A low-cost method to assess the epidemiological importance of individuals in controlling infectious disease outbreaks

Impact of contact data resolution on the evaluation of interventions in mathematical models of infectious diseases

Computational models offer a unique setting to test strategies to mitigate the spread of infectious diseases, providing useful insights to applied public health. To be actionable, models need to be informed by data, which can be available at different levels of detail. While high-resolution data describing contacts between individuals are increasingly available, data gathering remains challenging, especially during a health emergency. Many models thus use synthetic data or coarse information to evaluate intervention protocols. Here, we evaluate how the representation of contact data might affect the impact of various strategies in models, in the realm of COVID-19 transmission in educational and work contexts. Starting from high-resolution contact data, we use detailed to coarse data representations to inform a model of SARS-CoV-2 transmission and simulate different mitigation strategies. We find that coarse data representations estimate a lower risk of superspreading events. However, the rankings of protocols according to their efficiency or cost remain coherent across representations, ensuring the consistency of model findings to inform public health advice. Caution should be taken, however, on the quantitative estimations of those benefits and costs triggering the adoption of protocols, as these may depend on data representation.

Mitigating COVID-19 outbreaks in workplaces and schools by hybrid telecommuting

The COVID-19 epidemic has forced most countries to impose contact-limiting restrictions at workplaces, universities, schools, and more broadly in our societies. Yet, the effectiveness of these unprecedented interventions in containing the virus spread remain largely unquantified. Here, we develop a simulation study to analyze COVID-19 outbreaks on three real-life contact networks stemming from a workplace, a primary school and a high school in France. Our study provides a fine-grained analysis of the impact of contact-limiting strategies at workplaces, schools and high schools, including: (1) Rotating strategies, in which workers are evenly split into two shifts that alternate on a daily or weekly basis; and (2) On-Off strategies, where the whole group alternates periods of normal work interactions with complete telecommuting. We model epidemics spread in these different setups using a stochastic discrete-time agent-based transmission model that includes the coronavirus most salient features: super-spreaders, infectious asymptomatic individuals, and pre-symptomatic infectious periods. Our study yields clear results: the ranking of the strategies, based on their ability to mitigate epidemic propagation in the network from a first index case, is the same for all network topologies (workplace, primary school and high school). Namely, from best to worst: Rotating week-by-week, Rotating day-by-day, On-Off week-by-week, and On-Off day-by-day. Moreover, our results show that below a certain threshold for the original local reproduction number [Formula: see text] within the network (< 1.52 for primary schools, < 1.30 for the workplace, < 1.38 for the high school, and < 1.55 for the random graph), all four strategies efficiently control outbreak by decreasing effective local reproduction number to [Formula: see text] < 1. These results can provide guidance for public health decisions related to telecommuting.

Building surrogate temporal network data from observed backbones

Many systems of socioeconomic interests find a convenient representation in the form of temporal networks, i.e., sets of nodes and interactions occurring at specified times. In the corresponding data sets, however, crucial elements coexist with nonessential ones and noise. Several methods have thus been proposed to extract a "network backbone," i.e., the set of most important links in a network data set. The outcome of such methods can be seen as compressed versions of the original data. However, the question of how to practically use such reduced views of the data has not been tackled: for instance, using them directly in numerical simulations of processes on networks might lead to important biases. Overall, such reduced views of the data might not be actionable without an adequate decompression method. Here, we address this issue by putting forward and exploring several systematic procedures to build surrogate data from various kinds of temporal network backbones. In particular, we explore how much information about the original data needs to be retained alongside the backbone so that the surrogate data can be used in data-driven numerical simulations of spreading processes on a wide range of spreading parameters. We illustrate our results using empirical temporal networks with a broad variety of structures and properties. Our results give hints on how to best summarize complex data sets so that they remain actionable. Moreover, they show how ensembles of surrogate data with similar properties can be obtained from an original single data set, without any modeling assumptions.

Relevance of temporal cores for epidemic spread in temporal networks

Temporal networks are widely used to represent a vast diversity of systems, including in particular social interactions, and the spreading processes unfolding on top of them. The identification of structures playing important roles in such processes remains largely an open question, despite recent progresses in the case of static networks. Here, we consider as candidate structures the recently introduced concept of span-cores: the span-cores decompose a temporal network into subgraphs of controlled duration and increasing connectivity, generalizing the core-decomposition of static graphs. To assess the relevance of such structures, we explore the effectiveness of strategies aimed either at containing or maximizing the impact of a spread, based respectively on removing span-cores of high cohesiveness or duration to decrease the epidemic risk, or on seeding the process from such structures. The effectiveness of such strategies is assessed in a variety of empirical data sets and compared to baselines that use only static information on the centrality of nodes and static concepts of coreness, as well as to a baseline based on a temporal centrality measure. Our results show that the most stable and cohesive temporal cores play indeed an important role in epidemic processes on temporal networks, and that their nodes are likely to include influential spreaders.

Beyond ranking nodes: Predicting epidemic outbreak sizes by network centralities

Identifying important nodes for disease spreading is a central topic in network epidemiology. We investigate how well the position of a node, characterized by standard network measures, can predict its epidemiological importance in any graph of a given number of nodes. This is in contrast to other studies that deal with the easier prediction problem of ranking nodes by their epidemic importance in given graphs. As a benchmark for epidemic importance, we calculate the exact expected outbreak size given a node as the source. We study exhaustively all graphs of a given size, so do not restrict ourselves to certain generative models for graphs, nor to graph data sets. Due to the large number of possible nonisomorphic graphs of a fixed size, we are limited to ten-node graphs. We find that combinations of two or more centralities are predictive (R2 scores of 0.91 or higher) even for the most difficult parameter values of the epidemic simulation. Typically, these successful combinations include one normalized spectral centrality (such as PageRank or Katz centrality) and one measure that is sensitive to the number of edges in the graph.

