A susceptible-infected model of early detection of respiratory infection outbreaks on a background of influenza

The threat of biological warfare and the emergence of new infectious agents spreading at a global scale have highlighted the need for major enhancements to the public health infrastructure. Early detection of epidemics of infectious diseases requires both real-time data and real-time interpretation of data. Despite moderate advancements in data acquisition, the state of the practice for real-time analysis of data remains inadequate. We present a nonlinear mathematical framework for modeling the transient dynamics of influenza, applied to historical data sets of patients with influenza-like illness. We estimate the vital time-varying epidemiological parameters of infections from historical data, representing normal epidemiological trends. We then introduce simulated outbreaks of different shapes and magnitudes into the historical data, and estimate the parameters representing the infection rates of anomalous deviations from normal trends. Finally, a dynamic threshold-based detection algorithm is devised to assess the timeliness and sensitivity of detecting the irregularities in the data, under a fixed low false-positive rate. We find that the detection algorithm can identify such designated abnormalities in the data with high sensitivity with specificity held at 97%, but more importantly, early during an outbreak. The proposed methodology can be applied to a broad range of influenza-like infectious diseases, whether naturally occurring or a result of bioterrorism, and thus can be an integral component of a real-time surveillance system.     

Relating Phylogenetic Trees to Transmission Trees of Infectious Disease Outbreaks

Transmission events are the fundamental building blocks of the dynamics of any infectious disease. Much about the epidemiology of a disease can be learned when these individual transmission events are known or can be estimated. Such estimations are difficult and generally feasible only when detailed epidemiological data are available. The genealogy estimated from genetic sequences of sampled pathogens is another rich source of information on transmission history. Optimal inference of transmission events calls for the combination of genetic data and epidemiological data into one joint analysis. A key difficulty is that the transmission tree, which describes the transmission events between infected hosts, differs from the phylogenetic tree, which describes the ancestral relationships between pathogens sampled from these hosts. The trees differ both in timing of the internal nodes and in topology. These differences become more pronounced when a higher fraction of infected hosts is sampled. We show how the phylogenetic tree of sampled pathogens is related to the transmission tree of an outbreak of an infectious disease, by the within-host dynamics of pathogens. We provide a statistical framework to infer key epidemiological and mutational parameters by simultaneously estimating the phylogenetic tree and the transmission tree. We test the approach using simulations and illustrate its use on an outbreak of foot-and-mouth disease. The approach unifies existing methods in the emerging field of phylodynamics with transmission tree reconstruction methods that are used in infectious disease epidemiology.     

Disease Prevention versus Data Privacy: Using Landcover Maps to Inform Spatial Epidemic Models

The availability of epidemiological data in the early stages of an outbreak of an infectious disease is vital for modelers to make accurate predictions regarding the likely spread of disease and preferred intervention strategies. However, in some countries, the necessary demographic data are only available at an aggregate scale. We investigated the ability of models of livestock infectious diseases to predict epidemic spread and obtain optimal control policies in the event of imperfect, aggregated data. Taking a geographic information approach, we used land cover data to predict UK farm locations and investigated the influence of using these synthetic location data sets upon epidemiological predictions in the event of an outbreak of foot-and-mouth disease. When broadly classified land cover data were used to create synthetic farm locations, model predictions deviated significantly from those simulated on true data. However, when more resolved subclass land use data were used, moderate to highly accurate predictions of epidemic size, duration and optimal vaccination and ring culling strategies were obtained. This suggests that a geographic information approach may be useful where individual farm-level data are not available, to allow predictive analyses to be carried out regarding the likely spread of disease. This method can also be used for contingency planning in collaboration with policy makers to determine preferred control strategies in the event of a future outbreak of infectious disease in livestock.     

Modeling and real-time prediction of classical swine fever epidemics

We propose a new method to analyze outbreak data of an infectious disease such as classical swine fever. The underlying model is a two-type branching process. It is used to deduce information concerning the epidemic from detected cases. In particular, the method leads to prediction of the future course of the epidemic and hence can be used as a basis for control policy decisions. We test the model with data from the large 1997-1998 classical swine fever epidemic in The Netherlands. It turns out that our results are in good agreement with the data.     

