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The number of COVID-19 outbreaks reported in UK care homes rose rapidly in early March of 2020. Owing to the increased co-morbidities and therefore worse COVID-19 outcomes for care home residents, it is important that we understand this increase and its future implications. We demonstrate the use of an SIS model where each nursing home is an infective unit capable of either being susceptible to an outbreak (S) or in an active outbreak (I). We use a generalized additive model to approximate the trend in growth rate of outbreaks in care homes and find the fit to be improved in a model where the growth rate is proportional to the number of current care home outbreaks compared with a model with a constant growth rate. Using parameters found from the outbreak-dependent growth rate, we predict a 73% prevalence of outbreaks in UK care homes without intervention as a reasonable worst-case planning assumption. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.

We explore strategies of contact tracing, case isolation and quarantine of exposed contacts to control the SARS-CoV-2 epidemic using a branching process model with household structure. This structure reflects higher transmission risks among household members than among non-household members. We explore strategic implementation choices that make use of household structure, and investigate strategies including two-step tracing, backwards tracing, smartphone tracing and tracing upon symptom report rather than test results. The primary model outcome is the effect of contact tracing, in combination with different levels of physical distancing, on the growth rate of the epidemic. Furthermore, we investigate epidemic extinction times to indicate the time period over which interventions must be sustained. We consider effects of non-uptake of isolation/quarantine, non-adherence, and declining recall of contacts over time. Our results find that, compared to self-isolation of cases without contact tracing, a contact tracing strategy designed to take advantage of household structure allows for some relaxation of physical distancing measures but cannot completely control the epidemic absent of other measures. Even assuming no imported cases and sustainment of moderate physical distancing, testing and tracing efforts, the time to bring the epidemic to extinction could be in the order of months to years. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.

Background: Information on SARS-CoV-2 in representative community surveillance is limited, particularly cycle threshold (Ct) values (a proxy for viral load)., Methods: We included all positive nose and throat swabs 26 April 2020 to 13 March 2021 from the UK's national COVID-19 Infection Survey, tested by RT-PCR for the N, S, and ORF1ab genes. We investigated predictors of median Ct value using quantile regression., Results: Of 3,312,159 nose and throat swabs, 27,902 (0.83%) were RT-PCR-positive, 10,317 (37%), 11,012 (40%), and 6550 (23%) for 3, 2, or 1 of the N, S, and ORF1ab genes, respectively, with median Ct = 29.2 (~215 copies/ml; IQR Ct = 21.9-32.8, 14-56,400 copies/ml). Independent predictors of lower Cts (i.e. higher viral load) included self-reported symptoms and more genes detected, with at most small effects of sex, ethnicity, and age. Single-gene positives almost invariably had Ct > 30, but Cts varied widely in triple-gene positives, including without symptoms. Population-level Cts changed over time, with declining Ct preceding increasing SARS-CoV-2 positivity. Of 6189 participants with IgG S-antibody tests post-first RT-PCR-positive, 4808 (78%) were ever antibody-positive; Cts were significantly higher in those remaining antibody negative., Conclusions: Marked variation in community SARS-CoV-2 Ct values suggests that they could be a useful epidemiological early-warning indicator., Funding: Department of Health and Social Care, National Institutes of Health Research, Huo Family Foundation, Medical Research Council UK; Wellcome Trust., Competing Interests: AW, EP, TH, JR, PB, IB, JB, JN, JF, ID, RS, JH, KV, TP, NS, PM, KP No competing interests declared, DE declares lecture fees from Gilead, outside the submitted work., (© 2021, Walker et al.)

Competing Interests: IEB has received personal fees from AstraZeneca for his role as a chief data scientist advisor via the University of Liverpool. The other authors declare no competing interests.

Background: Achieving food security remains a key challenge for public policy throughout the world. As such, understanding the determinants of food insecurity and the causal relationships between them is an important scientific question. We aim to construct a Bayesian belief network model of food security in rural South Africa to act as a tool for decision support in the design of interventions., Methods: Here, we use data from the Agincourt Health and Socio-demographic Surveillance System (HDSS) study area, which is close to the Mozambique border in a low-income region of South Africa, together with Bayesian belief network (BBN) methodology to address this question., Results: We find that a combination of expert elicitation and learning from data produces the most credible set of causal relationships, as well as the greatest predictive performance with 10-fold cross validation resulting in a Briers score 0.0846, information reward of 0.5590, and Bayesian information reward of 0.0057. We report the resulting model as a directed acyclic graph (DAG) that can be used to model the expected effects of complex interventions to improve food security. Applications to sensitivity analyses and interventional simulations show ways the model can be applied as tool for decision support for human experts in deciding on interventions., Conclusions: The resulting models can form the basis of the iterative generation of a robust causal model of household food security in the Agincourt HDSS study area and in other similar populations.

