James O. Lloyd-Smith

Superspreading and the effect of individual variation on disease emergence

Population-level analyses often use average quantities to describe heterogeneous systems, particularly when variation does not arise from identifiable groups. A prominent example, central to our current understanding of epidemic spread, is the basic reproductive number, R0, which is defined as the mean number of infections caused by an infected individual in a susceptible population. Population estimates of R0 can obscure considerable individual variation in infectiousness, as highlighted during the global emergence of severe acute respiratory syndrome (SARS) by numerous ‘superspreading events’ in which certain individuals infected unusually large numbers of secondary cases. For diseases transmitted by non-sexual direct contacts, such as SARS or smallpox, individual variation is difficult to measure empirically, and thus its importance for outbreak dynamics has been unclear. Here we present an integrated theoretical and statistical analysis of the influence of individual variation in infectiousness on disease emergence. Using contact tracing data from eight directly transmitted diseases, we show that the distribution of individual infectiousness around R0 is often highly skewed. Model predictions accounting for this variation differ sharply from average-based approaches, with disease extinction more likely and outbreaks rarer but more explosive. Using these models, we explore implications for outbreak control, showing that individual-specific control measures outperform population-wide measures. Moreover, the dramatic improvements achieved through targeted control policies emphasize the need to identify predictive correlates of higher infectiousness. Our findings indicate that superspreading is a normal feature of disease spread, and to frame ongoing discussion we propose a rigorous definition for superspreading events and a method to predict their frequency.

The potential impact of male circumcision on HIV in Sub-Saharan Africa.

Background A randomized controlled trial (RCT) has shown that male circumcision (MC) reduces sexual transmission of HIV from women to men by 60% (32%−76%; 95% CI) offering an intervention of proven efficacy for reducing the sexual spread of HIV. We explore the implications of this finding for the promotion of MC as a public health intervention to control HIV in sub-Saharan Africa. Methods and Findings Using dynamical simulation models we consider the impact of MC on the relative prevalence of HIV in men and women and in circumcised and uncircumcised men. Using country level data on HIV prevalence and MC, we estimate the impact of increasing MC coverage on HIV incidence, HIV prevalence, and HIV-related deaths over the next ten, twenty, and thirty years in sub-Saharan Africa. Assuming that full coverage of MC is achieved over the next ten years, we consider three scenarios in which the reduction in transmission is given by the best estimate and the upper and lower 95% confidence limits of the reduction in transmission observed in the RCT. MC could avert 2.0 (1.1−3.8) million new HIV infections and 0.3 (0.1−0.5) million deaths over the next ten years in sub-Saharan Africa. In the ten years after that, it could avert a further 3.7 (1.9−7.5) million new HIV infections and 2.7 (1.5−5.3) million deaths, with about one quarter of all the incident cases prevented and the deaths averted occurring in South Africa. We show that a) MC will increase the proportion of infected people who are women from about 52% to 58%; b) where there is homogenous mixing but not all men are circumcised, the prevalence of infection in circumcised men is likely to be about 80% of that in uncircumcised men; c) MC is equivalent to an intervention, such as a vaccine or increased condom use, that reduces transmission in both directions by 37%. Conclusions This analysis is based on the result of just one RCT, but if the results of that trial are confirmed we suggest that MC could substantially reduce the burden of HIV in Africa, especially in southern Africa where the prevalence of MC is low and the prevalence of HIV is high. While the protective benefit to HIV-negative men will be immediate, the full impact of MC on HIV-related illness and death will only be apparent in ten to twenty years.

Epidemic dynamics at the human-animal interface.

