Hans Wackernagel

A 'small-world-like' model for comparing interventions aimed at preventing and controlling influenza pandemics.

BackgroundWith an influenza pandemic seemingly imminent, we constructed a model simulating the spread of influenza within the community, in order to test the impact of various interventions.MethodsThe model includes an individual level, in which the risk of influenza virus infection and the dynamics of viral shedding are simulated according to age, treatment, and vaccination status; and a community level, in which meetings between individuals are simulated on randomly generated graphs. We used data on real pandemics to calibrate some parameters of the model. The reference scenario assumes no vaccination, no use of antiviral drugs, and no preexisting herd immunity. We explored the impact of interventions such as vaccination, treatment/prophylaxis with neuraminidase inhibitors, quarantine, and closure of schools or workplaces.ResultsIn the reference scenario, 57% of realizations lead to an explosive outbreak, lasting a mean of 82 days (standard deviation (SD) 12 days) and affecting 46.8% of the population on average. Interventions aimed at reducing the number of meetings, combined with measures reducing individual transmissibility, would be partly effective: coverage of 70% of affected households, with treatment of the index patient, prophylaxis of household contacts, and confinement to home of all household members, would reduce the probability of an outbreak by 52%, and the remaining outbreaks would be limited to 17% of the population (range 0.8%–25%). Reactive vaccination of 70% of the susceptible population would significantly reduce the frequency, size, and mean duration of outbreaks, but the benefit would depend markedly on the interval between identification of the first case and the beginning of mass vaccination. The epidemic would affect 4% of the population if vaccination started immediately, 17% if there was a 14-day delay, and 36% if there was a 28-day delay. Closing schools when the number of infections in the community exceeded 50 would be very effective, limiting the size of outbreaks to 10% of the population (range 0.9%–22%).ConclusionThis flexible tool can help to determine the interventions most likely to contain an influenza pandemic. These results support the stockpiling of antiviral drugs and accelerated vaccine development.

Geostatistical Techniques for Interpreting Multivariate Spatial Information

Several geostatistical techniques for exploring the structure of spatially distributed multivariate data are presented. The techniques are based on a combination of variogram modelling, principal component analysis and cokriging. Some possibilities to map the essential features of the multivariate spatial structure of the data are discussed. An example using geochemical data is given with an interpretation.

Cokriging versus kriging in regionalized multivariate data analysis

Abstract Cokriging and kriging are compared in the case when all variables are available at the same sample locations. The advantage of cokriging over kriging is that it ensures the coherence between an estimation of a sum and the separate estimation of each of its terms. To spare modeling effort it is interesting to know in which situation the kriging of a variable is equivalent to its cokriging with respect to a set of auxiliary variables (autokrigeability). In regionalized multivariate data analysis (MDA) it is important to know whether a whole set of variables is autokrigeable (intrinsically correlated). Intrinsic correlation implies that underlying factors can be computed from a classical MDA instead of a coregionalization analysis and that they can be kriged instead of being cokriged. Three criteria for identifying intrinsic correlation are discussed.

Combining geostatistics and Kalman filtering for data assimilation in an estuarine system

Data assimilation (DA) has been applied in an estuarine system in order to implement operational analysis in the management of a coastal zone. The dynamical evolution of the estuarine variables and corresponding observations are modelled with a nonlinear state-space model. Two DA methods are used for controlling the evolution of the model state by integrating information from observations. These are the reduced rank square root (RRSQRT) Kalman filter, which is a suboptimal implementation of the extended Kalman filter, and the ensemble Kalman filter which allows for nonlinear evolution of error statistics while still applying a linear equation in the analysis. First, these methods are applied and examined with a simple 1D ecological model. Then the RRSQRT Kalman filter is applied to the 3D hydrodynamics of the Odra lagoon using the model TRIM3D and water elevation measurements from fixed pile stations. Geostatistical modelling ideas are discussed in the application of these algorithms. (Some figures in this article are in colour only in the electronic version)

OVERVIEW OF METHODS FOR COREGIONALIZATION ANALYSIS

The term coregionalization analysis refers to the analysis of coregionalization matrices obtained from multivariate spatial data using a nested variogram model. Several methods based on canonical correlations, principal component analysis, discriminant functions are reviewed and integrated into the framework of coregionalization analysis. Reference is made to applications in geochemical exploration, soil science, ecology and remote sensing.