Fibronectin (FN) is an extracellular matrix (ECM) glycoprotein that self-assembles into FN fibrils, forming a FN matrix contributing to the stiffness of the ECM. Stromal FN stiffness in cancer has been shown to impact epithelial functions such as migration, cancer metastasis, and epithelial-to-mesenchymal transition. The role of the FN matrix of epithelial cells in driving such processes remains less well understood and is the focus of this study. Hypoxia, defined by low oxygen tension (<5%) is one of the hallmarks of tumor microenvironments impacting fibril reorganization in stromal and epithelial cells. Here, using the MCF10 breast epithelial progression series of cell lines encompassing normal, preinvasive, and invasive states, we show that FN fibril formation decreases during hypoxia, coinciding with a decrease in migratory potential of these cells. Conversely, we find that FN fibril disruption during three-dimensional acinar growth of normal breast cells resulted in acinar luminal filling. Our data also demonstrates that the luminal filling upon fibril disruption in untransformed MCF10A cells results in a loss of apicobasal polarity, characteristic of pre-invasive and invasive breast cell lines MCF10AT and MCF10 DCIS.com. Overall this is the first study that relates fibril-mediated changes in epithelial cells as critical players in lumen clearing of breast acini and maintenance of the untransformed growth characteristic., (© 2021 The Authors. Journal of Cellular Biochemistry published by Wiley Periodicals LLC.)

Background: Decisions about the continued need for control measures to contain the spread of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) rely on accurate and up-to-date information about the number of people testing positive for SARS-CoV-2 and risk factors for testing positive. Existing surveillance systems are generally not based on population samples and are not longitudinal in design., Methods: Samples were collected from individuals aged 2 years and older living in private households in England that were randomly selected from address lists and previous Office for National Statistics surveys in repeated cross-sectional household surveys with additional serial sampling and longitudinal follow-up. Participants completed a questionnaire and did nose and throat self-swabs. The percentage of individuals testing positive for SARS-CoV-2 RNA was estimated over time by use of dynamic multilevel regression and poststratification, to account for potential residual non-representativeness. Potential changes in risk factors for testing positive over time were also assessed. The study is registered with the ISRCTN Registry, ISRCTN21086382., Findings: Between April 26 and Nov 1, 2020, results were available from 1 191 170 samples from 280 327 individuals; 5231 samples were positive overall, from 3923 individuals. The percentage of people testing positive for SARS-CoV-2 changed substantially over time, with an initial decrease between April 26 and June 28, 2020, from 0·40% (95% credible interval 0·29-0·54) to 0·06% (0·04-0·07), followed by low levels during July and August, 2020, before substantial increases at the end of August, 2020, with percentages testing positive above 1% from the end of October, 2020. Having a patient-facing role and working outside your home were important risk factors for testing positive for SARS-CoV-2 at the end of the first wave (April 26 to June 28, 2020), but not in the second wave (from the end of August to Nov 1, 2020). Age (young adults, particularly those aged 17-24 years) was an important initial driver of increased positivity rates in the second wave. For example, the estimated percentage of individuals testing positive was more than six times higher in those aged 17-24 years than in those aged 70 years or older at the end of September, 2020. A substantial proportion of infections were in individuals not reporting symptoms around their positive test (45-68%, dependent on calendar time., Interpretation: Important risk factors for testing positive for SARS-CoV-2 varied substantially between the part of the first wave that was captured by the study (April to June, 2020) and the first part of the second wave of increased positivity rates (end of August to Nov 1, 2020), and a substantial proportion of infections were in individuals not reporting symptoms, indicating that continued monitoring for SARS-CoV-2 in the community will be important for managing the COVID-19 pandemic moving forwards., Funding: Department of Health and Social Care., (Copyright © 2021 The Author(s). Published by Elsevier Ltd. This is an Open Access article under the CC BY 4.0 license. Published by Elsevier Ltd.. All rights reserved.)

Dry eye syndrome (DES) is a chronic condition of the eye with insufficient production of tears leading to inadequate lubrication of eyes. Symptoms of DES are associated with discomfort and redness of the eye, blurred vision, and tear film instability which leads to the damaged ocular surface. Inflammation and oxidative stress play a significant role in the pathogenesis of the disease. In this study, the protective effect of different doses (100 or 200 mg/kg) of a novel multi-component oral formulation of lutein/zeaxanthin, curcumin, and vitamin D3 (LCD) was evaluated using a rat model with benzalkonium chloride (BAC)-induced dry eye syndrome. The formulation was administered orally to rats for 4 weeks. We observed a significant improvement in tear volume, tear breakup time, tear film integrity, and reduction in overall inflammation in rats fed with the LCD at dose 200 mg/kg performing better than 100 mg/kg. Furthermore, the formulation helped in lowering oxidative stress by increasing antioxidant levels and restored protective tear protein levels including MUC1, MUC4, and MUC5AC with 200 mg of LCD having the most significant effect. The results strongly suggest that the combination of lutein/zeaxanthin, curcumin, and vitamin-D3 is effective in alleviating the symptoms of dry eye condition with a multi-modal mechanism of action.

Modern data and computational resources, coupled with algorithmic and theoretical advances to exploit these, allow disease dynamic models to be parameterised with increasing detail and accuracy. While this enhances models' usefulness in prediction and policy, major challenges remain. In particular, lack of identifiability of a model's parameters may limit the usefulness of the model. While lack of parameter identifiability may be resolved through incorporation into an inference procedure of prior knowledge, formulating such knowledge is often difficult. Furthermore, there are practical challenges associated with acquiring data of sufficient quantity and quality. Here, we discuss recent progress on these issues., (Copyright © 2020 The Author(s). Published by Elsevier B.V. All rights reserved.)

