David M. Walker

Super-spreaders and the rate of transmission of the SARS virus

Abstract We describe a stochastic small-world network model of transmission of the SARS virus. Unlike the standard Susceptible-Infected-Removed models of disease transmission, our model exhibits both geographically localised outbreaks and “super-spreaders”. Moreover, the combination of localised and long range links allows for more accurate modelling of partial isolation and various public health policies. From this model, we derive an expression for the probability of a widespread outbreak and a condition to ensure that the epidemic is controlled. Moreover, multiple simulations are used to make predictions of the likelihood of various eventual scenarios for fixed initial conditions. The main conclusions of this study are: (i) “super-spreaders” may occur even if the infectiousness of all infected individuals is constant; (ii) consistent with previous reports, extended exposure time beyond 3–5 days (i.e. significant nosocomial transmission) was the key factor in the severity of the SARS outbreak in Hong Kong; and, (iii) the spread of SARS can be effectively controlled by either limiting long range links (imposing a partial quarantine) or enforcing rapid hospitalisation and isolation of symptomatic individuals.

PARAMETER ESTIMATION USING KALMAN FILTERS WITH CONSTRAINTS

We suggest incorporating dynamical information such as locations of unstable fixed points into parameter estimation algorithms in order to improve the method of reconstructing dynamics from time series data. We show how the process of reconstruction using nonlinear filters such as the extended Kalman filter can be easily modified to take advantage of the additional information. We demonstrate the methods using data from two systems exhibiting chaotic dynamics — the Chua circuit and Chens equations. In both cases we find the models reconstructed using constraints that better approximate the unstable fixed point structure of the underlying systems.

Noise Reduction of Chaotic Systems by Kalman Filtering and by Shadowing

We investigate two techniques for filtering signals from noisy nonlinear systems. Both the dynamics and the observed signals may be subject to noise. The first technique is a modified Kalman filter which accounts for the noise-amplification properties of chaotic systems and has less tendency to diverge than the usual Kalman filter. The second is the noise-reduction algorithm of Hammel, based on the concept of shadowing from dynamical systems theory.

Parameter inference in small world network disease models with approximate Bayesian Computational methods

Abstract Small world network models have been effective in capturing the variable behaviour of reported case data of the SARS coronavirus outbreak in Hong Kong during 2003. Simulations of these models have previously been realized using informed “guesses” of the proposed model parameters and tested for consistency with the reported data by surrogate analysis. In this paper we attempt to provide statistically rigorous parameter distributions using Approximate Bayesian Computation sampling methods. We find that such sampling schemes are a useful framework for fitting parameters of stochastic small world network models where simulation of the system is straightforward but expressing a likelihood is cumbersome.

Reconstructing nonlinear dynamics by extended Kalman filtering

We investigate the use of the extended Kalman filter as a tool for the parameter estimation of radial basis function models. We show that the method is best used as an add-on to other estimation techniques such as subset selection of the centers using a minimum description length criterion rather than as a stand-alone method. We also show that the covariance matrix returned by the extended Kalman filter can be used to calculate Rissanens minimum description length criterion more easily. Illustrative examples are given for data from the Ikeda map and two time series of real world experimental systems.

Improving musculoskeletal clinical skills teaching. A regionwide audit and intervention study

OBJECTIVE To identify factors that influence medical students’ perceptions of the quality of a clinical skills course; to apply these factors to the course at one hospital; to measure the effect of this change. DESIGN Cross sectional questionnaire survey; application of identified factors; repeat questionnaire survey. SETTING Three teaching hospitals and five district general hospitals in north east England. SUBJECTS Third year medical students attending locomotor clinical skills courses in two consecutive years. MAIN OUTCOME MEASURES Score awarded by students in five categories; numbers of patients seen by each student; comparisons with other clinical skills weeks. RESULTS Response rates were 71 of 150 and 89 of 161. Factors associated with a high awarded score were: organisation of the course by a rheumatologist (p<0.01); teaching from a rheumatologist (p<0.01); higher number of patients seen (r=0.76). Mean number of patients seen varied widely, from 7 per student at one hospital to 20.4 at another. Teaching hospitals scored poorly. In the second year, after making changes at one teaching hospital the mean total score improved (p<0.01), and students saw more patients (p<0.01). The ranking of this hospital rose from 6 to 1. The additional cost of the modified course was £640 per student. CONCLUSIONS The standard of teaching of locomotor clinical skills varies widely and can be improved by application of factors identified in this survey, although additional costs are incurred.

Inferring networks from multivariate symbolic time series to unravel behavioural interactions among animals

A traditional way to quantify synchronous interactions between animals has been to use concordance indices, which commonly do not take into account the effects of the length of the sampling time and of behaviour driven by third parties. We overcame these issues by casting the process of investigating behavioural interactions into a network inference methodology. We summarized multivariate time series using a complex network whose construction depends on a surrogate hypothesis testing data analysis of synchronous interactions between animals. The method accounts for the effect of third parties on pairwise comparisons, allows one to test the effect of the size of the sampling window on the interactions between animals, and allows one to test behavioural models of increasing complexity. We used a continuous 1-month behavioural data set of the foraging activity of a mixed-sex group of 40 Soay sheep, Ovis aries. We uncovered underlying patterns of behavioural interaction between individual sheep by applying our inferential approach to the symbolic multivariate time series of activity, that is grazing, not grazing. Our findings clearly indicate that animals of the same sex are more synchronized than animals of different sex independent of body size. We advocate that the method proposed is more general and more efficient at detecting patterns of synchronization than traditional concordance indices. We provide the reader with a comprehensive software toolbox to apply the methodology proposed.

Constructing transportable behavioural models for nonlinear electronic devices

Abstract We use radial basis functions to model the input–output response of an electronic device. A new methodology for producing models that accurately describe the response of the device over a wide range of operating points is introduced. A key to the success of the method is the ability to find a polynomial relationship between the model parameters and the operating points of the device.

Analysis of grain-scale measurements of sand using kinematical complex networks

Plastic deformation in a plane strain compression test of a dense sand specimen is studied using functional networks. Kinematical information for the deforming material is obtained using digital image correlation (DIC) and summarized by two types of complex network with different connectivity rules establishing links between the network nodes which represent the DIC observation sites. In the first, nodes are connected to a minimum fixed number of neighbors with similar kinematics such that the resulting network forms one connected component. In the second, nodes are connected to other nodes whose kinematical behavior lies within a fixed distance of each other in an observation space. The fixed radius is determined using optimization with a stopping criterion again with the resulting network forming one connected component. We find different network properties of each network provide useful information about plastic deformation and nonaffine kinematical processes emerging within the material. In particular, persistent shear bands and mesoscale structures within them (e.g. vortices) appear to be closely related to values of network properties including closeness centrality, clustering coefficients, k-cores and the boundaries of community structures determined using local modularity.

A complex systems analysis of stick-slip dynamics of a laboratory fault.

We study the stick-slip behavior of a granular bed of photoelastic disks sheared by a rough slider pulled along the surface. Time series of a proxy for granular friction are examined using complex systems methods to characterize the observed stick-slip dynamics of this laboratory fault. Nonlinear surrogate time series methods show that the stick-slip behavior appears more complex than a periodic dynamics description. Phase space embedding methods show that the dynamics can be locally captured within a four to six dimensional subspace. These slider time series also provide an experimental test for recent complex network methods. Phase space networks, constructed by connecting nearby phase space points, proved useful in capturing the key features of the dynamics. In particular, network communities could be associated to slip events and the ranking of small network subgraphs exhibited a heretofore unreported ordering.