Detecting Presymptomatic Infection Is Necessary to Forecast Major Epidemics in the Earliest Stages of Infectious Disease Outbreaks

We assess how presymptomatic infection affects predictability of infectious disease epidemics. We focus on whether or not a major outbreak (i.e. an epidemic that will go on to infect a large number of individuals) can be predicted reliably soon after initial cases of disease have appeared within a population. For emerging epidemics, significant time and effort is spent recording symptomatic cases. Scientific attention has often focused on improving statistical methodologies to estimate disease transmission parameters from these data. Here we show that, even if symptomatic cases are recorded perfectly, and disease spread parameters are estimated exactly, it is impossible to estimate the probability of a major outbreak without ambiguity. Our results therefore provide an upper bound on the accuracy of forecasts of major outbreaks that are constructed using data on symptomatic cases alone. Accurate prediction of whether or not an epidemic will occur requires records of symptomatic individuals to be supplemented with data concerning the true infection status of apparently uninfected individuals. To forecast likely future behavior in the earliest stages of an emerging outbreak, it is therefore vital to develop and deploy accurate diagnostic tests that can determine whether asymptomatic individuals are actually uninfected, or instead are infected but just do not yet show detectable symptoms.     

Learning from history, predicting the future: the UK Dutch elm disease outbreak in relation to contemporary tree disease threats

Expanding international trade and increased transportation are heavily implicated in the growing threat posed by invasive pathogens to biodiversity and landscapes. With trees and woodland in the UK now facing threats from a number of disease systems, this paper looks to historical experience with the Dutch elm disease (DED) epidemic of the 1970s to see what can be learned about an outbreak and attempts to prevent, manage and control it. The paper draws on an interdisciplinary investigation into the history, biology and policy of the epidemic. It presents a reconstruction based on a spatial modelling exercise underpinned by archival research and interviews with individuals involved in the attempted management of the epidemic at the time. The paper explores what, if anything, might have been done to contain the outbreak and discusses the wider lessons for plant protection. Reading across to present-day biosecurity concerns, the paper looks at the current outbreak of ramorum blight in the UK and presents an analysis of the unfolding epidemiology and policy of this more recent, and potentially very serious, disease outbreak. The paper concludes by reflecting on the continuing contemporary relevance of the DED experience at an important juncture in the evolution of plant protection policy.     

A stochastic SIS epidemic with demography: initial stages and time to extinction

We study an open population stochastic epidemic model from the time of introduction of the disease, through a possible outbreak and to extinction. The model describes an SIS (susceptible–infective–susceptible) epidemic where all individuals, including infectious ones, reproduce at a given rate. An approximate expression for the outbreak probability is derived using a coupling argument. Further, we analyse the behaviour of the model close to quasi-stationarity, and the time to disease extinction, with the aid of a diffusion approximation. In this situation the number of susceptibles and infectives behaves as an Ornstein–Uhlenbeck process, centred around the stationary point, for an exponentially distributed time before going extinct.     

Linking community and disease ecology: the impact of biodiversity on pathogen transmission

The increasing number of zoonotic diseases spilling over from a range of wild animal species represents a particular concern for public health, especially in light of the current dramatic trend of biodiversity loss. To understand the ecology of these multi-host pathogens and their response to environmental degradation and species extinctions, it is necessary to develop a theoretical framework that takes into account realistic community assemblages. Here, we present a multi-host species epidemiological model that includes empirically determined patterns of diversity and composition derived from community ecology studies. We use this framework to study the interaction between wildlife diversity and directly transmitted pathogen dynamics. First, we demonstrate that variability in community composition does not affect significantly the intensity of pathogen transmission. We also show that the consequences of community diversity can differentially impact the prevalence of pathogens and the number of infectious individuals. Finally, we show that ecological interactions among host species have a weaker influence on pathogen circulation than inter-species transmission rates. We conclude that integration of a community perspective to study wildlife pathogens is crucial, especially in the context of understanding and predicting infectious disease emergence events.     

Mesoamerican nephropathy: a neglected tropical disease with an infectious etiology?