Efficient sentinel surveillance strategies for preventing epidemics on networks

Surveillance plays a crucial role in preventing emerging infectious diseases from becoming epidemic. In circumstances where it is possible to monitor the infection status of certain people, transport hubs, or hospitals, early detection of the disease allows interventions to be implemented before most of the damage can occur, or at least its impact can be mitigated. This paper addresses the question of which nodes we should select in a network of individuals susceptible to some infectious disease in order to minimize the number of casualties. By simulating disease outbreaks on a collection of empirical and synthetic networks we show that the best strategy depends on topological characteristics of the network. For highly modular or spatially embedded networks it is better to place the sentinels on nodes distributed across different regions. However, if the degree heterogeneity is high, then a strategy that targets network hubs is preferred. We further consider the consequences of having an incomplete sample of the network and demonstrate that the value of new information diminishes as more data is collected. Finally we find further marginal improvements using two heuristics informed by known results in graph theory that exploit the fragmented structure of sparse network data.

In a network of individuals susceptible to some infectious disease, what are the best locations to monitor in order to detect the infection before most damage can be done? In this paper we address this question by considering various heuristic strategies for sentinel placement that can potentially be implemented in real-world situations without requiring excessive amounts of computation, or even having perfect data about the structure of the network. We find that strategies that attempt to distribute sentinels over different regions of the network perform best in highly modular or spatially embedded networks, whereas the strategy of targeting the most well connected individuals works best when there is a considerable amount of contact heterogeneity between individuals. Our results may be used as a guideline to help decide when certain strategies should, or should not, be implemented.

Optimizing targeted vaccination across cyber-physical networks: an empirically based mathematical simulation study

Targeted vaccination, whether to minimize the forward transmission of infectious diseases or their clinical impact, is one of the 'holy grails' of modern infectious disease outbreak response, yet it is difficult to achieve in practice due to the challenge of identifying optimal targets in real time. If interruption of disease transmission is the goal, targeting requires knowledge of underlying person-to-person contact networks. Digital communication networks may reflect not only virtual but also physical interactions that could result in disease transmission, but the precise overlap between these cyber and physical networks has never been empirically explored in real-life settings. Here, we study the digital communication activity of more than 500 individuals along with their person-to-person contacts at a 5-min temporal resolution. We then simulate different disease transmission scenarios on the person-to-person physical contact network to determine whether cyber communication networks can be harnessed to advance the goal of targeted vaccination for a disease spreading on the network of physical proximity. We show that individuals selected on the basis of their closeness centrality within cyber networks (what we call 'cyber-directed vaccination') can enhance vaccination campaigns against diseases with short-range (but not full-range) modes of transmission.

Assessing the Dynamics and Control of Droplet- and Aerosol-Transmitted Influenza Using an Indoor Positioning System

There is increasing evidence that aerosol transmission is a major contributor to the spread of influenza. Despite this, virtually all studies assessing the dynamics and control of influenza assume that it is transmitted solely through direct contact and large droplets, requiring close physical proximity. Here, we use wireless sensors to measure simultaneously both the location and close proximity contacts in the population of a US high school. This dataset, highly resolved in space and time, allows us to model both droplet and aerosol transmission either in isolation or in combination. In particular, it allows us to computationally quantify the potential effectiveness of overlooked mitigation strategies such as improved ventilation that are available in the case of aerosol transmission. Our model suggests that recommendation-abiding ventilation could be as effective in mitigating outbreaks as vaccinating approximately half of the population. In simulations using empirical transmission levels observed in households, we find that bringing ventilation to recommended levels had the same mitigating effect as a vaccination coverage of 50% to 60%. Ventilation is an easy-to-implement strategy that has the potential to support vaccination efforts for effective control of influenza spread.

The importance of dog population contact network structures in rabies transmission

Canine rabies transmission was interrupted in N'Djaména, Chad, following two mass vaccination campaigns. However, after nine months cases resurged with re-establishment of endemic rabies transmission to pre-intervention levels. Previous analyses investigated district level spatial heterogeneity of vaccination coverage, and dog density; and importation, identifying the latter as the primary factor for rabies resurgence. Here we assess the impact of individual level heterogeneity on outbreak probability, effectiveness of vaccination campaigns and likely time to resurgence after a campaign. Geo-located contact sensors recorded the location and contacts of 237 domestic dogs in N'Djaména over a period of 3.5 days. The contact network data showed that urban dogs are socially related to larger communities and constrained by the urban architecture. We developed a network generation algorithm that extrapolates this empirical contact network to networks of large dog populations and applied it to simulate rabies transmission in N'Djaména. The model predictions aligned well with the rabies incidence data. Using the model we demonstrated, that major outbreaks are prevented when at least 70% of dogs are vaccinated. The probability of a minor outbreak also decreased with increasing vaccination coverage, but reached zero only when coverage was near total. Our results suggest that endemic rabies in N'Djaména may be explained by a series of importations with subsequent minor outbreaks. We show that highly connected dogs hold a critical role in transmission and that targeted vaccination of such dogs would lead to more efficient vaccination campaigns.

Mathematical models used to inform study design or surveillance systems in infectious diseases: a systematic review

BACKGROUND

Mathematical models offer the possibility to investigate the infectious disease dynamics over time and may help in informing design of studies. A systematic review was performed in order to determine to what extent mathematical models have been incorporated into the process of planning studies and hence inform study design for infectious diseases transmitted between humans and/or animals.

