Ken T. D. Eames

Networks and epidemic models

Networks and the epidemiology of directly transmitted infectious diseases are fundamentally linked. The foundations of epidemiology and early epidemiological models were based on population wide random-mixing, but in practice each individual has a finite set of contacts to whom they can pass infection; the ensemble of all such contacts forms a ‘mixing network’. Knowledge of the structure of the network allows models to compute the epidemic dynamics at the population scale from the individual-level behaviour of infections. Therefore, characteristics of mixing networks—and how these deviate from the random-mixing norm—have become important applied concerns that may enhance the understanding and prediction of epidemic patterns and intervention measures. Here, we review the basis of epidemiological theory (based on random-mixing models) and network theory (based on work from the social sciences and graph theory). We then describe a variety of methods that allow the mixing network, or an approximation to the network, to be ascertained. It is often the case that time and resources limit our ability to accurately find all connections within a network, and hence a generic understanding of the relationship between network structure and disease dynamics is needed. Therefore, we review some of the variety of idealized network types and approximation techniques that have been utilized to elucidate this link. Finally, we look to the future to suggest how the two fields of network theory and epidemiological modelling can deliver an improved understanding of disease dynamics and better public health through effective disease control.

Modeling dynamic and network heterogeneities in the spread of sexually transmitted diseases

A wide range of communicable human diseases can be considered as spreading through a network of possible transmission routes. The implied network structure is vital in determining disease dynamics, especially when the average number of connections per individual is small as is the case for many sexually transmitted diseases (STDs). Here we develop an intuitive mathematical framework to deal with the heterogeneities implicit within contact networks and those that arise because of the infection process. These models are compared with full stochastic simulations and show excellent agreement across a wide range of parameters. We show how such models can be used to estimate parameters of epidemiological importance, and how they can be extended to examine the effectiveness of various control strategies, in particular screening programs and contact tracing.

Dynamic social networks and the implications for the spread of infectious disease

Understanding the nature of human contact patterns is crucial for predicting the impact of future pandemics and devising effective control measures. However, few studies provide a quantitative description of the aspects of social interactions that are most relevant to disease transmission. Here, we present the results from a detailed diary-based survey of casual (conversational) and close contact (physical) encounters made by a small peer group of 49 adults who recorded 8661 encounters with 3528 different individuals over 14 non-consecutive days. We find that the stability of interactions depends on the intimacy of contact and social context. Casual contact encounters mostly occur in the workplace and are predominantly irregular, while close contact encounters mostly occur at home or in social situations and tend to be more stable. Simulated epidemics of casual contact transmission involve a large number of non-repeated encounters, and the social network is well captured by a random mixing model. However, the stability of the social network should be taken into account for close contact infections. Our findings have implications for the modelling of human epidemics and planning pandemic control policies based on social distancing methods.

Contact tracing and disease control

Contact tracing, followed by treatment or isolation, is a key control measure in the battle against infectious diseases. It is an extreme form of locally targeted control, and as such has the potential to be highly efficient when dealing with low numbers of cases. For this reason it is frequently used to combat sexually transmitted diseases and new invading pathogens. Accurate modelling of contact tracing requires explicit information about the disease–transmission pathways from each individual, and hence the network of contacts. Here, pairwise–approximation methods and full stochastic simulations are used to investigate the utility of contact tracing. A simple relationship is found between the efficiency of contact tracing necessary for eradication and the basic reproductive ratio of the disease. This holds for a wide variety of realistic situations including heterogeneous networks containing core–groups or super–spreaders, and asymptomatic individuals. Clustering (transitivity) within the transmission network is found to destroy the relationship, requiring lower efficiency than predicted.