An outbreak of unexplained and severe kidney disease, “Mesoamerican Nephropathy,” in mostly young, male sugar cane workers emerged in Central America in the late 1990's. As a result, an estimated 20,000 individuals have died, to date. Unfortunately, and with great consequence to human life, the etiology of the outbreak has yet to be identified. The sugarcane fields in Chichigalpa, Chinandega, Nicaragua, have been involved in the outbreak, and during our initial investigation, we interviewed case patients who experienced fever, nausea and vomiting, arthralgia, myalgia, headache, neck and back pain, weakness, and paresthesia at the onset of acute kidney disease. We also observed a heavy infestation of rodents, particularly of Sigmodon species, in the sugarcane fields. We hypothesize that infectious pathogens are being shed through the urine and feces of these rodents, and workers are exposed to these pathogens during the process of cultivating and harvesting sugarcane. In this paper, we will discuss the epidemic in the Chichigalpa area, potential pathogens responsible for Mesoamerican Nephropathy, and steps needed in order to diagnose, treat, and prevent future cases from occurring.     

Two-Step Source Tracing Strategy of Yersinia pestis and Its Historical Epidemiology in a Specific Region

Source tracing of pathogens is critical for the control and prevention of infectious diseases. Genome sequencing by high throughput technologies is currently feasible and popular, leading to the burst of deciphered bacterial genome sequences. Utilizing the flooding genomic data for source tracing of pathogens in outbreaks is promising, and challenging as well. Here, we employed Yersinia pestis genomes from a plague outbreak at Xinghai county of China in 2009 as an example, to develop a simple two-step strategy for rapid source tracing of the outbreak. The first step was to define the phylogenetic position of the outbreak strains in a whole species tree, and the next step was to provide a detailed relationship across the outbreak strains and their suspected relatives. Through this strategy, we observed that the Xinghai plague outbreak was caused by Y. pestis that circulated in the local plague focus, where the majority of historical plague epidemics in the Qinghai-Tibet Plateau may originate from. The analytical strategy developed here will be of great help in fighting against the outbreaks of emerging infectious diseases, by pinpointing the source of pathogens rapidly with genomic epidemiological data and microbial forensics information.     

Variational data assimilation with epidemic models

Mathematical modelling is playing an increasing role in developing an understanding of the dynamics of communicable disease and assisting the construction and implementation of intervention strategies. The threat of novel emergent pathogens in human and animal hosts implies the requirement for methods that can robustly estimate epidemiological parameters and provide forecasts. Here, a technique called variational data assimilation is introduced as a means of optimally melding dynamic epidemic models with epidemiological observations and data to provide forecasts and parameter estimates. Using data from a simulated epidemic process the method is used to estimate the start time of an epidemic, to provide a forecast of future epidemic behaviour and estimate the basic reproductive ratio. A feature of the method is that it uses a basic continuous-time SIR model, which is often the first point of departure for epidemiological modelling during the early stages of an outbreak. The method is illustrated by application to data gathered during an outbreak of influenza in a school environment.     

Identifying hosts of families of viruses: a machine learning approach

Identifying emerging viral pathogens and characterizing their transmission is essential to developing effective public health measures in response to an epidemic. Phylogenetics, though currently the most popular tool used to characterize the likely host of a virus, can be ambiguous when studying species very distant to known species and when there is very little reliable sequence information available in the early stages of the outbreak of disease. Motivated by an existing framework for representing biological sequence information, we learn sparse, tree-structured models, built from decision rules based on subsequences, to predict viral hosts from protein sequence data using popular discriminative machine learning tools. Furthermore, the predictive motifs robustly selected by the learning algorithm are found to show strong host-specificity and occur in highly conserved regions of the viral proteome.     

Network-based analysis of stochastic SIR epidemic models with random and proportionate mixing

In this paper, we outline the theory of epidemic percolation networks and their use in the analysis of stochastic susceptible-infectious-removed (SIR) epidemic models on undirected contact networks. We then show how the same theory can be used to analyze stochastic SIR models with random and proportionate mixing. The epidemic percolation networks for these models are purely directed because undirected edges disappear in the limit of a large population. In a series of simulations, we show that epidemic percolation networks accurately predict the mean outbreak size and probability and final size of an epidemic for a variety of epidemic models in homogeneous and heterogeneous populations. Finally, we show that epidemic percolation networks can be used to re-derive classical results from several different areas of infectious disease epidemiology. In an Appendix, we show that an epidemic percolation network can be defined for any time-homogeneous stochastic SIR model in a closed population and prove that the distribution of outbreak sizes given the infection of any given node in the SIR model is identical to the distribution of its out-component sizes in the corresponding probability space of epidemic percolation networks. We conclude that the theory of percolation on semi-directed networks provides a very general framework for the analysis of stochastic SIR models in closed populations.     

