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The basic reproduction number as a predictor for epidemic outbreaks in temporal networks.

ABSTRACT: The basic reproduction number R0--the number of individuals directly infected by an infectious person in an otherwise susceptible population--is arguably the most widely used estimator of how severe an epidemic outbreak can be. This severity can be more directly measured as the fraction of people infected once the outbreak is over, ?. In traditional mathematical epidemiology and common formulations of static network epidemiology, there is a deterministic relationship between R0 and ?. However, if one considers disease spreading on a temporal contact network--where one knows when contacts happen, not only between whom--then larger R0 does not necessarily imply larger ?. In this paper, we numerically investigate the relationship between R0 and ? for a set of empirical temporal networks of human contacts. Among 31 explanatory descriptors of temporal network structure, we identify those that make R0 an imperfect predictor of ?. We find that descriptors related to both temporal and topological aspects affect the relationship between R0 and ?, but in different ways.

SUBMITTER: Holme P

PROVIDER: S-EPMC4368036 | biostudies-literature | 2015

REPOSITORIES: biostudies-literature

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The basic reproduction number as a predictor for epidemic outbreaks in temporal networks.

Holme Petter P Masuda Naoki N

PloS one 20150320 3

The basic reproduction number R0--the number of individuals directly infected by an infectious person in an otherwise susceptible population--is arguably the most widely used estimator of how severe an epidemic outbreak can be. This severity can be more directly measured as the fraction of people infected once the outbreak is over, Ω. In traditional mathematical epidemiology and common formulations of static network epidemiology, there is a deterministic relationship between R0 and Ω. However, i ...[more]

PMID: 25793764

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Project description:After being cholera free for over 100 years, Peru experienced an unprecedented epidemic of Vibrio cholerae O1 that began in 1991 and generated multiple waves of disease over several years. We developed a mechanistic transmission model that accounts for seasonal variation in temperature to estimate spatial variability in the basic reproduction number ([Formula: see text]), the initial concentration of vibrios in the environment, and cholera reporting rates. From 1991-1997, cholera spread following a multi-wave pattern, with weekly incidence concentrated during warm seasons. The epidemic first hit the coastal departments of Peru and subsequently spread through the highlands and jungle regions. The correlation between model predictions and observations was high (range in R2: 58% to 97%). Department-level population size and elevation explained significant variation in spatial-temporal transmission patterns. The overall R0 across departments was estimated at 2.1 (95% CI: 0.8,7.3), high enough for sustained transmission. Geographic-region level [Formula: see text] varied substantially from 2.4 (95% CI: 1.1, 7.3) for the coastal region, 1.9 (0.7, 6.4) for the jungle region, and 1.5 (0.9, 2.2) for the highlands region. At the department level, mean [Formula: see text] ranged from 0.8 to 6.9. Department-level [Formula: see text] were correlated with overall observed attack rates (Spearman ρ = 0.59, P = 0.002), elevation (ρ = -0.4, P = 0.04), and longitude (ρ = -0.6, P = 0.004). We find that both [Formula: see text] and the initial concentration of vibrios were higher in coastal departments than other departments. Reporting rates were low, consistent with a substantial fraction of asymptomatic or mild cases associated with the El Tor cholera biotype. Our results suggest that cholera vibrios, autochthonous to plankton in the natural aquatic environment, may have triggered outbreaks in multiple coastal locations along the Pacific coast of Peru. Our methodology could be useful to investigate multi-wave epidemics of cholera and could be extended to conduct near real-time forecasts and investigate the impact of vaccination strategies.

Project description:BACKGROUND: Dengue, an infectious tropical disease, has recently emerged as one of the most important mosquito-borne viral diseases in the world. We perform a retrospective analysis of the 2011 dengue fever epidemic in Pakistan in order to assess the transmissibility of the disease. We obtain estimates of the basic reproduction number R 0 from epidemic data using different methodologies applied to different epidemic models in order to evaluate the robustness of our estimate. RESULTS: We first estimate model parameters by fitting a deterministic ODE vector-host model for the transmission dynamics of single-strain dengue to the epidemic data, using both a basic ordinary least squares (OLS) as well as a generalized least squares (GLS) scheme. Moreover, we perform the same analysis for a direct-transmission ODE model, thereby allowing us to compare our results across different models. In addition, we formulate a direct-transmission stochastic model for the transmission dynamics of dengue and obtain parameter estimates for the stochastic model using Markov chain Monte Carlo (MCMC) methods. In each of the cases we have considered, the estimate for the basic reproduction number R 0 is initially greater than unity leading to an epidemic outbreak. However, control measures implemented several weeks after the initial outbreak successfully reduce R 0 to less than unity, thus resulting in disease elimination. Furthermore, it is observed that there is strong agreement in our estimates for the pre-control value of R 0, both across different methodologies as well across different models. However, there are also significant differences between our estimates for the post-control value of the basic reproduction number across the two different models. CONCLUSION: In conclusion, we have obtained robust estimates for the value of the basic reproduction number R 0 associated with the 2011 dengue fever epidemic before the implementation of public health control measures. Furthermore, we have shown that there is close agreement between our estimates for the post-control value of R 0 across the different methodologies. Nevertheless, there are also significant differences between the estimates for the post-control value of R 0 across the two different models.

Dataset Information

The basic reproduction number as a predictor for epidemic outbreaks in temporal networks.

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The basic reproduction number as a predictor for epidemic outbreaks in temporal networks.

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