Modeling infectious disease dynamics in the complex landscape of global health

Mathematical modeling of infectious diseases The spread of infectious diseases can be unpredictable. With the emergence of antibiotic resistance and worrying new viruses, and with ambitious plans for global eradication of polio and the elimination of malaria, the stakes have never been higher. Anticipation and measurement of the multiple factors involved in infectious disease can be greatly assisted by mathematical methods. In particular, modeling techniques can help to compensate for imperfect knowledge, gathered from large populations and under difficult prevailing circumstances. Heesterbeek et al. review the development of mathematical models used in epidemiology and how these can be harnessed to develop successful control strategies and inform public health policy. Science, this issue 10.1126/science.aaa4339 BACKGROUND Despite many notable successes in prevention and control, infectious diseases remain an enormous threat to human and animal health. The ecological and evolutionary dynamics of pathogens play out on a wide range of interconnected temporal, organizational, and spatial scales that span hours to months, cells to ecosystems, and local to global spread. Some pathogens are directly transmitted between individuals of a single species, whereas others circulate among multiple hosts, need arthropod vectors, or persist in environmental reservoirs. Many factors, including increasing antimicrobial resistance, human connectivity, population growth, urbanization, environmental and land-use change, as well as changing human behavior, present global challenges for prevention and control. Faced with this complexity, mathematical models offer valuable tools for understanding epidemiological patterns and for developing and evaluating evidence for decision-making in global health. ADVANCES During the past 50 years, the study of infectious disease dynamics has matured into a rich interdisciplinary field at the intersection of mathematics, epidemiology, ecology, evolutionary biology, immunology, sociology, and public health. The practical challenges range from establishing appropriate data collection to managing increasingly large volumes of information. The theoretical challenges require fundamental study of many-layered, nonlinear systems in which infections evolve and spread and where key events can be governed by unpredictable pathogen biology or human behavior. In this Review, we start with an examination of real-time outbreak response using the West African Ebola epidemic as an example. Here, the challenges range from underreporting of cases and deaths, and missing information on the impact of control measures to understanding human responses. The possibility of future zoonoses tests our ability to detect anomalous outbreaks and to estimate human-to-human transmissibility against a backdrop of ongoing zoonotic spillover while also assessing the risk of more dangerous strains evolving. Increased understanding of the dynamics of infections in food webs and ecosystems where host and nonhost species interact is key. Simultaneous multispecies infections are increasingly recognized as a notable public health burden, yet our understanding of how different species of pathogens interact within hosts is rudimentary. Pathogen genomics has become an essential tool for drawing inferences about evolution and transmission and, here but also in general, heterogeneity is the major challenge. Methods that depart from simplistic assumptions about random mixing are yielding new insights into the dynamics of transmission and control. There is rapid growth in estimation of model parameters from mismatched or incomplete data, and in contrasting model output with real-world observations. New data streams on social connectivity and behavior are being used, and combining data collected from very different sources and scales presents important challenges. All these mathematical endeavors have the potential to feed into public health policy and, indeed, an increasingly wide range of models is being used to support infectious disease control, elimination, and eradication efforts. OUTLOOK Mathematical modeling has the potential to probe the apparently intractable complexity of infectious disease dynamics. Coupled to continuous dialogue between decision-makers and the multidisciplinary infectious disease community, and by drawing on new data streams, mathematical models can lay bare mechanisms of transmission and indicate new approaches to prevention and control that help to shape national and international public health policy. Modeling for public health. Policy questions define the model’s purpose. Initial model design is based on current scientific understanding and the available relevant data. Model validation and fit to disease data may require further adaptation; sensitivity and uncertainty analysis can point to requirements for collection of additional specific data. Cycles of model testing and analysis thus lead to policy advice and improved scientific understanding. 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.

Measured dynamic social contact patterns explain the spread of H1N1v influenza.

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

Web-based participatory surveillance of infectious diseases: the Influenzanet participatory surveillance experience

Abstract To overcome the limitations of the state-of-the-art influenza surveillance systems in Europe, we established in 2008 a European-wide consortium aimed at introducing an innovative information and communication technology approach for a web-based surveillance system across different European countries, called Influenzanet. The system, based on earlier efforts in The Netherlands and Portugal, works with the participation of the population in each country to collect real-time information on the distribution of influenza-like illness cases through web surveys administered to volunteers reporting their symptoms (or lack of symptoms) every week during the influenza season. Such a large European-wide web-based monitoring infrastructure is intended to rapidly identify public health emergencies, contribute to understanding global trends, inform data-driven forecast models to assess the impact on the population, optimize the allocation of resources, and help in devising mitigation and containment measures. In this article, we describe the scientific and technological issues faced during the development and deployment of a flexible and readily deployable web tool capable of coping with the requirements of different countries for data collection, during either a public health emergency or an ordinary influenza season. Even though the system is based on previous successful experience, the implementation in each new country represented a separate scientific challenge. Only after more than 5 years of development are the existing platforms based on a plug-and-play tool that can be promptly deployed in any country wishing to be part of the Influenzanet network, now composed of The Netherlands, Belgium, Portugal, Italy, the UK, France, Sweden, Spain, Ireland, and Denmark.