METHODS

We searched Ovid Medline and two trial registry platforms (Cochrane, WHO) using search terms related to infection, mathematical model, and study design from the earliest dates to October 2016. Eligible publications and registered trials included mathematical models (compartmental, individual-based, or Markov) which were described and used to inform the design of infectious disease studies. We extracted information about the investigated infection, population, model characteristics, and study design.

RESULTS

We identified 28 unique publications but no registered trials. Focusing on compartmental and individual-based models we found 12 observational/surveillance studies and 11 clinical trials. Infections studied were equally animal and human infectious diseases for the observational/surveillance studies, while all but one between humans for clinical trials. The mathematical models were used to inform, amongst other things, the required sample size (n = 16), the statistical power (n = 9), the frequency at which samples should be taken (n = 6), and from whom (n = 6).

CONCLUSIONS

Despite the fact that mathematical models have been advocated to be used at the planning stage of studies or surveillance systems, they are used scarcely. With only one exception, the publications described theoretical studies, hence, not being utilised in real studies.

Measuring distance through dense weighted networks: The case of hospital-associated pathogens

Hospital networks, formed by patients visiting multiple hospitals, affect the spread of hospital-associated infections, resulting in differences in risks for hospitals depending on their network position. These networks are increasingly used to inform strategies to prevent and control the spread of hospital-associated pathogens. However, many studies only consider patients that are received directly from the initial hospital, without considering the effect of indirect trajectories through the network. We determine the optimal way to measure the distance between hospitals within the network, by reconstructing the English hospital network based on shared patients in 2014–2015, and simulating the spread of a hospital-associated pathogen between hospitals, taking into consideration that each intermediate hospital conveys a delay in the further spread of the pathogen. While the risk of transferring a hospital-associated pathogen between directly neighbouring hospitals is a direct reflection of the number of shared patients, the distance between two hospitals far-away in the network is determined largely by the number of intermediate hospitals in the network. Because the network is dense, most long distance transmission chains in fact involve only few intermediate steps, spreading along the many weak links. The dense connectivity of hospital networks, together with a strong regional structure, causes hospital-associated pathogens to spread from the initial outbreak in a two-step process: first, the directly surrounding hospitals are affected through the strong connections, second all other hospitals receive introductions through the multitude of weaker links. Although the strong connections matter for local spread, weak links in the network can offer ideal routes for hospital-associated pathogens to travel further faster. This hold important implications for infection prevention and control efforts: if a local outbreak is not controlled in time, colonised patients will appear in other regions, irrespective of the distance to the initial outbreak, making import screening ever more difficult.

Shared patients can spread hospital-associated pathogens between hospitals, together forming a large network in which all hospitals are connected. We set out to measure the distance between hospitals in such a network, best reflecting the risk of a hospital-associated pathogen spreading from one to the other. The central problem is that this risk may not be a directly reflected by the weight of the direct connections between hospitals, because the pathogen could arrive through a longer indirect route, first causing a problem in an intermediate hospital. We determined the optimal balance between connection weights and path length, by testing different weighting factors between them against simulated spread of a pathogen. We found that while strong connections are important risk factor for a hospital’s direct neighbours, weak connections offer ideal indirect routes for hospital-associated pathogens to travel further faster. These routes should not be underestimated when designing control strategies.

The interplay between individual social behavior and clinical symptoms in small clustered groups

Background

Mixing patterns of human populations play a crucial role in shaping the spreading paths of infectious diseases. The diffusion of mobile and wearable devices able to record close proximity interactions represents a great opportunity for gathering detailed data on social interactions and mixing patterns in human populations. The aim of this study is to investigate how social interactions are affected by the onset of symptomatic conditions and to what extent the heterogeneity in human behavior can reflect a different risk of infection.

Methods

We study the relation between individuals’ social behavior and the onset of different symptoms, by making use of data collected in 2009 among students sharing a dormitory in a North America university campus. The dataset combines Bluetooth proximity records between study participants with self-reported daily records on their health state. Specifically, we investigate whether individuals’ social activity significantly changes during different symptomatic conditions, including those defining Influenza-like illness, and highlight to what extent possible heterogeneities in social behaviors among individuals with similar age and daily routines may be responsible for a different risk of infection for influenza.

Results

Our results suggest that symptoms associated with Influenza-like illness can be responsible of a reduction of about 40% in the average duration of contacts and of 30% in the daily time spent in social interactions, possibly driven by the onset of fever. However, differences in the number of daily contacts were found to be not statistically significant. In addition, we found that individuals who experienced clinical influenza during the study period were characterized by a significantly higher social activity. In particular, both the number of person-to-person contacts and the time spent in social interactions emerged as significant risk factors for influenza infection.

Conclusions

Our findings highlight that Influenza-like illness can remarkably reduce the social activity of individuals and strengthen the idea that the heterogeneity in social habits among individuals can significantly contribute in shaping differences among the individuals’ risk of infection.

Electronic supplementary material

The online version of this article (doi:10.1186/s12879-017-2623-2) contains supplementary material, which is available to authorized users.