Infections on Temporal Networks—A Matrix-Based Approach

We extend the concept of accessibility in temporal networks to model infections with a finite infectious period such as the susceptible-infected-recovered (SIR) model. This approach is entirely based on elementary matrix operations and unifies the disease and network dynamics within one algebraic framework. We demonstrate the potential of this formalism for three examples of networks with high temporal resolution: networks of social contacts, sexual contacts, and livestock-trade. Our investigations provide a new methodological framework that can be used, for instance, to estimate the epidemic threshold, a quantity that determines disease parameters, for which a large-scale outbreak can be expected.     

Estimating individual and household reproduction numbers in an emerging epidemic

Reproduction numbers, defined as averages of the number of people infected by a typical case, play a central role in tracking infectious disease outbreaks. The aim of this paper is to develop methods for estimating reproduction numbers which are simple enough that they could be applied with limited data or in real time during an outbreak. I present a new estimator for the individual reproduction number, which describes the state of the epidemic at a point in time rather than tracking individuals over time, and discuss some potential benefits. Then, to capture more of the detail that micro-simulations have shown is important in outbreak dynamics, I analyse a model of transmission within and between households, and develop a method to estimate the household reproduction number, defined as the number of households infected by each infected household. This method is validated by numerical simulations of the spread of influenza and measles using historical data, and estimates are obtained for would-be emerging epidemics of these viruses. I argue that the household reproduction number is useful in assessing the impact of measures that target the household for isolation, quarantine, vaccination or prophylactic treatment, and measures such as social distancing and school or workplace closures which limit between-household transmission, all of which play a key role in current thinking on future infectious disease mitigation.     

A Bayesian Inference Framework to Reconstruct Transmission Trees Using Epidemiological and Genetic Data

The accurate identification of the route of transmission taken by an infectious agent through a host population is critical to understanding its epidemiology and informing measures for its control. However, reconstruction of transmission routes during an epidemic is often an underdetermined problem: data about the location and timings of infections can be incomplete, inaccurate, and compatible with a large number of different transmission scenarios. For fast-evolving pathogens like RNA viruses, inference can be strengthened by using genetic data, nowadays easily and affordably generated. However, significant statistical challenges remain to be overcome in the full integration of these different data types if transmission trees are to be reliably estimated. We present here a framework leading to a bayesian inference scheme that combines genetic and epidemiological data, able to reconstruct most likely transmission patterns and infection dates. After testing our approach with simulated data, we apply the method to two UK epidemics of Foot-and-Mouth Disease Virus (FMDV): the 2007 outbreak, and a subset of the large 2001 epidemic. In the first case, we are able to confirm the role of a specific premise as the link between the two phases of the epidemics, while transmissions more densely clustered in space and time remain harder to resolve. When we consider data collected from the 2001 epidemic during a time of national emergency, our inference scheme robustly infers transmission chains, and uncovers the presence of undetected premises, thus providing a useful tool for epidemiological studies in real time. The generation of genetic data is becoming routine in epidemiological investigations, but the development of analytical tools maximizing the value of these data remains a priority. Our method, while applied here in the context of FMDV, is general and with slight modification can be used in any situation where both spatiotemporal and genetic data are available.     

The construction and analysis of epidemic trees with reference to the 2001 UK foot-and-mouth outbreak

The case-reproduction ratio for the spread of an infectious disease is a critically important concept for understanding dynamics of epidemics and for evaluating impact of control measures on spread of infection. Reliable estimation of this ratio is a problem central to epidemiology and is most often accomplished by fitting dynamic models to data and estimating combinations of parameters that equate to the case-reproduction ratio. Here, we develop a novel parameter-free method that permits direct estimation of the history of transmission events recoverable from detailed observation of a particular epidemic. From these reconstructed 'epidemic trees', case-reproduction ratios can be estimated directly. We develop a bootstrap algorithm that generates percentile intervals for these estimates that shows the procedure to be both precise and robust to possible uncertainties in the historical reconstruction. Identifying and 'pruning' branches from these trees whose occurrence might have been prevented by implementation of more stringent control measures permits estimation of the possible efficacy of these alternative measures. Examination of the cladistic structure of these trees as a function of the distance of each case from its infection source reveals useful insights about the relationship between long-distance transmission events and epidemic size. We demonstrate the utility of these methods by applying them to data from the 2001 foot-and-mouth disease outbreak in the UK.     

