A class of pairwise models for epidemic dynamics on weighted networks

In this paper, we study the $SIS$ (susceptible-infected-susceptible) and $SIR$ (susceptible-infected-removed) epidemic models on undirected, weighted networks by deriving pairwise-type approximate models coupled with individual-based network simulation. Two different types of theoretical/synthetic weighted network models are considered. Both models start from non-weighted networks with fixed topology followed by the allocation of link weights in either (i) random or (ii) fixed/deterministic way. The pairwise models are formulated for a general discrete distribution of weights, and these models are then used in conjunction with network simulation to evaluate the impact of different weight distributions on epidemic threshold and dynamics in general. For the $SIR$ dynamics, the basic reproductive ratio $R_0$ is computed, and we show that (i) for both network models $R_{0}$ is maximised if all weights are equal, and (ii) when the two models are equally matched, the networks with a random weight distribution give rise to a higher $R_0$ value. The models are also used to explore the agreement between the pairwise and simulation models for different parameter combinations

A proposed methodology for deriving tsunami fragility functions for buildings using optimum intensity measures

Tsunami fragility curves are statistical models which form a key component of tsunami risk models, as they provide a probabilistic link between a tsunami intensity measure (TIM) and building damage. Existing studies apply different TIMs (e.g. depth, velocity, force etc.) with conflicting recommendations of which to use. This paper presents a rigorous methodology using advanced statistical methods for the selection of the optimal TIM for fragility function derivation for any given dataset. This methodology is demonstrated using a unique, detailed, disaggregated damage dataset from the 2011 Great East Japan earthquake and tsunami (total 67,125 buildings), identifying the optimum TIM for describing observed damage for the case study locations. This paper first presents the proposed methodology, which is broken into three steps: (1) exploratory analysis, (2) statistical model selection and trend analysis and (3) comparison and selection of TIMs. The case study dataset is then presented, and the methodology is then applied to this dataset. In Step 1, exploratory analysis on the case study dataset suggests that fragility curves should be constructed for the sub-categories of engineered (RC and steel) and non-engineered (wood and masonry) construction materials. It is shown that the exclusion of buildings of unknown construction material (common practice in existing studies) may introduce bias in the results; hence, these buildings are estimated as engineered or non-engineered through use of multiple imputation (MI) techniques. In Step 2, a sensitivity analysis of several statistical methods for fragility curve derivation is conducted in order to select multiple statistical models with which to conduct further exploratory analysis and the TIM comparison (to draw conclusions which are non-model-specific). Methods of data aggregation and ordinary least squares parameter estimation (both used in existing studies) are rejected as they are quantitatively shown to reduce fragility curve accuracy and increase uncertainty. Partially ordered probit models and generalised additive models (GAMs) are selected for the TIM comparison of Step 3. In Step 3, fragility curves are then constructed for a number of TIMs, obtained from numerical simulation of the tsunami inundation of the 2011 GEJE. These fragility curves are compared using K-fold cross-validation (KFCV), and it is found that for the case study dataset a force-based measure that considers different flow regimes (indicated by Froude number) proves the most efficient TIM. It is recommended that the methodology proposed in this paper be applied for defining future fragility functions based on optimum TIMs. With the introduction of several concepts novel to the field of fragility assessment (MI, GAMs, KFCV for model optimisation and comparison), this study has significant implications for the future generation of empirical and analytical fragility functions

FishFace: interactive atlas of zebrafish craniofacial development at cellular resolution

Background: The vertebrate craniofacial skeleton may exhibit anatomical complexity and diversity, but its genesis and evolution can be understood through careful dissection of developmental programs at cellular resolution. Resources are lacking that include introductory overviews of skeletal anatomy coupled with descriptions of craniofacial development at cellular resolution. In addition to providing analytical guidelines for other studies, such an atlas would suggest cellular mechanisms underlying development. Description We present the Fish Face Atlas, an online, 3D-interactive atlas of craniofacial development in the zebrafish Danio rerio. Alizarin red-stained skulls scanned by fluorescent optical projection tomography and segmented into individual elements provide a resource for understanding the 3D structure of the zebrafish craniofacial skeleton. These data provide the user an anatomical entry point to confocal images of Alizarin red-stained zebrafish with transgenically-labelled pharyngeal arch ectomesenchyme, chondrocytes, and osteoblasts, which illustrate the appearance, morphogenesis, and growth of the mandibular and hyoid cartilages and bones, as viewed in live, anesthetized zebrafish during embryonic and larval development. Confocal image stacks at high magnification during the same stages provide cellular detail and suggest developmental and evolutionary hypotheses. Conclusion: The FishFace Atlas is a novel learning tool for understanding craniofacial skeletal development, and can serve as a reference for a variety of studies, including comparative and mutational analyses

Effects of Contact Network Models on Stochastic Epidemic Simulations

The importance of modeling the spread of epidemics through a population has led to the development of mathematical models for infectious disease propagation. A number of empirical studies have collected and analyzed data on contacts between individuals using a variety of sensors. Typically one uses such data to fit a probabilistic model of network contacts over which a disease may propagate. In this paper, we investigate the effects of different contact network models with varying levels of complexity on the outcomes of simulated epidemics using a stochastic Susceptible-Infectious-Recovered (SIR) model. We evaluate these network models on six datasets of contacts between people in a variety of settings. Our results demonstrate that the choice of network model can have a significant effect on how closely the outcomes of an epidemic simulation on a simulated network match the outcomes on the actual network constructed from the sensor data. In particular, preserving degrees of nodes appears to be much more important than preserving cluster structure for accurate epidemic simulations.Comment: To appear at International Conference on Social Informatics (SocInfo) 201