Combinations of intense non-pharmaceutical interventions (lockdowns) were introduced worldwide to reduce SARS-CoV-2 transmission. Many governments have begun to implement exit strategies that relax restrictions while attempting to control the risk of a surge in cases. Mathematical modelling has played a central role in guiding interventions, but the challenge of designing optimal exit strategies in the face of ongoing transmission is unprecedented. Here, we report discussions from the Isaac Newton Institute 'Models for an exit strategy' workshop (11-15 May 2020). A diverse community of modellers who are providing evidence to governments worldwide were asked to identify the main questions that, if answered, would allow for more accurate predictions of the effects of different exit strategies. Based on these questions, we propose a roadmap to facilitate the development of reliable models to guide exit strategies. This roadmap requires a global collaborative effort from the scientific community and policymakers, and has three parts: (i) improve estimation of key epidemiological parameters; (ii) understand sources of heterogeneity in populations; and (iii) focus on requirements for data collection, particularly in low-to-middle-income countries. This will provide important information for planning exit strategies that balance socio-economic benefits with public health.

During an infectious disease outbreak, biases in the data and complexities of the underlying dynamics pose significant challenges in mathematically modelling the outbreak and designing policy. Motivated by the ongoing response to COVID-19, we provide a toolkit of statistical and mathematical models beyond the simple SIR-type differential equation models for analysing the early stages of an outbreak and assessing interventions. In particular, we focus on parameter estimation in the presence of known biases in the data, and the effect of non-pharmaceutical interventions in enclosed subpopulations, such as households and care homes. We illustrate these methods by applying them to the COVID-19 pandemic., Competing Interests: The authors declare no competing interests., (© 2020 The Authors.)

Introduction: Major advances in the field of pediatric oncology have resulted from rigorous, prospective clinical oncology research trials. Optimizing access for all children and adolescents to clinical research trials is an important goal. Barriers to clinical trial enrollment are numerous, involving the health care system, research infrastructure, access to care, providers, and participants. The perspectives of pediatric oncologists may provide insight into the barriers of clinical trial enrollment for this unique population., Methods and Materials: We conducted qualitative structured interviews over two months of pediatric oncologists in a community-based clinical network as part of a quality improvement project aimed at increasing enrollment rates at St. Jude Affiliate Clinics. We assessed barriers and facilitators to clinical trial opportunities for racial and ethnic minority pediatric participants. In the same fiscal year of the interviews, we tracked clinical trial enrollment by race and ethnicity of the participant over 12 months., Results: The major barriers to clinical trial enrollment for pediatric cancer minority participants included language discordance, travel difficulties, and complex trial designs. In contrast, the major facilitators included building trust with participants and their parents, and education on the merits of clinical research studies. We did not observe any disparities in clinical trial enrollment among the racial and ethnic minority participants of the clinical trials conducted across our network of pediatric oncology clinics., Conclusions: Identifying barriers and facilitators may improve clinical trial enrollment for underrepresented participant groups., (© 2019 The Authors. Pediatric Blood & Cancer published by Wiley Periodicals, Inc.)

Patients with chronic pain commonly believe their pain is related to the weather. Scientific evidence to support their beliefs is inconclusive, in part due to difficulties in getting a large dataset of patients frequently recording their pain symptoms during a variety of weather conditions. Smartphones allow the opportunity to collect data to overcome these difficulties. Our study Cloudy with a Chance of Pain analysed daily data from 2658 patients collected over a 15-month period. The analysis demonstrated significant yet modest relationships between pain and relative humidity, pressure and wind speed, with correlations remaining even when accounting for mood and physical activity. This research highlights how citizen-science experiments can collect large datasets on real-world populations to address long-standing health questions. These results will act as a starting point for a future system for patients to better manage their health through pain forecasts., Competing Interests: Competing interestsW.G.D. has received consultancy fees from Bayer Pharmaceuticals and Google, unrelated to this study. B.J. and B.H. are co-founders of uMotif. All other authors declare no competing interests., (© The Author(s) 2019.)

The Pompe model is the term used by the Pompe community to describe the relationship that exists between the patient community, the medical/scientific community, and industry. The development of the Pompe model represented a new paradigm for the involvement of patients in new treatments-and also for scientists and pharmaceutical companies. It saw patients developing a sense of agency, of involvement in the process of treatment development rather than powerless recipients or (if lucky) occasional spectators. At the same time, as described below, it benefited the other partners in the process with the result that the different components of the model added up to more than the sum of their parts. However, in order for this to happen, each part had to undergo a transformation in mindset. The development of enzyme replacement therapy (ERT) for Pompe disease represented a unique set of circumstances and individuals that helped to bring about this change and, in doing so, created a model that has had far wider applications., Competing Interests: Conflicts of Interest: The authors have no conflicts of interest to declare.

In Bangladesh, the poultry industry is an economically and socially important sector, but it is persistently threatened by the effects of H5N1 highly pathogenic avian influenza. Thus, identifying the optimal control policy in response to an emerging disease outbreak is a key challenge for policy-makers. To inform this aim, a common approach is to carry out simulation studies comparing plausible strategies, while accounting for known capacity restrictions. In this study we perform simulations of a previously developed H5N1 influenza transmission model framework, fitted to two separate historical outbreaks, to assess specific control objectives related to the burden or duration of H5N1 outbreaks among poultry farms in the Dhaka division of Bangladesh. In particular, we explore the optimal implementation of ring culling, ring vaccination and active surveillance measures when presuming disease transmission predominately occurs from premises-to-premises, versus a setting requiring the inclusion of external factors. Additionally, we determine the sensitivity of the management actions under consideration to differing levels of capacity constraints and outbreaks with disparate transmission dynamics. While we find that reactive culling and vaccination policies should pay close attention to these factors to ensure intervention targeting is optimised, across multiple settings the top performing control action amongst those under consideration were targeted proactive surveillance schemes. Our findings may advise the type of control measure, plus its intensity, that could potentially be applied in the event of a developing outbreak of H5N1 amongst originally H5N1 virus-free commercially-reared poultry in the Dhaka division of Bangladesh., Competing Interests: The authors have declared that no competing interests exist.

Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights into the near-critical regime by considering the stochastic SIS logistic epidemic, a well-known birth-and-death chain used to model the spread of an epidemic within a population of a given size N. We study the behaviour of the process as the population size N tends to infinity. Our results cover the entire subcritical regime, including the "barely subcritical" regime, where the recovery rate exceeds the infection rate by an amount that tends to 0 as [Formula: see text] but more slowly than [Formula: see text]. We derive precise asymptotics for the distribution of the extinction time and the total number of cases throughout the subcritical regime, give a detailed description of the course of the epidemic, and compare to numerical results for a range of parameter values. We hypothesise that features of the course of the epidemic will be seen in a wide class of other epidemic models, and we use real data to provide some tentative and preliminary support for this theory.

We present a flexible framework for deriving and quantifying the accuracy of Gaussian process approximations to non-linear stochastic individual-based models of epidemics. We develop this for the SIR and SEIR models, and we show how it can be used to perform quick maximum likelihood inference for the underlying parameters given population estimates of the number of infecteds or cases at given time points. We also show how the unobserved processes can be inferred at the same time as the underlying parameters., (Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.)

In the context of an ageing population, understanding the transmission of infectious diseases such as scabies through well-connected sub-units of the population, such as residential care homes, is particularly important for the design of efficient interventions to mitigate against the effects of those diseases. Here, we present a modelling methodology based on the efficient solution of a large-scale system of linear differential equations that allows statistical calibration of individual-based random models to real data on scabies in residential care homes. In particular, we review and benchmark different numerical methods for the integration of the differential equation system, and then select the most appropriate of these methods to perform inference using Markov chain Monte Carlo. We test the goodness-of-fit of this model using posterior predictive intervals and propagate forward the resulting parameter uncertainty in a Bayesian framework to consider the economic cost of delayed interventions against scabies, quantifying the benefits of prompt action in the event of detection. We also revisit the previous methodology used to assess the safety of treatments in small population sub-units-in this context ivermectin-and demonstrate that even a very slight relaxation of the implicit assumption of homogeneous death rates significantly increases the plausibility of the hypothesis that ivermectin does not cause excess mortality based upon the data of Barkwell and Shields.

Background: Central to the study of populations, and therefore to the analysis of the development of countries undergoing major transitions, is the calculation of fertility patterns and their dependence on different variables such as age, education, and socio-economic status. Most epidemiological research on these matters rely on the often unjustified assumption of (generalised) linearity, or alternatively makes a parametric assumption (e.g. for age-patterns)., Methods: We consider nonlinearity of fertility in the covariates by combining an established nonlinear parametric model for fertility over age with nonlinear modelling of fertility over other covariates. For the latter, we use the semi-parametric method of Gaussian process regression which is a popular methodology in many fields including machine learning, computer science, and systems biology. We applied the method to data from the Agincourt Health and Socio-Demographic Surveillance System, annual census rounds performed on a poor rural region of South Africa since 1992, to analyse fertility patterns over age and socio-economic status., Results: We capture a previously established age-pattern of fertility, whilst being able to more robustly model the relationship between fertility and socio-economic status without unjustified a priori assumptions of linearity. Peak fertility over age is shown to be increasing over time, as well as for adolescents but not for those later in life for whom fertility is generally decreasing over time., Conclusions: Combining Gaussian process regression with nonlinear parametric modelling of fertility over age allowed for the incorporation of further covariates into the analysis without needing to assume a linear relationship. This enabled us to provide further insights into the fertility patterns of the Agincourt study area, in particular the interaction between age and socio-economic status.

Objective: To investigate the frequency and distribution of characteristics of the Achilles tendon (AT) in people with tophaceous gout using musculoskeletal ultrasound (US)., Methods: Twenty-four participants with tophaceous gout and 24 age- and sex-matched controls without gout or other arthritis were recruited. All participants underwent a greyscale and power Doppler US examination. The AT was divided into 3 anatomical zones (insertion, pre-insertional, and proximal to the mid-section). The following US characteristics were assessed: tophus, tendon echogenicity, tendon vascularity, tendon morphology, entheseal characteristics, bursal morphology, and calcaneal bone profile., Results: The majority of the participants with tophaceous gout were middle-aged men (n = 22, 92%) predominately of European ethnicity (n = 14, 58%). Tophus deposition was observed in 73% (n = 35) of tendons in those with gout and in none of the controls (p < 0.01). Intratendinous hyperechoic spots (p < 0.01) and intratendinous power Doppler signal (p < 0.01) were more frequent in participants with gout compared to controls. High prevalence of entheseal calcifications, calcaneal bone cortex irregularities, and calcaneal enthesophytes were observed in both gout participants and controls, without differences between groups. Intratendinous structural damage was rare. Hyperechoic spots were significantly more common at the insertion compared to the zone proximal to the mid-section (p < 0.01), but between-zone differences were not observed for other features., Conclusion: US features of urate deposition, tophus, and vascularization are present throughout the AT in patients with tophaceous gout. Despite crystal deposition, intratendinous structural changes are infrequent. Many characteristics observed in the AT in people with tophaceous gout, particularly at the calcaneal enthesis, are not disease-specific.

