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Real time bayesian estimation of the epidemic potential of emerging infectious diseases.

Bettencourt LM, Ribeiro RM - PLoS ONE (2008)

Bottom Line: Currently there is worldwide alert for H5N1 avian influenza becoming as transmissible in humans as seasonal influenza, and potentially causing a pandemic of unprecedented proportions.Violations of these significance tests define statistical anomalies that may signal changes in the epidemiology of emerging diseases and should trigger further field investigation.We apply the methodology to case data from World Health Organization reports to place bounds on the current transmissibility of H5N1 influenza in humans and establish a statistical basis for monitoring its evolution in real time.

View Article: PubMed Central - PubMed

Affiliation: Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico, United States of America. lmbett@lanl.gov

ABSTRACT

Background: Fast changes in human demographics worldwide, coupled with increased mobility, and modified land uses make the threat of emerging infectious diseases increasingly important. Currently there is worldwide alert for H5N1 avian influenza becoming as transmissible in humans as seasonal influenza, and potentially causing a pandemic of unprecedented proportions. Here we show how epidemiological surveillance data for emerging infectious diseases can be interpreted in real time to assess changes in transmissibility with quantified uncertainty, and to perform running time predictions of new cases and guide logistics allocations.

Methodology/principal findings: We develop an extension of standard epidemiological models, appropriate for emerging infectious diseases, that describes the probabilistic progression of case numbers due to the concurrent effects of (incipient) human transmission and multiple introductions from a reservoir. The model is cast in terms of surveillance observables and immediately suggests a simple graphical estimation procedure for the effective reproductive number R (mean number of cases generated by an infectious individual) of standard epidemics. For emerging infectious diseases, which typically show large relative case number fluctuations over time, we develop a bayesian scheme for real time estimation of the probability distribution of the effective reproduction number and show how to use such inferences to formulate significance tests on future epidemiological observations.

Conclusions/significance: Violations of these significance tests define statistical anomalies that may signal changes in the epidemiology of emerging diseases and should trigger further field investigation. We apply the methodology to case data from World Health Organization reports to place bounds on the current transmissibility of H5N1 influenza in humans and establish a statistical basis for monitoring its evolution in real time.

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Evolution of R estimates over time (weeks) for single realization simulated data with R0 = 0.8, 1.0, 1.4 and 1.7 (left to right, top to bottom).Dashed lines indicate the value of R0 in the simulation. The decay of R estimates over time in standard epidemics is due to the depletion of susceptibles. For R0 = 1.0, 1.4 and 1.7 the mean is indistinguishable from the estimate of R with maximum probability and is not shown.
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pone-0002185-g003: Evolution of R estimates over time (weeks) for single realization simulated data with R0 = 0.8, 1.0, 1.4 and 1.7 (left to right, top to bottom).Dashed lines indicate the value of R0 in the simulation. The decay of R estimates over time in standard epidemics is due to the depletion of susceptibles. For R0 = 1.0, 1.4 and 1.7 the mean is indistinguishable from the estimate of R with maximum probability and is not shown.

Mentions: The effective reproduction number, R, calculated by our method changes over time, because of decreases in the fraction of susceptibles, S(t)/N(t), and the availability of more information, as more cases are observed. Thus, we use the values obtained for R at early times, when S(t)/N(t) approximates its initial value, to estimate R0 of the simulation by assuming that max(R) = R0. As shown in Figure 3, in all circumstances, the method gives an excellent estimation of R0 as outbreaks unfold, usually making accurate predictions when supplied with a mere two or three observation points. Uncertainty, measured by the width of the 95% credible interval, is reduced by larger case numbers, so that it typically remains higher the smaller the R0. In all instances uncertainty is reduced as more cases are reported over time.


Real time bayesian estimation of the epidemic potential of emerging infectious diseases.

Bettencourt LM, Ribeiro RM - PLoS ONE (2008)

Evolution of R estimates over time (weeks) for single realization simulated data with R0 = 0.8, 1.0, 1.4 and 1.7 (left to right, top to bottom).Dashed lines indicate the value of R0 in the simulation. The decay of R estimates over time in standard epidemics is due to the depletion of susceptibles. For R0 = 1.0, 1.4 and 1.7 the mean is indistinguishable from the estimate of R with maximum probability and is not shown.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2366072&req=5

pone-0002185-g003: Evolution of R estimates over time (weeks) for single realization simulated data with R0 = 0.8, 1.0, 1.4 and 1.7 (left to right, top to bottom).Dashed lines indicate the value of R0 in the simulation. The decay of R estimates over time in standard epidemics is due to the depletion of susceptibles. For R0 = 1.0, 1.4 and 1.7 the mean is indistinguishable from the estimate of R with maximum probability and is not shown.
Mentions: The effective reproduction number, R, calculated by our method changes over time, because of decreases in the fraction of susceptibles, S(t)/N(t), and the availability of more information, as more cases are observed. Thus, we use the values obtained for R at early times, when S(t)/N(t) approximates its initial value, to estimate R0 of the simulation by assuming that max(R) = R0. As shown in Figure 3, in all circumstances, the method gives an excellent estimation of R0 as outbreaks unfold, usually making accurate predictions when supplied with a mere two or three observation points. Uncertainty, measured by the width of the 95% credible interval, is reduced by larger case numbers, so that it typically remains higher the smaller the R0. In all instances uncertainty is reduced as more cases are reported over time.

Bottom Line: Currently there is worldwide alert for H5N1 avian influenza becoming as transmissible in humans as seasonal influenza, and potentially causing a pandemic of unprecedented proportions.Violations of these significance tests define statistical anomalies that may signal changes in the epidemiology of emerging diseases and should trigger further field investigation.We apply the methodology to case data from World Health Organization reports to place bounds on the current transmissibility of H5N1 influenza in humans and establish a statistical basis for monitoring its evolution in real time.

View Article: PubMed Central - PubMed

Affiliation: Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico, United States of America. lmbett@lanl.gov

ABSTRACT

Background: Fast changes in human demographics worldwide, coupled with increased mobility, and modified land uses make the threat of emerging infectious diseases increasingly important. Currently there is worldwide alert for H5N1 avian influenza becoming as transmissible in humans as seasonal influenza, and potentially causing a pandemic of unprecedented proportions. Here we show how epidemiological surveillance data for emerging infectious diseases can be interpreted in real time to assess changes in transmissibility with quantified uncertainty, and to perform running time predictions of new cases and guide logistics allocations.

Methodology/principal findings: We develop an extension of standard epidemiological models, appropriate for emerging infectious diseases, that describes the probabilistic progression of case numbers due to the concurrent effects of (incipient) human transmission and multiple introductions from a reservoir. The model is cast in terms of surveillance observables and immediately suggests a simple graphical estimation procedure for the effective reproductive number R (mean number of cases generated by an infectious individual) of standard epidemics. For emerging infectious diseases, which typically show large relative case number fluctuations over time, we develop a bayesian scheme for real time estimation of the probability distribution of the effective reproduction number and show how to use such inferences to formulate significance tests on future epidemiological observations.

Conclusions/significance: Violations of these significance tests define statistical anomalies that may signal changes in the epidemiology of emerging diseases and should trigger further field investigation. We apply the methodology to case data from World Health Organization reports to place bounds on the current transmissibility of H5N1 influenza in humans and establish a statistical basis for monitoring its evolution in real time.

Show MeSH
Related in: MedlinePlus