An ecological and digital epidemiology analysis on the role of human behavior on the 2014 Chikungunya outbreak in Martinique

Understanding the spatio-temporal dynamics of endemic infections is of critical importance for a deeper understanding of pathogen transmission, and for the design of more efficient public health strategies. However, very few studies in this domain have focused on emerging infections, generating a gap of knowledge that hampers epidemiological response planning. Here, we analyze the case of a Chikungunya outbreak that occurred in Martinique in 2014. Using time series estimates from a network of sentinel practitioners covering the entire island, we first analyze the spatio-temporal dynamics and show that the largest city has served as the epicenter of this epidemic. We further show that the epidemic spread from there through two different propagation waves moving northwards and southwards, probably by individuals moving along the road network. We then develop a mathematical model to explore the drivers of the temporal dynamics of this mosquito-borne virus. Finally, we show that human behavior, inferred by a textual analysis of messages published on the social network Twitter, is required to explain the epidemiological dynamics over time. Overall, our results suggest that human behavior has been a key component of the outbreak propagation, and we argue that such results can lead to more efficient public health strategies specifically targeting the propagation process.

How Behaviour and the Environment Influence Transmission in Mobile Groups

The movement of individuals living in groups leads to the formation of physical interaction networks over which signals such as information or disease can be transmitted. Direct contacts represent the most obvious opportunities for a signal to be transmitted. However, because signals that persist after being deposited into the environment may later be acquired by other group members, indirect environmentally-mediated transmission is also possible. To date, studies of signal transmission within groups have focused on direct physical interactions and ignored the role of indirect pathways. Here, we use an agent-based model to study how the movement of individuals and characteristics of the signal being transmitted modulate transmission. By analysing the dynamic interaction networks generated from these simulations, we show that the addition of indirect pathways speeds up signal transmission, while the addition of physically-realistic collisions between individuals in densely packed environments hampers it. Furthermore, the inclusion of spatial biases that induce the formation of individual territories, reveals the existence of a trade-off such that optimal signal transmission at the group level is only achieved when territories are of intermediate sizes. Our findings provide insight into the selective pressures guiding the evolution of behavioural traits in natural groups, and offer a means by which multi-agent systems can be engineered to achieve desired transmission capabilities.

Recalibrating disease parameters for increasing realism in modeling epidemics in closed settings

Background

The homogeneous mixing assumption is widely adopted in epidemic modelling for its parsimony and represents the building block of more complex approaches, including very detailed agent-based models. The latter assume homogeneous mixing within schools, workplaces and households, mostly for the lack of detailed information on human contact behaviour within these settings. The recent data availability on high-resolution face-to-face interactions makes it now possible to assess the goodness of this simplified scheme in reproducing relevant aspects of the infection dynamics.

Methods

We consider empirical contact networks gathered in different contexts, as well as synthetic data obtained through realistic models of contacts in structured populations. We perform stochastic spreading simulations on these contact networks and in populations of the same size under a homogeneous mixing hypothesis. We adjust the epidemiological parameters of the latter in order to fit the prevalence curve of the contact epidemic model. We quantify the agreement by comparing epidemic peak times, peak values, and epidemic sizes.

Results

Good approximations of the peak times and peak values are obtained with the homogeneous mixing approach, with a median relative difference smaller than 20 % in all cases investigated. Accuracy in reproducing the peak time depends on the setting under study, while for the peak value it is independent of the setting. Recalibration is found to be linear in the epidemic parameters used in the contact data simulations, showing changes across empirical settings but robustness across groups and population sizes.

Conclusions

An adequate rescaling of the epidemiological parameters can yield a good agreement between the epidemic curves obtained with a real contact network and a homogeneous mixing approach in a population of the same size. The use of such recalibrated homogeneous mixing approximations would enhance the accuracy and realism of agent-based simulations and limit the intrinsic biases of the homogeneous mixing.

Electronic supplementary material

The online version of this article (doi:10.1186/s12879-016-2003-3) contains supplementary material, which is available to authorized users.

Contact diaries versus wearable proximity sensors in measuring contact patterns at a conference: method comparison and participants' attitudes

BACKGROUND

Studies measuring contact networks have helped to improve our understanding of infectious disease transmission. However, several methodological issues are still unresolved, such as which method of contact measurement is the most valid. Further, complete network analysis requires data from most, ideally all, members of a network and, to achieve this, acceptance of the measurement method. We aimed at investigating measurement error by comparing two methods of contact measurement - paper diaries vs. wearable proximity sensors - that were applied concurrently to the same population, and we measured acceptability.

METHODS

We investigated the contact network of one day of an epidemiology conference in September 2014. Seventy-six participants wore proximity sensors throughout the day while concurrently recording their contacts with other study participants in a paper-diary; they also reported on method acceptability.

RESULTS

There were 329 contact reports in the paper diaries, corresponding to 199 contacts, of which 130 were noted by both parties. The sensors recorded 316 contacts, which would have resulted in 632 contact reports if there had been perfect concordance in recording. We estimated the probabilities that a contact was reported in a diary as: P = 72 % for <5 min contact duration (significantly lower than the following, p < 0.05), P = 86 % for 5-15 min, P = 89 % for 15-60 min, and P = 94 % for >60 min. The sets of sensor-measured and self-reported contacts had a large intersection, but neither was a subset of the other. Participants' aggregated contact duration was mostly substantially longer in the diary data than in the sensor data. Twenty percent of respondents (>1 reported contact) stated that filling in the diary was too much work, 25 % of respondents reported difficulties in remembering contacts, and 93 % were comfortable having their conference contacts measured by sensors.

CONCLUSION

Reporting and recording were not complete; reporting was particularly incomplete for contacts <5 min. The types of contact that both methods are capable of detecting are partly different. Participants appear to have overestimated the duration of their contacts. Conducting a study with diaries or wearable sensors was acceptable to and mostly easily done by participants. Both methods can be applied meaningfully if their specific limitations are considered and incompleteness is accounted for.