Constructing Rigorous and Broad Biosurveillance Networks for Detecting Emerging Zoonotic Outbreaks

Determining optimal surveillance networks for an emerging pathogen is difficult since it is not known beforehand what the characteristics of a pathogen will be or where it will emerge. The resources for surveillance of infectious diseases in animals and wildlife are often limited and mathematical modeling can play a supporting role in examining a wide range of scenarios of pathogen spread. We demonstrate how a hierarchy of mathematical and statistical tools can be used in surveillance planning help guide successful surveillance and mitigation policies for a wide range of zoonotic pathogens. The model forecasts can help clarify the complexities of potential scenarios, and optimize biosurveillance programs for rapidly detecting infectious diseases. Using the highly pathogenic zoonotic H5N1 avian influenza 2006-2007 epidemic in Nigeria as an example, we determined the risk for infection for localized areas in an outbreak and designed biosurveillance stations that are effective for different pathogen strains and a range of possible outbreak locations. We created a general multi-scale, multi-host stochastic SEIR epidemiological network model, with both short and long-range movement, to simulate the spread of an infectious disease through Nigerian human, poultry, backyard duck, and wild bird populations. We chose parameter ranges specific to avian influenza (but not to a particular strain) and used a Latin hypercube sample experimental design to investigate epidemic predictions in a thousand simulations. We ranked the risk of local regions by the number of times they became infected in the ensemble of simulations. These spatial statistics were then complied into a potential risk map of infection. Finally, we validated the results with a known outbreak, using spatial analysis of all the simulation runs to show the progression matched closely with the observed location of the farms infected in the 2006-2007 epidemic.     

Infectious disease in the Pleistocene: Old friends or old foes?

The impact of endemic and epidemic disease on humans has traditionally been seen as a comparatively recent historical phenomenon associated with the Neolithisation of human groups, an increase in population size led by sedentarism, and increasing contact with domesticated animals as well as species occupying opportunistic symbiotic and ectosymbiotic relationships with humans. The orthodox approach is that Neolithisation created the conditions for increasing population size able to support a reservoir of infectious disease sufficient to act as selective pressure. This orthodoxy is the result of an overly simplistic reliance on skeletal data assuming that no skeletal lesions equated to a healthy individual, underpinned by the assumption that hunter-gatherer groups were inherently healthy while agricultural groups acted as infectious disease reservoirs. The work of van Blerkom, Am. J. Phys. Anthropol., vol. suppl 37 (2003), Wolfe et al., Nature, vol. 447 (2007) and Houldcroft and Underdown, Am. J. Phys. Anthropol., vol. 160, (2016) has changed this landscape by arguing that humans and pathogens have long been fellow travelers. The package of infectious diseases experienced by our ancient ancestors may not be as dissimilar to modern infectious diseases as was once believed. The importance of DNA, from ancient and modern sources, to the study of the antiquity of infectious disease, and its role as a selective pressure cannot be overstated. Here we consider evidence of ancient epidemic and endemic infectious diseases with inferences from modern and ancient human and hominin DNA, and from circulating and extinct pathogen genomes. We argue that the pandemics of the past are a vital tool to unlock the weapons needed to fight pandemics of the future.     

Estimation and inference of R0 of an infectious pathogen by a removal method

The basic reproductive ratio, R0, is a central quantity in the investigation and management of infectious pathogens. The standard model for describing stochastic epidemics is the continuous time epidemic birth-and-death process. The incidence data used to fit this model tend to be collected in discrete units (days, weeks, etc.), which makes model fitting, and estimation of R0 difficult. Discrete time epidemic models better match the time scale of data collection but make simplistic assumptions about the stochastic epidemic process. By investigating the nature of the assumptions of a discrete time epidemic model, we derive a bias corrected maximum likelihood estimate of R0 based on the chain binomial model. The resulting 'removal' estimators provide estimates of R0 and the initial susceptible population size from time series of infectious case counts. We illustrate the performance of the estimators on both simulated data and real epidemics. Lastly, we discuss methods to address data collected with observation error.