Zeroing in on Zoonoses Influenza, plague, and Lyme disease are classic examples of zoonoses—diseases that circulate in livestock and wildlife, as well as in humans. When a pathogen transfers among multiple hosts, the dynamics of circulation, transmission, and outbreak are complex. Lloyd-Smith et al. (p. 1362) review the use of analytical mathematical tools, particularly modeling, in the development of control policies and research agendas. Significant gaps are highlighted in analytical efforts during spillover transmission from animals into humans. Moreover, the tendency has been to focus on pathogens with simpler life cycles and of immediate global urgency, such as influenza, whereas insect-transmitted pathogens with complex, multihost life cycles are less well understood. Few infectious diseases are entirely human-specific: Most human pathogens also circulate in animals or else originated in nonhuman hosts. Influenza, plague, and trypanosomiasis are classic examples of zoonotic infections that transmit from animals to humans. The multihost ecology of zoonoses leads to complex dynamics, and analytical tools, such as mathematical modeling, are vital to the development of effective control policies and research agendas. Much attention has focused on modeling pathogens with simpler life cycles and immediate global urgency, such as influenza and severe acute respiratory syndrome. Meanwhile, vector-transmitted, chronic, and protozoan infections have been neglected, as have crucial processes such as cross-species transmission. Progress in understanding and combating zoonoses requires a new generation of models that addresses a broader set of pathogen life histories and integrates across host species and scientific disciplines.

Evidence for the unique function of docosahexaenoic acid during the evolution of the modern hominid brain

The African savanna ecosystem of the large mammals and primates was associated with a dramatic decline in relative brain capacity associated with little docosahexaenoic acid (DHA), which is required for brain structures and growth. The biochemistry implies that the expansion of the human brain required a plentiful source of preformed DHA. The richest source of DHA is the marine food chain, while the savanna environment offers very little of it. ConsequentlyHomo sapiens could not have evolved on the savannas. Recent fossil evidence indicates that the lacustrine and marine food chain was being extensively exploited at the time cerebral expansion took place and suggests the alternative that the transition from the archaic to modern humans took place at the land/water interface. Contemporary data on tropical lakeshore dwellers reaffirm the above view with nutritional support for the vascular system, the development of which would have been a prerequisite for cerebral expansion. Both arachidonic acid and DHA would have been freely available from such habitats providing the double stimulus of preformed acyl components for the developing blood vessels and brain. The n-3 docosapentaenoic acid precursor (n-3 DPA) was the major n-3-metabolite in the savanna mammals. Despite this abundance, neither it nor the corresponding n-6 DPA was used for the photoreceptor nor the synapse. A substantial difference between DHA and other fatty acids is required to explain this high specificity. Studies on fluidity and other mechanical features of cell membranes did not reveal a difference of such magnitude between even α-linolenic acid and DHA sufficient to explain the exclusive use of DHA. We suggest that the evolution of the large human brain depended on a rich source of DHA from the land/water interface. We review a number of proposals for the possible influence of DHA on physical properties of the brain that are essential for its function.

Ecology of zoonoses: natural and unnatural histories

Summary More than 60% of human infectious diseases are caused by pathogens shared with wild or domestic animals. Zoonotic disease organisms include those that are endemic in human populations or enzootic in animal populations with frequent cross-species transmission to people. Some of these diseases have only emerged recently. Together, these organisms are responsible for a substantial burden of disease, with endemic and enzootic zoonoses causing about a billion cases of illness in people and millions of deaths every year. Emerging zoonoses are a growing threat to global health and have caused hundreds of billions of US dollars of economic damage in the past 20 years. We aimed to review how zoonotic diseases result from natural pathogen ecology, and how other circumstances, such as animal production, extraction of natural resources, and antimicrobial application change the dynamics of disease exposure to human beings. In view of present anthropogenic trends, a more effective approach to zoonotic disease prevention and control will require a broad view of medicine that emphasises evidence-based decision making and integrates ecological and evolutionary principles of animal, human, and environmental factors. This broad view is essential for the successful development of policies and practices that reduce probability of future zoonotic emergence, targeted surveillance and strategic prevention, and engagement of partners outside the medical community to help improve health outcomes and reduce disease threats.

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.