Contact diaries versus wearable proximity sensors in measuring contact patterns at a conference: method comparison and participants' attitudes

Background

Studies measuring contact networks have helped to improve our understanding of infectious disease transmission. However, several methodological issues are still unresolved, such as which method of contact measurement is the most valid. Further, complete network analysis requires data from most, ideally all, members of a network and, to achieve this, acceptance of the measurement method. We aimed at investigating measurement error by comparing two methods of contact measurement – paper diaries vs. wearable proximity sensors – that were applied concurrently to the same population, and we measured acceptability.

Methods

We investigated the contact network of one day of an epidemiology conference in September 2014. Seventy-six participants wore proximity sensors throughout the day while concurrently recording their contacts with other study participants in a paper-diary; they also reported on method acceptability.

Results

There were 329 contact reports in the paper diaries, corresponding to 199 contacts, of which 130 were noted by both parties. The sensors recorded 316 contacts, which would have resulted in 632 contact reports if there had been perfect concordance in recording. We estimated the probabilities that a contact was reported in a diary as: P = 72 % for <5 min contact duration (significantly lower than the following, p < 0.05), P = 86 % for 5-15 min, P = 89 % for 15-60 min, and P = 94 % for >60 min. The sets of sensor-measured and self-reported contacts had a large intersection, but neither was a subset of the other. Participants’ aggregated contact duration was mostly substantially longer in the diary data than in the sensor data. Twenty percent of respondents (>1 reported contact) stated that filling in the diary was too much work, 25 % of respondents reported difficulties in remembering contacts, and 93 % were comfortable having their conference contacts measured by sensors.

Conclusion

Reporting and recording were not complete; reporting was particularly incomplete for contacts <5 min. The types of contact that both methods are capable of detecting are partly different. Participants appear to have overestimated the duration of their contacts. Conducting a study with diaries or wearable sensors was acceptable to and mostly easily done by participants. Both methods can be applied meaningfully if their specific limitations are considered and incompleteness is accounted for.

Electronic supplementary material

The online version of this article (doi:10.1186/s12879-016-1676-y) contains supplementary material, which is available to authorized users.

Disease Surveillance on Complex Social Networks

As infectious disease surveillance systems expand to include digital, crowd-sourced, and social network data, public health agencies are gaining unprecedented access to high-resolution data and have an opportunity to selectively monitor informative individuals. Contact networks, which are the webs of interaction through which diseases spread, determine whether and when individuals become infected, and thus who might serve as early and accurate surveillance sensors. Here, we evaluate three strategies for selecting sensors-sampling the most connected, random, and friends of random individuals-in three complex social networks-a simple scale-free network, an empirical Venezuelan college student network, and an empirical Montreal wireless hotspot usage network. Across five different surveillance goals-early and accurate detection of epidemic emergence and peak, and general situational awareness-we find that the optimal choice of sensors depends on the public health goal, the underlying network and the reproduction number of the disease (R0). For diseases with a low R0, the most connected individuals provide the earliest and most accurate information about both the onset and peak of an outbreak. However, identifying network hubs is often impractical, and they can be misleading if monitored for general situational awareness, if the underlying network has significant community structure, or if R0 is high or unknown. Taking a theoretical approach, we also derive the optimal surveillance system for early outbreak detection but find that real-world identification of such sensors would be nearly impossible. By contrast, the friends-of-random strategy offers a more practical and robust alternative. It can be readily implemented without prior knowledge of the network, and by identifying sensors with higher than average, but not the highest, epidemiological risk, it provides reasonably early and accurate information.

How to Estimate Epidemic Risk from Incomplete Contact Diaries Data?

Social interactions shape the patterns of spreading processes in a population. Techniques such as diaries or proximity sensors allow to collect data about encounters and to build networks of contacts between individuals. The contact networks obtained from these different techniques are however quantitatively different. Here, we first show how these discrepancies affect the prediction of the epidemic risk when these data are fed to numerical models of epidemic spread: low participation rate, under-reporting of contacts and overestimation of contact durations in contact diaries with respect to sensor data determine indeed important differences in the outcomes of the corresponding simulations with for instance an enhanced sensitivity to initial conditions. Most importantly, we investigate if and how information gathered from contact diaries can be used in such simulations in order to yield an accurate description of the epidemic risk, assuming that data from sensors represent the ground truth. The contact networks built from contact sensors and diaries present indeed several structural similarities: this suggests the possibility to construct, using only the contact diary network information, a surrogate contact network such that simulations using this surrogate network give the same estimation of the epidemic risk as simulations using the contact sensor network. We present and compare several methods to build such surrogate data, and show that it is indeed possible to obtain a good agreement between the outcomes of simulations using surrogate and sensor data, as long as the contact diary information is complemented by publicly available data describing the heterogeneity of the durations of human contacts.

Schools, offices, hospitals play an important role in the spreading of epidemics. Information about interactions between individuals in such contexts can help understand the patterns of transmission and design ad hoc immunization strategies. Data about contacts can be collected through various techniques such as diaries or proximity sensors. Here, we first ask if the corresponding datasets give similar predictions of the epidemic risk when they are used to build a network of contacts among individuals. Not surprisingly, the answer is negative: indeed, if we consider data from sensors as the ground truth, diaries are affected by low participation rate, underreporting and overestimation of durations. Is it however possible, despite these biases, to use data from contact diaries to obtain sensible epidemic risk predictions? We show here that, thanks to the structural similarities between the two networks, it is possible to use the contact diaries to build surrogate versions of the contact network obtained from the sensor data, such that both yield the same epidemic risk estimation. We show that the construction of such surrogate networks can be performed using solely the information contained in the contact diaries, complemented by publicly available data on the heterogeneity of cumulative contact durations between individuals.

