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

Incidence and risk factors for influenza-like-illness in the UK: online surveillance using Flusurvey.

BACKGROUND: Influenza and Influenza-like-illness (ILI) represents a substantial public health problem, but it is difficult to measure the overall burden as many cases do not access health care. Community cohorts have the advantage of not requiring individuals to present at hospitals and surgeries and therefore can potentially monitor a wider variety of cases. This study reports on the incidence and risk factors for ILI in the UK as measured using Flusurvey, an internet-based open community cohort. METHODS: Upon initial online registration participants were asked background characteristics, and every week were asked to complete a symptoms survey. We compared the representativeness of our sample to the overall population. We used two case definitions of ILI, which differed in whether fever/chills was essential. We calculated ILI incidence week by week throughout the season, and investigated risk factors associated with ever reporting ILI over the course of the season. Risk factor analysis was conducted using binomial regression. RESULTS: 5943 participants joined the survey, and 4532 completed the symptoms survey at least twice. Participants who filled in symptoms surveys at least twice filled in a median of nine symptoms surveys over the course of the study. 46.1% of participants reported at least one episode of ILI, and 6.0% of all reports were positive for ILI. Females had slightly higher incidence, and individuals over 65 had the lowest incidence. Incidence peaked just before Christmas and declined dramatically during school holidays. Multivariate regression showed that, for both definitions of ILI considered, being female, unvaccinated, having underlying health issues, having contact with children, being aged between 35 and 64, and being a smoker were associated with the highest risk of reporting an ILI. The use of public transport was not associated with an increased risk of ILI. CONCLUSIONS: Our results show that internet based surveillance can be used to measure ILI and understand risk factors. Vaccination is shown to be linked to a reduced risk of reporting ILI. Taking public transport does not increase the risk of reporting ILI. Flusurvey and other participatory surveillance techniques can be used to provide reliable information to policy makers in nearly real-time

Assessing the role of contact tracing in a suspected H7N2 influenza A outbreak in humans in Wales.

BACKGROUND: The detailed analysis of an outbreak database has been undertaken to examine the role of contact tracing in controlling an outbreak of possible avian influenza in humans. The outbreak, initiating from the purchase of infected domestic poultry, occurred in North Wales during May and June 2007. During this outbreak, extensive contact tracing was carried out. Following contact tracing, cases and contacts believed to be at risk of infection were given treatment/prophylaxis. METHODS: We analyse the database of cases and their contacts identified for the purposes of contact tracing in relation to both the contact tracing burden and effectiveness. We investigate the distribution of numbers of contacts identified, and use network structure to explore the speed with which treatment/prophylaxis was made available and to estimate the risk of transmission in different settings. RESULTS: Fourteen cases of suspected H7N2 influenza A in humans were associated with a confirmed outbreak among poultry in May-June 2007. The contact tracing dataset consisted of 254 individuals (cases and contacts, of both poultry and humans) who were linked through a network of social contacts. Of these, 102 individuals were given treatment or prophylaxis. Considerable differences between individuals' contact patterns were observed. Home and workplace encounters were more likely to result in transmission than encounters in other settings. After an initial delay, while the outbreak proceeded undetected, contact tracing rapidly caught up with the cases and was effective in reducing the time between onset of symptoms and treatment/prophylaxis. CONCLUSIONS: Contact tracing was used to link together the individuals involved in this outbreak in a social network, allowing the identification of the most likely paths of transmission and the risks of different types of interactions to be assessed. The outbreak highlights the substantial time and cost involved in contact tracing, even for an outbreak affecting few individuals. However, when sufficient resources are available, contact tracing enables cases to be identified before they result in further transmission and thus possibly assists in preventing an outbreak of a novel virus.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are

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

Structure and consistency of self-reported social contact networks in British secondary schools.

Self-reported social mixing patterns are commonly used in mathematical models of infectious diseases. It is particularly important to quantify patterns for school-age children given their disproportionate role in transmission, but it remains unclear how the structure of such social interactions changes over time. By integrating data collection into a public engagement programme, we examined self-reported contact networks in year 7 groups in four UK secondary schools. We collected data from 460 unique participants across four rounds of data collection conducted between January and June 2015, with 7,315 identifiable contacts reported in total. Although individual-level contacts varied over the study period, we were able to obtain out-of-sample accuracies of more than 90% and F-scores of 0.49-0.84 when predicting the presence or absence of social contacts between specific individuals across rounds of data collection. Network properties such as clustering and number of communities were broadly consistent within schools between survey rounds, but varied significantly between schools. Networks were assortative according to gender, and to a lesser extent school class, with the estimated clustering coefficient larger among males in all surveyed co-educational schools. Our results demonstrate that it is feasible to collect longitudinal self-reported social contact data from school children and that key properties of these data are consistent between rounds of data collection

Nine challenges in incorporating the dynamics of behaviour in infectious diseases models.

Traditionally, the spread of infectious diseases in human populations has been modelled with static parameters. These parameters, however, can change when individuals change their behaviour. If these changes are themselves influenced by the disease dynamics, there is scope for mechanistic models of behaviour to improve our understanding of this interaction. Here, we present challenges in modelling changes in behaviour relating to disease dynamics, specifically: how to incorporate behavioural changes in models of infectious disease dynamics, how to inform measurement of relevant behaviour to parameterise such models, and how to determine the impact of behavioural changes on observed disease dynamics

Seven challenges in modeling vaccine preventable diseasesC

Vaccination has been one of the most successful public health measures since the introduction of basic sanitation. Substantial mortality and morbidity reductions have been achieved via vaccination against many infections, and the list of diseases that are potentially controllable by vaccines is growing steadily. We introduce key challenges for modelling in shaping our understanding and guiding policy decisions related to vaccine preventable diseases

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#