Disentangling association patterns in fission-fusion societies using African buffalo as an example

A description of the social network of a population aids us in understanding dispersal, the spread of disease, and genetic structure in that population. Many animal populations can be classified as fission–fusion societies, whereby groups form and separate over time. Examples discussed in the literature include ungulates, primates and cetaceans (Lott & Minta 1983; Whitehead et al. 1991; Henzi et al. 1997; Christal et al. 1998; Chilvers & Corkeron 2002). In this study, we use a heuristic simulation model to illustrate potential problems in applying traditional techniques of association analysis to fission– fusion societies and propose a new index of association: the fission decision index (FDI). We compare the conclusions resulting from traditional methods with those of the FDI using data from African buffalo, Syncerus caffer, in the Kruger National Park. The traditional approach suggested that the buffalo population was spatially and temporally structured into four different ‘herds’ with adult males only peripherally associated with mixed herds. Our FDI method indicated that association decisions of adult males appeared random, but those of other sex and age categories were nonrandom, particularly when we included the fission events associated with adult males. Furthermore, the amount of time that individuals spent together was only weakly correlated with their propensity to remain together during fission events. We conclude

Curtailing transmission of severe acute respiratory syndrome within a community and its hospital

Severe acute respiratory syndrome (SARS) has been transmitted extensively within hospitals, and healthcare workers (HCWs) have comprised a large proportion of SARS cases worldwide. We present a stochastic model of a SARS outbreak in a community and its hospital. For a range of basic reproductive numbers (R0) corresponding to conditions in different cities (but with emphasis on R0 ∽ 3 as reported for Hong Kong and Singapore), we evaluate contact precautions and case management (quarantine and isolation) as containment measures. Hospital–based contact precautions emerge as the most potent measures, with hospital–wide measures being particularly important if screening of HCWs is inadequate. For R0 = 3, case isolation alone can control a SARS outbreak only if isolation reduces transmission by at least a factor of four and the mean symptom–onset–to–isolation time is less than 3 days. Delays of a few days in contact tracing and case identification severely degrade the utility of quarantine and isolation, particularly in high–transmission settings. Still more detrimental are delays between the onset of an outbreak and the implementation of control measures; for given control scenarios, our model identifies windows of opportunity beyond which the efficacy of containment efforts is reduced greatly. By considering pathways of transmission in our system, we show that if hospital–based transmission is not halted, measures that reduce community–HCW contact are vital to preventing a widespread epidemic. The implications of our results for future emerging pathogens are discussed.

Maximum Likelihood Estimation of the Negative Binomial Dispersion Parameter for Highly Overdispersed Data, with Applications to Infectious Diseases

Background The negative binomial distribution is used commonly throughout biology as a model for overdispersed count data, with attention focused on the negative binomial dispersion parameter, k. A substantial literature exists on the estimation of k, but most attention has focused on datasets that are not highly overdispersed (i.e., those with k≥1), and the accuracy of confidence intervals estimated for k is typically not explored. Methodology This article presents a simulation study exploring the bias, precision, and confidence interval coverage of maximum-likelihood estimates of k from highly overdispersed distributions. In addition to exploring small-sample bias on negative binomial estimates, the study addresses estimation from datasets influenced by two types of event under-counting, and from disease transmission data subject to selection bias for successful outbreaks. Conclusions Results show that maximum likelihood estimates of k can be biased upward by small sample size or under-reporting of zero-class events, but are not biased downward by any of the factors considered. Confidence intervals estimated from the asymptotic sampling variance tend to exhibit coverage below the nominal level, with overestimates of k comprising the great majority of coverage errors. Estimation from outbreak datasets does not increase the bias of k estimates, but can add significant upward bias to estimates of the mean. Because k varies inversely with the degree of overdispersion, these findings show that overestimation of the degree of overdispersion is very rare for these datasets.

Assembling evidence for identifying reservoirs of infection

Many pathogens persist in multihost systems, making the identification of infection reservoirs crucial for devising effective interventions. Here, we present a conceptual framework for classifying patterns of incidence and prevalence, and review recent scientific advances that allow us to study and manage reservoirs simultaneously. We argue that interventions can have a crucial role in enriching our mechanistic understanding of how reservoirs function and should be embedded as quasi-experimental studies in adaptive management frameworks. Single approaches to the study of reservoirs are unlikely to generate conclusive insights whereas the formal integration of data and methodologies, involving interventions, pathogen genetics, and contemporary surveillance techniques, promises to open up new opportunities to advance understanding of complex multihost systems.