Apparently-Different Clearance Rates from Cohort Studies of Mycoplasma genitalium Are Consistent after Accounting for Incidence of Infection, Recurrent Infection, and Study Design

Mycoplasma genitalium is a potentially major cause of urethritis, cervicitis, pelvic inflammatory disease, infertility, and increased HIV risk. A better understanding of its natural history is crucial to informing control policy. Two extensive cohort studies (students in London, UK; Ugandan sex workers) suggest very different clearance rates; we aimed to understand the reasons and obtain improved estimates by making maximal use of the data from the studies. As M. genitalium is a sexually-transmitted infectious disease, we developed a model for time-to-event analysis that incorporates the processes of (re)infection and clearance, and fitted to data from the two cohort studies to estimate incidence and clearance rates under different scenarios of sexual partnership dynamics and study design (including sample handling and associated test sensitivity). In the London students, the estimated clearance rate is 0.80p.a. (mean duration 15 months), with incidence 1.31%-3.93%p.a. Without adjusting for study design, corresponding estimates from the Ugandan data are 3.44p.a. (mean duration 3.5 months) and 58%p.a. Apparent differences in clearance rates are probably mostly due to lower testing sensitivity in the Uganda study due to differences in sample handling, with 'true' clearance rates being similar, and adjusted incidence in Uganda being 28%p.a. Some differences are perhaps due to the sex workers having more-frequent antibiotic treatment, whilst reinfection within ongoing sexual partnerships might have caused some of the apparently-persistent infection in the London students. More information on partnership dynamics would inform more accurate estimates of natural-history parameters. Detailed studies in men are also required.

Compensating for population sampling in simulations of epidemic spread on temporal contact networks

Data describing human interactions often suffer from incomplete sampling of the underlying population. As a consequence, the study of contagion processes using data-driven models can lead to a severe underestimation of the epidemic risk. Here we present a systematic method to alleviate this issue and obtain a better estimation of the risk in the context of epidemic models informed by high-resolution time-resolved contact data. We consider several such data sets collected in various contexts and perform controlled resampling experiments. We show how the statistical information contained in the resampled data can be used to build a series of surrogate versions of the unknown contacts. We simulate epidemic processes on the resulting reconstructed data sets and show that it is possible to obtain good estimates of the outcome of simulations performed using the complete data set. We discuss limitations and potential improvements of our method.

Modeling workplace contact networks: The effects of organizational structure, architecture, and reporting errors on epidemic predictions

Face-to-face social contacts are potentially important transmission routes for acute respiratory infections, and understanding the contact network can improve our ability to predict, contain, and control epidemics. Although workplaces are important settings for infectious disease transmission, few studies have collected workplace contact data and estimated workplace contact networks. We use contact diaries, architectural distance measures, and institutional structures to estimate social contact networks within a Swiss research institute. Some contact reports were inconsistent, indicating reporting errors. We adjust for this with a latent variable model, jointly estimating the true (unobserved) network of contacts and duration-specific reporting probabilities. We find that contact probability decreases with distance, and that research group membership, role, and shared projects are strongly predictive of contact patterns. Estimated reporting probabilities were low only for 0-5 min contacts. Adjusting for reporting error changed the estimate of the duration distribution, but did not change the estimates of covariate effects and had little effect on epidemic predictions. Our epidemic simulation study indicates that inclusion of network structure based on architectural and organizational structure data can improve the accuracy of epidemic forecasting models.

Detailed contact data and the dissemination of Staphylococcus aureus in hospitals

Close proximity interactions (CPIs) measured by wireless electronic devices are increasingly used in epidemiological models. However, no evidence supports that electronically collected CPIs inform on the contacts leading to transmission. Here, we analyzed Staphylococcus aureus carriage and CPIs recorded simultaneously in a long-term care facility for 4 months in 329 patients and 261 healthcare workers to test this hypothesis. In the broad diversity of isolated S. aureus strains, 173 transmission events were observed between participants. The joint analysis of carriage and CPIs showed that CPI paths linking incident cases to other individuals carrying the same strain (i.e. possible infectors) had fewer intermediaries than predicted by chance (P < 0.001), a feature that simulations showed to be the signature of transmission along CPIs. Additional analyses revealed a higher dissemination risk between patients via healthcare workers than via other patients. In conclusion, S. aureus transmission was consistent with contacts defined by electronically collected CPIs, illustrating their potential as a tool to control hospital-acquired infections and help direct surveillance.

Recent advances in communication technologies allow monitoring high-resolution contact networks. Close proximity interactions (CPIs) measured by wireless sensors are increasingly used to inform contact networks for the dissemination of pathogens in computational models, although empirical justification is lacking. Here, we conducted a longitudinal prospective study for four months in a hospital, including both patients and healthcare workers (HCWs). High-resolution CPIs were recorded continuously, and participants undertook weekly nasal swabs to detect S. aureus carriage. We set out to test whether the contact network measured by CPIs supported observed transmission episodes. A simulation study was first conducted to choose a test statistic for the association of CPI paths with transmission, showing that CPI path length from transmitter to incident case was the most powerful. Then, we selected patients presenting incident S. aureus colonization in the data. We showed that CPI paths existed to carriers of the same strain, with path lengths significantly shorter than between random pairs of participants, in agreement with the transmission hypothesis. In-hospital contact networks measured by CPIs inform on opportunities for pathogen transmission. These could be used in surveillance systems to help prevent the spread of nosocomial pathogens.

