (3.45, 3.62). This larger value could be an overestimate since the goodness-of-fit to the initial exponential phase worsened when we fitted the model to the entire epidemic curve, and because the model is established as an autonomous system without time-varying assumptions. These estimates were shown to be robust to parameter uncertainties, but the theoretical exponential-growth approximation (Method 1) shows wide uncertainty. Method 4 provided a maximum-likelihood effective reproduction number 2.10 (1.21, 2.95) using the first 17 epidemic days, which is consistent with estimates obtained from the other methods and an estimate of 2.36 (2.07, 2.65) for the entire autumn wave. We conclude that the reproduction number for pandemic influenza (Spanish flu) at the city level can be robustly assessed to lie in the range of 2.0-3.0, in broad agreement with previous estimates using distinct data.

Project description:Estimating the basic reproduction number of a pandemic and the changes that appear on this value over time provide a good understanding of the contagious nature of the virus and efficiency of the controlling strategies. In this paper, we focus on studying the basic reproduction number (R0) for two important variants of COVID-19 pandemic in Iran: Alpha and Delta variants. We use four different methods, three statistical models and one mathematical model, to compute R0: Exponential Growth Rate (EGR), Maximum Likelihood (ML), Sequential Bayesian (SB), and time-dependent SIR model. Alpha variant of COVID-19 was active in Iran from March 10, 2021 until June 10, 2021. Our computations indicate that total R0 of this variant according to EGR, ML, SB, and SIR model is respectively 0.9999 (95% CI: 0.9994-1), 1.046 (95% CI: 1.044-1.049), 1.06 (95% CI: 1.03-1.08), and 2.79 (95% CI: 2.77-2.81) in the whole active time interval. Moreover, during the time interval from April 3, 2021 to April 9, 2021 in which this variant was in its exponential growth in Iran, R0 of Alpha variant in Iran according to SB, EGR, ML, and SIR model is respectively 2.26 (95% CI: 2.04-2.49), 2.64 (95% CI: 2.58-2.7), 11.38 (95% CI: 11.28-11.48), and 12.13 (95% CI: 12.12-12.14). Delta variant was active in Iran during the time interval from June 22, 2021 until September 22, 2021. Our computations show that during the time interval from July 3, 2021 to July 8, 2021 in which this variant was in its exponential growth in Iran, R0 of Delta variant in Iran according to SB, EGR, ML, and SIR model is respectively 3 (95% CI: 2.34-3.66), 3.1 (95% CI: 3.02-3.17), 12 (95% CI: 11.89-12.12), and 23.3 (95% CI: 23.19-23.41). Further, total R0 of Delta variant in Iran in the whole active time interval according to EGR, ML, SB, and SIR model is respectively 1.042 (95% CI: 1.04-1.043), 1.053 (95% CI: 1.051-1.055), 0.79 (95% CI: 0.63-0.95), and 5.65 (95% CI: 5.6-5.7). As the results show Delta variant was more severe than Alpha variant in Iran. Chasing the changes in R0 during each variant shows that the controlling strategies applied were effective in controlling the virus spread.

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The effective reproduction number of pandemic influenza: prospective estimation.

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The effective reproduction number of pandemic influenza: prospective estimation.

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