Recent research has provided evidence that mood can spread over social networks via social contagion, but that, in seeming contradiction to this, depression does not. Here, we investigate whether there is evidence for the individual components of mood (such as appetite, tiredness and sleep) spreading through US adolescent friendship networks while adjusting for confounding by modelling the transition probabilities of changing mood state over time. We find that having more friends with worse mood is associated with a higher probability of an adolescent worsening in mood and a lower probability of improving, and vice versa for friends with better mood, for the overwhelming majority of mood components. We also show, however, that this effect is not strong enough in the negative direction to lead to a significant increase in depression incidence, helping to resolve the seeming contradictory nature of existing research. Our conclusions, therefore, link in to current policy discussions on the importance of subthreshold levels of depressive symptoms and could help inform interventions against depression in high schools., Competing Interests: The authors declare that they have no competing interests.

Highly pathogenic avian influenza H5N1 remains a persistent public health threat, capable of causing infection in humans with a high mortality rate while simultaneously negatively impacting the livestock industry. A central question is to determine regions that are likely sources of newly emerging influenza strains with pandemic causing potential. A suitable candidate is Bangladesh, being one of the most densely populated countries in the world and having an intensifying farming system. It is therefore vital to establish the key factors, specific to Bangladesh, that enable both continued transmission within poultry and spillover across the human-animal interface. We apply a modelling framework to H5N1 epidemics in the Dhaka region of Bangladesh, occurring from 2007 onwards, that resulted in large outbreaks in the poultry sector and a limited number of confirmed human cases. This model consisted of separate poultry transmission and zoonotic transmission components. Utilising poultry farm spatial and population information a set of competing nested models of varying complexity were fitted to the observed case data, with parameter inference carried out using Bayesian methodology and goodness-of-fit verified by stochastic simulations. For the poultry transmission component, successfully identifying a model of minimal complexity, which enabled the accurate prediction of the size and spatial distribution of cases in H5N1 outbreaks, was found to be dependent on the administration level being analysed. A consistent outcome of non-optimal reporting of infected premises materialised in each poultry epidemic of interest, though across the outbreaks analysed there were substantial differences in the estimated transmission parameters. The zoonotic transmission component found the main contributor to spillover transmission of H5N1 in Bangladesh was found to differ from one poultry epidemic to another. We conclude by discussing possible explanations for these discrepancies in transmission behaviour between epidemics, such as changes in surveillance sensitivity and biosecurity practices., (Copyright © 2017 The Authors. Published by Elsevier B.V. All rights reserved.)

Recent years have seen a large amount of interest in epidemics on networks as a way of representing the complex structure of contacts capable of spreading infections through the modern human population. The configuration model is a popular choice in theoretical studies since it combines the ability to specify the distribution of the number of contacts (degree) with analytical tractability. Here we consider the early real-time behaviour of the Markovian SIR epidemic model on a configuration model network using a multitype branching process. We find closed-form analytic expressions for the mean and variance of the number of infectious individuals as a function of time and the degree of the initially infected individual(s), and write down a system of differential equations for the probability of extinction by time t that are numerically fast compared to Monte Carlo simulation. We show that these quantities are all sensitive to the degree distribution-in particular we confirm that the mean prevalence of infection depends on the first two moments of the degree distribution and the variance in prevalence depends on the first three moments of the degree distribution. In contrast to most existing analytic approaches, the accuracy of these results does not depend on having a large number of infectious individuals, meaning that in the large population limit they would be asymptotically exact even for one initial infectious individual.

Social influence can lead to behavioural 'fads' that are briefly popular and quickly die out. Various models have been proposed for these phenomena, but empirical evidence of their accuracy as real-world predictive tools has so far been absent. Here we find that a 'complex contagion' model accurately describes the spread of behaviours driven by online sharing. We found that standard, 'simple', contagion often fails to capture both the rapid spread and the long tails of popularity seen in real fads, where our complex contagion model succeeds. Complex contagion also has predictive power: it successfully predicted the peak time and duration of the ALS Icebucket Challenge. The fast spread and longer duration of fads driven by complex contagion has important implications for activities such as publicity campaigns and charity drives.

Background: As service provision and patient behaviour varies by day, healthcare data used for public health surveillance can exhibit large day of the week effects. These regular effects are further complicated by the impact of public holidays. Real-time syndromic surveillance requires the daily analysis of a range of healthcare data sources, including family doctor consultations (called general practitioners, or GPs, in the UK). Failure to adjust for such reporting biases during analysis of syndromic GP surveillance data could lead to misinterpretations including false alarms or delays in the detection of outbreaks. The simplest smoothing method to remove a day of the week effect from daily time series data is a 7-day moving average. Public Health England developed the working day moving average in an attempt also to remove public holiday effects from daily GP data. However, neither of these methods adequately account for the combination of day of the week and public holiday effects., Methods: The extended working day moving average was developed. This is a further data-driven method for adding a smooth trend curve to a time series graph of daily healthcare data, that aims to take both public holiday and day of the week effects into account. It is based on the assumption that the number of people seeking healthcare services is a combination of illness levels/severity and the ability or desire of patients to seek healthcare each day. The extended working day moving average was compared to the seven-day and working day moving averages through application to data from two syndromic indicators from the GP in-hours syndromic surveillance system managed by Public Health England., Results: The extended working day moving average successfully smoothed the syndromic healthcare data by taking into account the combined day of the week and public holiday effects. In comparison, the seven-day and working day moving averages were unable to account for all these effects, which led to misleading smoothing curves., Conclusions: The results from this study make it possible to identify trends and unusual activity in syndromic surveillance data from GP services in real-time independently of the effects caused by day of the week and public holidays, thereby improving the public health action resulting from the analysis of these data.

