A motif-based approach to network epidemics

Networks have become an indispensable tool in modelling infectious diseases, with the structure of epidemiologically relevant contacts known to affect both the dynamics of the infection process and the efficacy of intervention strategies. One of the key reasons for this is the presence of clustering in contact networks, which is typically analysed in terms of prevalence of triangles in the network. We present a more general approach, based on the prevalence of different four-motifs, in the context of ODE approximations to network dynamics. This is shown to outperform existing models for a range of small world networks

Modelling the impact of local reactive school closures on critical care provision during an influenza pandemic

Despite the fact that the 2009 H1N1 pandemic influenza strain was less severe than had been feared, both seasonal epidemics of influenza-like-illness and future influenza pandemics have the potential to place a serious burden on health services. The closure of schools has been postulated as a means of reducing transmission between children and hence reducing the number of cases at the peak of an epidemic; this is supported by the marked reduction in cases during school holidays observed across the world during the 2009 pandemic. However, a national policy of long-duration school closures could have severe economic costs. Reactive short-duration closure of schools in regions where health services are close to capacity offers a potential compromise, but it is unclear over what spatial scale and time frame closures would need to be made to be effective. Here, using detailed geographical information for England, we assess how localized school closures could alleviate the burden on hospital intensive care units (ICUs) that are reaching capacity. We show that, for a range of epidemiologically plausible assumptions, considerable local coordination of school closures is needed to achieve a substantial reduction in the number of hospitals where capacity is exceeded at the peak of the epidemic. The heterogeneity in demand per hospital ICU bed means that even widespread school closures are unlikely to have an impact on whether demand will exceed capacity for many hospitals. These results support the UK decision not to use localized school closures as a control mechanism, but have far wider international public-health implications. The spatial heterogeneities in both population density and hospital capacity that give rise to our results exist in many developed countries, while our model assumptions are sufficiently general to cover a wide range of pathogens. This leads us to believe that when a pandemic has severe implications for ICU capacity, only widespread school closures (with their associated costs and organizational challenges) are sufficient to mitigate the burden on the worst-affected hospitals

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

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#

Characterizing contributions of glacier melt and groundwater during the dry season in a poorly gauged catchment of the Cordillera Blanca (Peru)

The retreat of glaciers in the tropics will have a significant impact on water resources. In order to overcome limitations with discontinuous to nonexistent hydrologic measurements in remote mountain watersheds, a hydrochemical and isotopic mass balance model is used to identify and characterize dry season water origins at the glacier fed Querococha basin located in southern Cordillera Blanca, Peru. Dry season water samples, collected intermittently between 1998 and 2007, were analyzed for major ions and the stable isotopes of water (δ<sup>18</sup>O and δ<sup>2</sup>H). The hydrochemical and isotopic data are analysed using conservative characteristics of selected tracers and relative contributions are calculated based on pre-identified contributing sources at mixing points sampled across the basin. The results show that during the dry-season, groundwater is the largest contributor to basin outflow and that the flux of groundwater is temporally variable. The groundwater contribution significantly correlates (P-value=0.004 to 0.044) to the antecedent precipitation regime at 3 and 18–36 months. Assuming this indicates a maximum of 4 years of precipitation accumulation in groundwater reserves, the Querococha watershed outflows are potentially vulnerable to multi-year droughts and climate related changes in the precipitation regime. The results show that the use of hydrochemical and isotopic data can contribute to hydrologic studies in remote, data poor regions, and that groundwater contribution to tropical proglacial hydrologic systems is a critical component of dry season discharge

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

Measured Dynamic Social Contact Patterns Explain the Spread of H1N1v Influenza

Patterns of social mixing are key determinants of epidemic spread. Here we present the results of an internet-based social contact survey completed by a cohort of participants over 9,000 times between July 2009 and March 2010, during the 2009 H1N1v influenza epidemic. We quantify the changes in social contact patterns over time, finding that school children make 40% fewer contacts during holiday periods than during term time. We use these dynamically varying contact patterns to parameterise an age-structured model of influenza spread, capturing well the observed patterns of incidence; the changing contact patterns resulted in a fall of approximately 35% in the reproduction number of influenza during the holidays. This work illustrates the importance of including changing mixing patterns in epidemic models. We conclude that changes in contact patterns explain changes in disease incidence, and that the timing of school terms drove the 2009 H1N1v epidemic in the UK. Changes in social mixing patterns can be usefully measured through simple internet-based surveys