Gerardo Chowell

SUMMARY: Recurrent epidemics of influenza are observed seasonally around the world with considerable health and economic consequences. A key quantity for the control of infectious diseases is the reproduction number, which measures the transmissibility of a pathogen and determines the magnitude of public health interventions necessary to control epidemics. Here we applied a simple epidemic model to weekly indicators of influenza mortality to estimate the reproduction numbers of seasonal influenza epidemics spanning three decades in the United States, France, and Australia. We found similar distributions of reproduction number estimates in the three countries, with mean value 1·3 and important year-to-year variability (range 0·9–2·1). Estimates derived from two different mortality indicators (pneumonia and influenza excess deaths and influenza-specific deaths) were in close agreement for the United States (correlation=0·61,PP60%) in healthy individuals who respond well to vaccine, in addition to periodic re-vaccination due to evolving viral antigens and waning population immunity.

The reproduction number, , 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 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 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 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 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 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.

Dengue is a public health problem on the rise in many tropical regions and affects approximately 100 million people every year worldwide. In this paper, the authors retrospectively assess the association between five climatological variables and dengue incidence using data from the 2002 dengue epidemic in Colima, Mexico. Pluvial precipitation (mm), evaporation (mm), and mean, maximum, and minimum temperatures (degrees C) were obtained from local meteorological stations. The highest correlation of dengue incidence with maximum temperature was found at a lag of one month, and the highest correlation for evaporation was found at a lag of three months. A multiple-linear-regression model that includes all the climatological variables was correlated with 94 percent of the observed variance. Two simpler linear models with variables significant at the 99 percent confidence level were correlated with 88 percent (Precipitation + Evaporation) and 79 percent (Precipitation + Maximum Temperature) of the observed variance.