Data on face-to-face contacts in an office building suggest a low-cost vaccination strategy based on community linkers

Empirical data on contacts between individuals in social contexts play an important role in providing information for models describing human behavior and how epidemics spread in populations. Here, we analyze data on face-to-face contacts collected in an office building. The statistical properties of contacts are similar to other social situations, but important differences are observed in the contact network structure. In particular, the contact network is strongly shaped by the organization of the offices in departments, which has consequences in the design of accurate agent-based models of epidemic spread. We consider the contact network as a potential substrate for infectious disease spread and show that its sparsity tends to prevent outbreaks of rapidly spreading epidemics. Moreover, we define three typical behaviors according to the fraction f of links each individual shares outside its own department: residents, wanderers, and linkers. Linkers (f ~ 50%) act as bridges in the network and have large betweenness centralities. Thus, a vaccination strategy targeting linkers efficiently prevents large outbreaks. As such a behavior may be spotted a priori in the offices' organization or from surveys, without the full knowledge of the time-resolved contact network, this result may help the design of efficient, low-cost vaccination or social-distancing strategies.

Mitigation of infectious disease at school: targeted class closure vs school closure

Background

School environments are thought to play an important role in the community spread of infectious diseases such as influenza because of the high mixing rates of school children. The closure of schools has therefore been proposed as an efficient mitigation strategy. Such measures come however with high associated social and economic costs, making alternative, less disruptive interventions highly desirable. The recent availability of high-resolution contact network data from school environments provides an opportunity to design models of micro-interventions and compare the outcomes of alternative mitigation measures.

Methods and results

We model mitigation measures that involve the targeted closure of school classes or grades based on readily available information such as the number of symptomatic infectious children in a class. We focus on the specific case of a primary school for which we have high-resolution data on the close-range interactions of children and teachers. We simulate the spread of an influenza-like illness in this population by using an SEIR model with asymptomatics, and compare the outcomes of different mitigation strategies. We find that targeted class closure affords strong mitigation effects: closing a class for a fixed period of time – equal to the sum of the average infectious and latent durations – whenever two infectious individuals are detected in that class decreases the attack rate by almost 70% and significantly decreases the probability of a severe outbreak. The closure of all classes of the same grade mitigates the spread almost as much as closing the whole school.

Conclusions

Our model of targeted class closure strategies based on readily available information on symptomatic subjects and on limited information on mixing patterns, such as the grade structure of the school, shows that these strategies might be almost as effective as whole-school closure, at a much lower cost. This may inform public health policies for the management and mitigation of influenza-like outbreaks in the community.

Electronic supplementary material

The online version of this article (doi:10.1186/s12879-014-0695-9) contains supplementary material, which is available to authorized users.

Measuring contact patterns with wearable sensors: methods, data characteristics and applications to data-driven simulations of infectious diseases

Thanks to recent technological advances, measuring real-world interactions by the use of mobile devices and wearable sensors has become possible, allowing researchers to gather data on human social interactions in a variety of contexts with high spatial and temporal resolution. Empirical data describing contact networks have thus acquired a high level of detail that may yield new insights into the dynamics of infection transmission between individuals. At the same time, such data bring forth new challenges related to their statistical description and analysis, and to their use in mathematical models. In particular, the integration of highly detailed empirical data in computational frameworks designed to model the spread of infectious diseases raises the issue of assessing which representations of the raw data work best to inform the models. There is an emerging need to strike a balance between simplicity and detail in order to ensure both generalizability and accuracy of predictions. Here, we review recent work on the collection and analysis of highly detailed data on temporal networks of face-to-face human proximity, carried out in the context of the SocioPatterns collaboration. We discuss the various levels of coarse-graining that can be used to represent the data in order to inform models of infectious disease transmission. We also discuss several limitations of the data and future avenues for data collection and modelling efforts in the field of infectious diseases.

Efficient detection of contagious outbreaks in massive metropolitan encounter networks

Physical contact remains difficult to trace in large metropolitan networks, though it is a key vehicle for the transmission of contagious outbreaks. Co-presence encounters during daily transit use provide us with a city-scale time-resolved physical contact network, consisting of 1 billion contacts among 3 million transit users. Here, we study the advantage that knowledge of such co-presence structures may provide for early detection of contagious outbreaks. We first examine the "friend sensor" scheme--a simple, but universal strategy requiring only local information--and demonstrate that it provides significant early detection of simulated outbreaks. Taking advantage of the full network structure, we then identify advanced "global sensor sets", obtaining substantial early warning times savings over the friends sensor scheme. Individuals with highest number of encounters are the most efficient sensors, with performance comparable to individuals with the highest travel frequency, exploratory behavior and structural centrality. An efficiency balance emerges when testing the dependency on sensor size and evaluating sensor reliability; we find that substantial and reliable lead-time could be attained by monitoring only 0.01% of the population with the highest degree.

How should social mixing be measured: comparing web-based survey and sensor-based methods

Background

Contact surveys and diaries have conventionally been used to measure contact networks in different settings for elucidating infectious disease transmission dynamics of respiratory infections. More recently, technological advances have permitted the use of wireless sensor devices, which can be worn by individuals interacting in a particular social context to record high resolution mixing patterns. To date, a direct comparison of these two different methods for collecting contact data has not been performed.