Influenza A viruses have caused a number of global pandemics, with considerable mortality in humans. Here, we analyse the time periods between influenza pandemics since 1700 under different assumptions to determine whether the emergence of new pandemic strains is a memoryless or history-dependent process. Bayesian model selection between exponential and gamma distributions for these time periods gives support to the hypothesis of history-dependence under eight out of nine sets of modelling assumptions. Using the fitted parameters to make predictions shows a high level of variability in the modelled number of pandemics from 2010-2110. The approach we take here relies on limited data, so is uncertain, but it provides cheap, safe and direct evidence relating to pandemic emergence, a field where indirect measurements are often made at great risk and cost.

Emergence of new diseases and elimination of existing diseases is a key public health issue. In mathematical models of epidemics, such phenomena involve the process of infections and recoveries passing through a critical threshold where the basic reproductive ratio is 1. In this paper, we study near-critical behaviour in the context of a susceptible-infective-recovered epidemic on a random (multi)graph on n vertices with a given degree sequence. We concentrate on the regime just above the threshold for the emergence of a large epidemic, where the basic reproductive ratio is [Formula: see text], with [Formula: see text] tending to infinity slowly as the population size, n, tends to infinity. We determine the probability that a large epidemic occurs, and the size of a large epidemic. Our results require basic regularity conditions on the degree sequences, and the assumption that the third moment of the degree of a random susceptible vertex stays uniformly bounded as [Formula: see text]. As a corollary, we determine the probability and size of a large near-critical epidemic on a standard binomial random graph in the 'sparse' regime, where the average degree is constant. As a further consequence of our method, we obtain an improved result on the size of the giant component in a random graph with given degrees just above the critical window, proving a conjecture by Janson and Luczak.

Network-based infectious disease models have been highly effective in elucidating the role of contact structure in the spread of infection. As such, pair- and neighbourhood-based approximation models have played a key role in linking findings from network simulations to standard (random-mixing) results. Recently, for SIR-type infections (that produce one epidemic in a closed population) on locally tree-like networks, these approximations have been shown to be exact. However, network models are ideally suited for Sexually Transmitted Infections (STIs) due to the greater level of detail available for sexual contact networks, and these diseases often possess SIS-type dynamics. Here, we consider the accuracy of three systematic approximations that can be applied to arbitrary disease dynamics, including SIS behaviour. We focus in particular on low degree networks, in which the small number of neighbours causes build-up of local correlations between the state of adjacent nodes that are challenging to capture. By examining how and when these approximation models converge to simulation results, we generate insights into the role of network structure in the infection dynamics of SIS-type infections., Competing Interests: The authors have declared that no competing interests exist.

Networks of contacts capable of spreading infectious diseases are often observed to be highly heterogeneous, with the majority of individuals having fewer contacts than the mean, and a significant minority having relatively very many contacts. We derive a two-dimensional diffusion model for the full temporal behavior of the stochastic susceptible-infectious-recovered (SIR) model on such a network, by making use of a time-scale separation in the deterministic limit of the dynamics. This low-dimensional process is an accurate approximation to the full model in the limit of large populations, even for cases when the time-scale separation is not too pronounced, provided the maximum degree is not of the order of the population size.

Background: Children aged <16 years account for 25% of deaths on all-terrain vehicles (ATVs), despite public health and industry warning against paediatric use. Parents often underestimate instability and other risks associated with ATVs., Objective: To determine if a brief intervention consisting of validated computer simulations of ATV performance with a child driver changes attitudes, beliefs and planned safety behaviours of parents of children who ride ATVs., Design/methods: Participants were parents of children presenting to a children's hospital emergency department. All participants had children who had ridden an ATV in the past year. Subjects viewed a video simulation of ATVs in scenarios featuring 6-year-old and 10-year-old biofidelic anthropomorphic test devices. Parents completed a survey both before and after viewing the video to report attitudes/beliefs on ATV safety for children, use of safety equipment and family ATV use, as well as risk and safety perception., Results: Surveys were collected from 99 parents, mostly mothers (79%), Caucasian (61%) and had high school education or less (64%). The intervention shifted parents' belief in overall ATV safety (48% unsafe pre-intervention, 73% unsafe post-intervention, p<0.001). After viewing the video simulation, parents were almost six times more likely to perceive ATVs as unsafe (OR 5.96, 95% CI 2.32 to 15.31, p<0.001) and many parents (71%) planned to change family ATV safety rules., Conclusion: Video simulations of ATV performance with child riders changed short-term risk perception and planned safety behaviours of parents whose children ride ATVs. Similar educational interventions hold promise for larger-scale studies in at-risk populations., (Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/)

Infectious diseases exert a large and in many contexts growing burden on human health, but violate most of the assumptions of classical epidemiological statistics and hence require a mathematically sophisticated approach. Viral shedding data are collected during human studies-either where volunteers are infected with a disease or where existing cases are recruited-in which the levels of live virus produced over time are measured. These have traditionally been difficult to analyse due to strong, complex correlations between parameters. Here, we show how a Bayesian approach to the inverse problem together with modern Markov chain Monte Carlo algorithms based on information geometry can overcome these difficulties and yield insights into the disease dynamics of two of the most prevalent human pathogens-influenza and norovirus-as well as Ebola virus disease., (© 2016 The Authors.)