Using an online survey of healthcare-seeking behaviour to estimate the magnitude and severity of the 2009 H1N1v influenza epidemic in England

BackgroundDuring the 2009 H1N1v influenza epidemic, the total number of symptomatic cases was estimated by combining influenza-like illness (ILI) consultations, virological surveillance and assumptions about healthcare-seeking behaviour. Changes in healthcare-seeking behaviour due to changing scientific information, media coverage and public anxiety, were not included in case estimates. The purpose of the study was to improve estimates of the number of symptomatic H1N1v cases and the case fatality rate (CFR) in England by quantifying healthcare-seeking behaviour using an internet-based survey carried out during the course of the 2009 H1N1v influenza epidemic.MethodsWe used an online survey that ran continuously from July 2009 to March 2010 to estimate the proportion of ILI cases that sought healthcare during the 2009 H1N1v influenza epidemic. We used dynamic age- and gender-dependent measures of healthcare-seeking behaviour to re-interpret consultation numbers and estimate the true number of cases of symptomatic ILI in 2009 and the case fatality rate (CFR).ResultsThere were significant differences between age groups in healthcare usage. From the start to the end of the epidemic, the percentage of individuals with influenza-like symptoms who sought medical attention decreased from 43% to 32% (p < 0.0001). Adjusting official numbers accordingly, we estimate that there were 1.1 million symptomatic cases in England, over 320,000 (40%) more cases than previously estimated and that the autumn epidemic wave was 45% bigger than previously thought. Combining symptomatic case numbers with reported deaths leads to a reduced overall CFR estimate of 17 deaths per 100,000 cases, with the largest reduction in adults.ConclusionsActive surveillance of healthcare-seeking behaviour, which can be achieved using novel data collection methods, is vital for providing accurate real-time estimates of epidemic size and disease severity. The differences in healthcare-seeking between different population groups and changes over time have significant implications for estimates of total case numbers and the case fatality rate.

Internet-based surveillance of Influenza-like-illness in the UK during the 2009 H1N1 influenza pandemic.

BackgroundInternet-based surveillance systems to monitor influenza-like illness (ILI) have advantages over traditional (physician-based) reporting systems, as they can potentially monitor a wider range of cases (i.e. including those that do not seek care). However, the requirement for participants to have internet access and to actively participate calls into question the representativeness of the data. Such systems have been in place in a number of European countries over the last few years, and in July 2009 this was extended to the UK. Here we present results of this survey with the aim of assessing the reliability of the data, and to evaluate methods to correct for possible biases.MethodsInternet-based monitoring of ILI was launched near the peak of the first wave of the UK H1N1v influenza pandemic. We compared the recorded ILI incidence with physician-recorded incidence and an estimate of the true number of cases over the course of the epidemic. We also compared overall attack rates. The effect of using different ILI definitions and alternative denominator assumptions on incidence estimates was explored.ResultsThe crude incidence measured by the internet-based system appears to be influenced by individuals who participated only once in the survey and who appeared more likely to be ill. This distorted the overall incidence trend. Concentrating on individuals who reported more than once results in a time series of ILI incidence that matches the trend of case estimates reasonably closely, with a correlation of 0.713 (P-value: 0.0001, 95% CI: 0.435, 0.867). Indeed, the internet-based system appears to give a better estimate of the relative height of the two waves of the UK pandemic than the physician-recorded incidence. The overall attack rate is, however, higher than other estimates, at about 16% when compared with a model-based estimate of 6%.ConclusionInternet-based monitoring of ILI can capture the trends in case numbers if appropriate weighting is used to correct for differential response. The overall level of incidence is, however, difficult to measure. Internet-based systems may be a useful adjunct to existing ILI surveillance systems as they capture cases that do not necessarily contact health care. However, further research is required before they can be used to accurately assess the absolute level of incidence in the community.

Epidemic prediction and control in weighted networks

Contact networks are often used in epidemiological studies to describe the patterns of interactions within a population. Often, such networks merely indicate which individuals interact, without giving any indication of the strength or intensity of interactions. Here, we use weighted networks, in which every connection has an associated weight, to explore the influence of heterogeneous contact strengths on the effectiveness of control measures. We show that, by using contact weights to evaluate an individuals influence on an epidemic, individual infection risk can be estimated and targeted interventions such as preventative vaccination can be applied effectively. We use a diary study of social mixing behaviour to indicate the patterns of contact weights displayed by a real population in a range of different contexts, including physical interactions; we use these data to show that considerations of link weight can in some cases lead to improved interventions in the case of infections that spread through close contact interactions. However, we also see that simpler measures, such as an individuals total number of social contacts or even just their number of contacts during a single day, can lead to great improvements on random vaccination. We therefore conclude that, for many infections, enhanced social contact data can be simply used to improve disease control but that it is not necessary to have full social mixing information in order to enhance interventions.