History matching of petroleum reservoir models by the Ensemble Kalman Filter and parameterization methods

The Ensemble Kalman Filter (EnKF) has been successfully applied in petroleum engineering during the past few years to constrain reservoir models to production or seismic data. This sequential assimilation method provides a set of updated static variables (porosity, permeability) and dynamic variables (pressure, saturation) at each assimilation time. However, several limitations can be pointed out. In particular, the method does not prevent petrophysical realizations from departing from prior information. In addition, petrophysical properties can reach extreme (non-physical) values. In this work, we propose to combine the EnKF with two parameterization methods designed to preserve second-order statistical properties: pilot points and gradual deformation. The aim is to prevent the departure of the constrained petrophysical property distributions from prior information. Over/under estimations should also be avoided. The two algorithms are applied to a synthetic case. Several parameter configurations are investigated in order to identify solutions improving the performance of the method.

Description of a computer program for analyzing multi-variate spatially distributed data

Abstract This paper gives a detailed description of a program for the factor analysis of multivariate data from samples taken in a physical environment. The spatial correlation of the samples is represented by a model of nested spatial structures. The correlations of the variables are summarized by performing a principal component analysis on the coefficients of the spatial structures. The result is a linear model of the coregionalization that can be used for factorial kriging, conditional simulation, and cokriging. The program could be written for a microcomputer connected to a mainframe.

Geostatistical modeling of sound propagation: Principles and a field application experiment

The assessment of noise sources for environmental purposes requires reliable methods for mapping. Numerical models are well adapted for sophisticated simulations and sensitivity analyses; however, real-time mapping of large frequency bands must be based on fast and acceptable computations and honor in situ measurements. In this paper, a real-time mapping procedure of noise exposure is proposed. The procedure is based on geostatistical modeling of spatial variations and applied to a case study taken from an experimental campaign, where a point source was placed on a flat meadow. An analytical approximation of the acoustic field was first computed with the Embleton model. The difference between this approximation and the actual measurements (L(eq15 min) 1/3-octave bands samples from 19 microphones spread over the meadow) showed spatial structure, which has been modeled with a variogram. Finally, the geostatistical technique of kriging with external drift provided an optimal interpolation of the acoustic field data while encapsulating the first approximation from the Embleton model. Systematic geostatistical inference and real-time mapping with the proposed procedure can be envisaged in simple cases.

Caractérisation d'anomalies géochimiques par la géostatistique multivariable

Abstract The behavior of geochemical elements is different inside and outside a mineral deposit. The correlations which can be measured between geochemical elements depend on the spatial scale at which a data analysis is performed. Multivariate geostatistics conceptualize this observation by defining various spatial categories on the basis of a variogram model, which represent a classification of regional, local and pointwise spatial scales. Factor analysis is then performed using correlation matrices associated to the spatial categories. The scores of the spatial factors for each sample are estimated by cokriging. Distinguishing between pointwise and local anomalies, it can be seen that geostatistics provide concepts for emphasizing local anomalies which are often more difficult to identify than pointwise anomalies.

The circlet transform: A robust tool for detecting features with circular shapes

We present a novel method for detecting circles on digital images. This transform is called the circlet transform and can be seen as an extension of classical 1D wavelets to 2D; each basic element is a circle convolved by a 1D oscillating function. In comparison with other circle-detector methods, mainly the Hough transform, the circlet transform takes into account the finite frequency aspect of the data; a circular shape is not restricted to a circle but has a certain width. The transform operates directly on image gradient and does not need further binary segmentation. The implementation is efficient as it consists of a few fast Fourier transforms. The circlet transform is coupled with a soft-thresholding process and applied to a series of real images from different fields: ophthalmology, astronomy and oceanography. The results show the effectiveness of the method to deal with real images with blurry edges.