Fast variables determine the epidemic threshold in the pairwise model with an improved closure

Pairwise models are used widely to model epidemic spread on networks. These include the modelling of susceptible-infected-removed (SIR) epidemics on regular networks and extensions to SIS dynamics and contact tracing on more exotic networks exhibiting degree heterogeneity, directed and/or weighted links and clustering. However, extra features of the disease dynamics or of the network lead to an increase in system size and analytical tractability becomes problematic. Various `closures' can be used to keep the system tractable. Focusing on SIR epidemics on regular but clustered networks, we show that even for the most complex closure we can determine the epidemic threshold as an asymptotic expansion in terms of the clustering coefficient.We do this by exploiting the presence of a system of fast variables, specified by the correlation structure of the epidemic, whose steady state determines the epidemic threshold. While we do not find the steady state analytically, we create an elegant asymptotic expansion of it. We validate this new threshold by comparing it to the numerical solution of the full system and find excellent agreement over a wide range of values of the clustering coefficient, transmission rate and average degree of the network. The technique carries over to pairwise models with other closures [1] and we note that the epidemic threshold will be model dependent. This emphasises the importance of model choice when dealing with realistic outbreaks

A pattern matching technique for measuring sediment displacement levels

This paper describes a novel technique for obtaining accurate, high (spatial) resolution measurements of sediment redeposition levels. A sequence of different random patterns are projected onto a sediment layer and captured using a high-resolution camera, producing a set of reference images. The same patterns are used to obtain a corresponding sequence of deformed images after a region of the sediment layer has been displaced and redeposited, allowing the use of a high-accuracy pattern matching algorithm to quantify the distribution of the redeposited sediment. A set of experiments using the impact of a vortex ring with a glass ballotini particle layer as the resuspension mechanism are described to test and illustrate the technique. The accuracy of the procedure is assessed using a known crater profile, manufactured to simulate the features of the craters observed in the experiments

Dynamics of multi-stage infections on networks

This paper investigates the dynamics of infectious diseases with a nonexponentially distributed infectious period. This is achieved by considering a multistage infection model on networks. Using pairwise approximation with a standard closure, a number of important characteristics of disease dynamics are derived analytically, including the final size of an epidemic and a threshold for epidemic outbreaks, and it is shown how these quantities depend on disease characteristics, as well as the number of disease stages. Stochastic simulations of dynamics on networks are performed and compared to output of pairwise models for several realistic examples of infectious diseases to illustrate the role played by the number of stages in the disease dynamics. These results show that a higher number of disease stages results in faster epidemic outbreaks with a higher peak prevalence and a larger final size of the epidemic. The agreement between the pairwise and simulation models is excellent in the cases we consider

Epidemics on contact networks: a general stochastic approach

Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach is especially well adapted for modelling spreading processes and/or population dynamics. In particular, the generality of our systematic framework and the fact that its assumptions are explicitly stated suggests that it could be used as a common ground for comparing existing epidemics models too complex for direct comparison, such as agent-based computer simulations. We provide many examples for the special cases of susceptible-infectious-susceptible (SIS) and susceptible-infectious-removed (SIR) dynamics (e.g., epidemics propagation) and we observe multiple situations where accurate results may be obtained at low computational cost. Our perspective reveals a subtle balance between the complex requirements of a realistic model and its basic assumptions.Comment: Main document: 16 pages, 7 figures. Electronic Supplementary Material (included): 6 pages, 1 tabl

School's Out: Seasonal Variation in the Movement Patterns of School Children.

School children are core groups in the transmission of many common infectious diseases, and are likely to play a key role in the spatial dispersal of disease across multiple scales. However, there is currently little detailed information about the spatial movements of this epidemiologically important age group. To address this knowledge gap, we collaborated with eight secondary schools to conduct a survey of movement patterns of school pupils in primary and secondary schools in the United Kingdom. We found evidence of a significant change in behaviour between term time and holidays, with term time weekdays characterised by predominately local movements, and holidays seeing much broader variation in travel patterns. Studies that use mathematical models to examine epidemic transmission and control often use adult commuting data as a proxy for population movements. We show that while these data share some features with the movement patterns reported by school children, there are some crucial differences between the movements of children and adult commuters during both term-time and holidays.AJK was supported by the Medical Research Council (fellowship MR/K021524/1, http://www.mrc.ac.uk/) and the RAPIDD program of the Science & Technology Directorate, Department of Homeland Security, and the Fogarty International Center, National Institutes of Health (http://www.fic.nih.gov/about/staff/pages​/epidemiology-population.aspx#rapidd). AJKC was supported by the Alborada Trust (http://www.alboradatrust.com/). KTDE was supported by the NIHR (CDF-2011-04- 019, http://www.nihr.ac.uk/). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.This is the final version. It was first published by PLOS at http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0128070#

Robust modeling of human contact networks across different scales and proximity-sensing techniques

The problem of mapping human close-range proximity networks has been tackled using a variety of technical approaches. Wearable electronic devices, in particular, have proven to be particularly successful in a variety of settings relevant for research in social science, complex networks and infectious diseases dynamics. Each device and technology used for proximity sensing (e.g., RFIDs, Bluetooth, low-power radio or infrared communication, etc.) comes with specific biases on the close-range relations it records. Hence it is important to assess which statistical features of the empirical proximity networks are robust across different measurement techniques, and which modeling frameworks generalize well across empirical data. Here we compare time-resolved proximity networks recorded in different experimental settings and show that some important statistical features are robust across all settings considered. The observed universality calls for a simplified modeling approach. We show that one such simple model is indeed able to reproduce the main statistical distributions characterizing the empirical temporal networks