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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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Epidemic time delay diagrams for different R0.(a) Relation between new cases at consecutive time periods (weeks) for H3N2 isolates in the US 2004–05 season, and for simulated data with (b) R0 = 1.7, (c) R0 = 1.0 and (d) R0 = 0.8. For these simulations, the introduction of new cases from the reservoir follows the Vietnam case history, Figure 1a. New cases are then generated using expression [11], according to a Poisson distribution. The trajectories connecting new cases at consecutive times (red arrows) eventually return to the origin because depletion of susceptibles reduces the effective reproduction number (i.e. the actual number of secondary cases produced by an infectious individual). Dashed lines in (a) and (b) are the tangents at the origin to the case number trajectories (red arrows), with slope b(R).
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pone-0002185-g002: Epidemic time delay diagrams for different R0.(a) Relation between new cases at consecutive time periods (weeks) for H3N2 isolates in the US 2004–05 season, and for simulated data with (b) R0 = 1.7, (c) R0 = 1.0 and (d) R0 = 0.8. For these simulations, the introduction of new cases from the reservoir follows the Vietnam case history, Figure 1a. New cases are then generated using expression [11], according to a Poisson distribution. The trajectories connecting new cases at consecutive times (red arrows) eventually return to the origin because depletion of susceptibles reduces the effective reproduction number (i.e. the actual number of secondary cases produced by an infectious individual). Dashed lines in (a) and (b) are the tangents at the origin to the case number trajectories (red arrows), with slope b(R).

Mentions: We see that the well known multiplicative progression between new cases at successive times due to contagion appears, on average, as a linear relation between ΔT(t+τ) and ΔT(t) in an epidemic time delay diagram, Figures 2a–d. Expression [6] generalizes similar relations in the TSIR literature by casting them in terms of new cases over arbitrarily chosen observation intervals τ, not necessarily coinciding with the average generation time γ−1. Expression [6] also shows how the initial Rt can be estimated geometrically (without the need for parameter search or numerical optimization) from an epidemic time delay plot of surveillance data: b(Rt) is the slope of the tangent at the origin of case trajectories (dashed line in Fig. 2a, b). For emerging infectious diseases relative fluctuations in case numbers are large, see e.g. Figure 2d, and this simple geometric approach is not valid, thus making more robust estimation methods, as the one presented here, necessary.


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

Bettencourt LM, Ribeiro RM - PLoS ONE (2008)

Epidemic time delay diagrams for different R0.(a) Relation between new cases at consecutive time periods (weeks) for H3N2 isolates in the US 2004–05 season, and for simulated data with (b) R0 = 1.7, (c) R0 = 1.0 and (d) R0 = 0.8. For these simulations, the introduction of new cases from the reservoir follows the Vietnam case history, Figure 1a. New cases are then generated using expression [11], according to a Poisson distribution. The trajectories connecting new cases at consecutive times (red arrows) eventually return to the origin because depletion of susceptibles reduces the effective reproduction number (i.e. the actual number of secondary cases produced by an infectious individual). Dashed lines in (a) and (b) are the tangents at the origin to the case number trajectories (red arrows), with slope b(R).
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2366072&req=5

pone-0002185-g002: Epidemic time delay diagrams for different R0.(a) Relation between new cases at consecutive time periods (weeks) for H3N2 isolates in the US 2004–05 season, and for simulated data with (b) R0 = 1.7, (c) R0 = 1.0 and (d) R0 = 0.8. For these simulations, the introduction of new cases from the reservoir follows the Vietnam case history, Figure 1a. New cases are then generated using expression [11], according to a Poisson distribution. The trajectories connecting new cases at consecutive times (red arrows) eventually return to the origin because depletion of susceptibles reduces the effective reproduction number (i.e. the actual number of secondary cases produced by an infectious individual). Dashed lines in (a) and (b) are the tangents at the origin to the case number trajectories (red arrows), with slope b(R).
Mentions: We see that the well known multiplicative progression between new cases at successive times due to contagion appears, on average, as a linear relation between ΔT(t+τ) and ΔT(t) in an epidemic time delay diagram, Figures 2a–d. Expression [6] generalizes similar relations in the TSIR literature by casting them in terms of new cases over arbitrarily chosen observation intervals τ, not necessarily coinciding with the average generation time γ−1. Expression [6] also shows how the initial Rt can be estimated geometrically (without the need for parameter search or numerical optimization) from an epidemic time delay plot of surveillance data: b(Rt) is the slope of the tangent at the origin of case trajectories (dashed line in Fig. 2a, b). For emerging infectious diseases relative fluctuations in case numbers are large, see e.g. Figure 2d, and this simple geometric approach is not valid, thus making more robust estimation methods, as the one presented here, necessary.

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