Background: It is well known that safe delivery in a health facility reduces the risks of maternal and infant mortality resulting from perinatal complications. What is less understood are the factors associated with safe delivery practices. We investigate factors influencing health facility delivery practices while adjusting for multiple other factors simultaneously, spatial heterogeneity, and trends over time., Methods: We fitted a logistic regression model to Lot Quality Assurance Sampling (LQAS) data from Uganda in a framework that considered individual-level covariates, geographical features, and variations over five time points. We accounted for all two-covariate interactions and all three-covariate interactions for which two of the covariates already had a significant interaction, were able to quantify uncertainty in outputs using computationally intensive cluster bootstrap methods, and displayed outputs using a geographical information system. Finally, we investigated what information could be predicted about districts at future time-points, before the next LQAS survey is carried out. To do this, we applied the model to project a confidence interval for the district level coverage of health facility delivery at future time points, by using the lower and upper end values of known demographics to construct a confidence range for the prediction and define priority groups., Results: We show that ease of access, maternal age and education are strongly associated with delivery in a health facility; after accounting for this, there remains a significant trend towards greater uptake over time. We use this model together with known demographics to formulate a nascent early warning system that identifies candidate districts expected to have low prevalence of facility-based delivery in the immediate future., Conclusions: Our results support the hypothesis that increased development, particularly related to education and access to health facilities, will act to increase facility-based deliveries, a factor associated with reducing perinatal associated mortality. We provide a statistical method for using inexpensive and routinely collected monitoring and evaluation data to answer complex epidemiology and public health questions in a resource-poor setting. We produced a model based on this data that explained the spatial distribution of facility-based delivery in Uganda. Finally, we used this model to make a prediction about the future priority of districts that was validated by monitoring and evaluation data collected in the next year.

Moment-closure techniques are commonly used to generate low-dimensional deterministic models to approximate the average dynamics of stochastic systems on networks. The quality of such closures is usually difficult to asses and furthermore the relationship between model assumptions and closure accuracy are often difficult, if not impossible, to quantify. Here we carefully examine some commonly used moment closures, in particular a new one based on the concept of maximum entropy, for approximating the spread of epidemics on networks by reconstructing the probability distributions over triplets based on those over pairs. We consider various models (SI, SIR, SEIR and Reed-Frost-type) under Markovian and non-Markovian assumption characterising the latent and infectious periods. We initially study with care two special networks, namely the open triplet and closed triangle, for which we can obtain analytical results. We then explore numerically the exactness of moment closures for a wide range of larger motifs, thus gaining understanding of the factors that introduce errors in the approximations, in particular the presence of a random duration of the infectious period and the presence of overlapping triangles in a network. We also derive a simpler and more intuitive proof than previously available concerning the known result that pair-based moment closure is exact for the Markovian SIR model on tree-like networks under pure initial conditions. We also extend such a result to all infectious models, Markovian and non-Markovian, in which susceptibles escape infection independently from each infected neighbour and for which infectives cannot regain susceptible status, provided the network is tree-like and initial conditions are pure. This works represent a valuable step in enriching intuition and deepening understanding of the assumptions behind moment closure approximations and for putting them on a more rigorous mathematical footing., (Copyright © 2015 Elsevier Ltd. All rights reserved.)

Networks have become an important tool for infectious disease epidemiology. Most previous theoretical studies of transmission network models have either considered simple Markovian dynamics at the individual level, or have focused on the invasion threshold and final outcome of the epidemic. Here, we provide a general theory for early real-time behaviour of epidemics on large configuration model networks (i.e. static and locally unclustered), in particular focusing on the computation of the Malthusian parameter that describes the early exponential epidemic growth. Analytical, numerical and Monte-Carlo methods under a wide variety of Markovian and non-Markovian assumptions about the infectivity profile are presented. Numerous examples provide explicit quantification of the impact of the network structure on the temporal dynamics of the spread of infection and provide a benchmark for validating results of large scale simulations., (Copyright © 2015. Published by Elsevier Inc.)

Moment closure on general discrete structures often requires one of the following: (i) an absence of short-closed loops (zero clustering); (ii) existence of a spatial scale; (iii) ad hoc assumptions. Algebraic methods are presented to avoid the use of such assumptions for populations based on clumps and are applied to both SIR and macroparasite disease dynamics. One approach involves a series of approximations that can be derived systematically, and another is exact and based on Lie algebraic methods.

I argue for a principled approach to model fitting in mathematical biology that combines statistical and mechanistic insights.