Methods

We studied the contact network at a United States high school in the spring of 2012. All school members (i.e., students, teachers, and other staff) were invited to wear wireless sensor devices for a single school day, and asked to remember and report the name and duration of all of their close proximity conversational contacts for that day in an online contact survey. We compared the two methods in terms of the resulting network densities, nodal degrees, and degree distributions. We also assessed the correspondence between the methods at the dyadic and individual levels.

Results

We found limited congruence in recorded contact data between the online contact survey and wireless sensors. In particular, there was only negligible correlation between the two methods for nodal degree, and the degree distribution differed substantially between both methods. We found that survey underreporting was a significant source of the difference between the two methods, and that this difference could be improved by excluding individuals who reported only a few contact partners. Additionally, survey reporting was more accurate for contacts of longer duration, and very inaccurate for contacts of shorter duration. Finally, female participants tended to report more accurately than male participants.

Conclusions

Online contact surveys and wireless sensor devices collected incongruent network data from an identical setting. This finding suggests that these two methods cannot be used interchangeably for informing models of infectious disease dynamics.

Efficient surveillance for healthcare-associated infections spreading between hospitals

Early detection of new or novel variants of nosocomial pathogens is a public health priority. We show that, for healthcare-associated infections that spread between hospitals as a result of patient movements, it is possible to design an effective surveillance system based on a relatively small number of sentinel hospitals. We apply recently developed mathematical models to patient admission data from the national healthcare systems of England and The Netherlands. Relatively short detection times are achieved once 10-20% hospitals are recruited as sentinels and only modest reductions are seen as more hospitals are recruited thereafter. Using a heuristic optimization approach to sentinel selection, the same expected time to detection can be achieved by recruiting approximately half as many hospitals. Our study provides a robust evidence base to underpin the design of an efficient sentinel hospital surveillance system for novel nosocomial pathogens, delivering early detection times for reduced expenditure and effort.

Estimating potential infection transmission routes in hospital wards using wearable proximity sensors

Background

Contacts between patients, patients and health care workers (HCWs) and among HCWs represent one of the important routes of transmission of hospital-acquired infections (HAI). A detailed description and quantification of contacts in hospitals provides key information for HAIs epidemiology and for the design and validation of control measures.

Methods and Findings

We used wearable sensors to detect close-range interactions (“contacts”) between individuals in the geriatric unit of a university hospital. Contact events were measured with a spatial resolution of about 1.5 meters and a temporal resolution of 20 seconds. The study included 46 HCWs and 29 patients and lasted for 4 days and 4 nights. 14,037 contacts were recorded overall, 94.1% of which during daytime. The number and duration of contacts varied between mornings, afternoons and nights, and contact matrices describing the mixing patterns between HCW and patients were built for each time period. Contact patterns were qualitatively similar from one day to the next. 38% of the contacts occurred between pairs of HCWs and 6 HCWs accounted for 42% of all the contacts including at least one patient, suggesting a population of individuals who could potentially act as super-spreaders.

Conclusions

Wearable sensors represent a novel tool for the measurement of contact patterns in hospitals. The collected data can provide information on important aspects that impact the spreading patterns of infectious diseases, such as the strong heterogeneity of contact numbers and durations across individuals, the variability in the number of contacts during a day, and the fraction of repeated contacts across days. This variability is however associated with a marked statistical stability of contact and mixing patterns across days. Our results highlight the need for such measurement efforts in order to correctly inform mathematical models of HAIs and use them to inform the design and evaluation of prevention strategies.

Epidemiologically optimal static networks from temporal network data

One of network epidemiology's central assumptions is that the contact structure over which infectious diseases propagate can be represented as a static network. However, contacts are highly dynamic, changing at many time scales. In this paper, we investigate conceptually simple methods to construct static graphs for network epidemiology from temporal contact data. We evaluate these methods on empirical and synthetic model data. For almost all our cases, the network representation that captures most relevant information is a so-called exponential-threshold network. In these, each contact contributes with a weight decreasing exponentially with time, and there is an edge between a pair of vertices if the weight between them exceeds a threshold. Networks of aggregated contacts over an optimally chosen time window perform almost as good as the exponential-threshold networks. On the other hand, networks of accumulated contacts over the entire sampling time, and networks of concurrent partnerships, perform worse. We discuss these observations in the context of the temporal and topological structure of the data sets.

To understand how diseases spread in a population, it is important to study the network of people in contact. Many methods to model epidemic outbreaks make the assumption that one can treat this network as static. In reality, we know that contact patterns between people change in time, and old contacts are soon irrelevant—it does not matter that we know Marie Antoinette's lovers to understand the HIV epidemic. This paper investigates methods for constructing networks of people that are as relevant as possible for disease spreading. The most promising method we call exponential-threshold network works by letting contacts contribute less, the further from the beginning of an outbreak they take place. We investigate the methods both on artificial models of the contact patterns and empirical data. Except searching for the optimal network representation, we also investigate how the structure of the original data set affects the performance of the representations.

A practical method to target individuals for outbreak detection and control

Identification of individuals or subpopulations that contribute the most to disease transmission is key to target surveillance and control efforts. In a recent study in BMC Medicine, Smieszek and Salathé introduced a novel method based on readily available information about spatial proximity in high schools, to help identify individuals at higher risk of infection and those more likely to be infected early in the outbreak. By combining simulation models for influenza transmission with high-resolution data on school contact patterns, the authors showed that their proximity method compares favorably to more sophisticated methods using detailed contact tracing information. The proximity method is simple and promising, but further research is warranted to confront this method against real influenza outbreak data, and to assess the generalizability of the approach to other important transmission units, such as work, households, and transportation systems.See related research article here http://www.biomedcentral.com/1741-7015/11/35.