Despite some notable successes in the control of infectious diseases, transmissible pathogens still pose an enormous threat to human and animal health. The ecological and evolutionary dynamics of infections play out on a wide range of interconnected temporal, organizational, and spatial scales, which span hours to months, cells to ecosystems, and local to global spread. Moreover, some pathogens are directly transmitted between individuals of a single species, whereas others circulate among multiple hosts, need arthropod vectors, or can survive in environmental reservoirs. Many factors, including increasing antimicrobial resistance, increased human connectivity and changeable human behavior, elevate prevention and control from matters of national policy to international challenge. In the face of this complexity, mathematical models offer valuable tools for synthesizing information to understand epidemiological patterns, and for developing quantitative evidence for decision-making in global health., (Copyright © 2015, American Association for the Advancement of Science.)

Networks offer a fertile framework for studying the spread of infection in human and animal populations. However, owing to the inherent high-dimensionality of networks themselves, modelling transmission through networks is mathematically and computationally challenging. Even the simplest network epidemic models present unanswered questions. Attempts to improve the practical usefulness of network models by including realistic features of contact networks and of host-pathogen biology (e.g. waning immunity) have made some progress, but robust analytical results remain scarce. A more general theory is needed to understand the impact of network structure on the dynamics and control of infection. Here we identify a set of challenges that provide scope for active research in the field of network epidemic models., (Copyright © 2014 The Authors. Published by Elsevier B.V. All rights reserved.)

Public health-related decision-making on policies aimed at controlling epidemics is increasingly evidence-based, exploiting multiple sources of data. Policy makers rely on complex models that are required to be robust, realistically approximating epidemics and consistent with all relevant data. Meeting these requirements in a statistically rigorous and defendable manner poses a number of challenging problems. How to weight evidence from different datasets and handle dependence between them, efficiently estimate and critically assess complex models are key challenges that we expound in this paper, using examples from influenza modelling., (Copyright © 2014 The Authors. Published by Elsevier B.V. All rights reserved.)

This paper considers metapopulation models in the general sense, i.e. where the population is partitioned into sub-populations (groups, patches,...), irrespective of the biological interpretation they have, e.g. spatially segregated large sub-populations, small households or hosts themselves modelled as populations of pathogens. This framework has traditionally provided an attractive approach to incorporating more realistic contact structure into epidemic models, since it often preserves analytic tractability (in stochastic as well as deterministic models) but also captures the most salient structural inhomogeneity in contact patterns in many applied contexts. Despite the progress that has been made in both the theory and application of such metapopulation models, we present here several major challenges that remain for future work, focusing on models that, in contrast to agent-based ones, are amenable to mathematical analysis. The challenges range from clarifying the usefulness of systems of weakly-coupled large sub-populations in modelling the spread of specific diseases to developing a theory for endemic models with household structure. They include also developing inferential methods for data on the emerging phase of epidemics, extending metapopulation models to more complex forms of human social structure, developing metapopulation models to reflect spatial population structure, developing computationally efficient methods for calculating key epidemiological model quantities, and integrating within- and between-host dynamics in models., (Copyright © 2014 The Authors. Published by Elsevier B.V. All rights reserved.)

The most basic stochastic epidemic models are those involving global transmission, meaning that infection rates depend only on the type and state of the individuals involved, and not on their location in the population. Simple as they are, there are still several open problems for such models. For example, when will such an epidemic go extinct and with what probability (questions depending on the population being fixed, changing or growing)? How can a model be defined explaining the sometimes observed scenario of frequent mid-sized epidemic outbreaks? How can evolution of the infectious agent transmission rates be modelled and fitted to data in a robust way?, (Copyright © 2014 The Authors. Published by Elsevier B.V. All rights reserved.)

The hypothesis of preferential attachment (PA) - whereby better connected individuals make more connections - is hotly debated, particularly in the context of epidemiological networks. The simplest models of PA, for example, are incompatible with the eradication of any disease through population-level control measures such as random vaccination. Typically, evidence has been sought for the presence or absence of preferential attachment via asymptotic power-law behaviour. Here, we present a general statistical method to test directly for evidence of PA in count data and apply this to data for contacts relevant to the spread of respiratory diseases. We find that while standard methods for model selection prefer a form of PA, careful analysis of the best fitting PA models allows for a level of contact heterogeneity that in fact allows control of respiratory diseases. Our approach is based on a flexible but numerically cheap likelihood-based model that could in principle be applied to other integer data where the hypothesis of PA is of interest.

Processes that spread through local contact, including outbreaks of infectious diseases, are inherently noisy, and are frequently observed to be far noisier than predicted by standard stochastic models that assume homogeneous mixing. One way to reproduce the observed levels of noise is to introduce significant individual-level heterogeneity with respect to infection processes, such that some individuals are expected to generate more secondary cases than others. Here we consider a population where individuals can be naturally aggregated into clumps (subpopulations) with stronger interaction within clumps than between them. This clumped structure induces significant increases in the noisiness of a spreading process, such as the transmission of infection, despite complete homogeneity at the individual level. Given the ubiquity of such clumped aggregations (such as homes, schools and workplaces for humans or farms for livestock) we suggest this as a plausible explanation for noisiness of many epidemic time series., (Copyright © 2014 Elsevier Ltd. All rights reserved.)

Ebola is a deadly virus that causes frequent disease outbreaks in the human population. In this study, we analyse its rate of new introductions, case fatality ratio, and potential to spread from person to person. The analysis is performed for all completed outbreaks and for a scenario where these are augmented by a more severe outbreak of several thousand cases. The results show a fast rate of new outbreaks, a high case fatality ratio, and an effective reproductive ratio of just less than 1.