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

The epidemic forest reveals the spatial pattern of the spread of acute respiratory infections in Jakarta, Indonesia

Acute respiratory infection (ARI) is a communicable disease of the respiratory tract that implies impaired breathing. The infection can expand from one to the neighboring areas at a region-scale level through a human mobility network. Specific to this study, we leverage a record of ARI incidences in four periods of outbreaks for 42 regions in Jakarta to study its spatio-temporal spread using the concept of the epidemic forest. This framework generates a forest-like graph representing an explicit spread of disease that takes the onset time, spatio-temporal distance, and case prevalence into account. To support this framework, we use logistic curves to infer the onset time of the outbreak for each region. The result shows that regions with earlier onset dates tend to have a higher burden of cases, leading to the idea that the culprits of the disease spread are those with a high load of cases. To justify this, we generate the epidemic forest for the four periods of ARI outbreaks and identify the implied dominant trees (that with the most children cases). We find that the primary infected city of the dominant tree has a relatively higher burden of cases than other trees. In addition, we can investigate the timely ( R t ) and spatial reproduction number ( R c ) by directly evaluating them from the inferred graphs. We find that R t for dominant trees are significantly higher than non-dominant trees across all periods, with regions in western Jakarta tend to have higher values of R c . Lastly, we provide simulated-implied graphs by suppressing 50% load of cases of the primary infected city in the dominant tree that results in a reduced R c , suggesting a potential target of intervention to depress the overall ARI spread.

Inferring transmission routes for foot-and-mouth disease virus within a cattle herd using approximate Bayesian computation

To control an outbreak of an infectious disease it is essential to understand the different routes of transmission and how they contribute to the overall spread of the pathogen. With this information, policy makers can choose the most efficient methods of detection and control during an outbreak. Here we assess the contributions of direct contact and environmental contamination to the transmission of foot-and-mouth disease virus (FMDV) in a cattle herd using an individual-based model that includes both routes. Model parameters are inferred using approximate Bayesian computation with sequential Monte Carlo sampling (ABC-SMC) applied to data from transmission experiments and the 2007 epidemic in Great Britain. This demonstrates that the parameters derived from transmission experiments are applicable to outbreaks in the field, at least for closely related strains. Under the assumptions made in the model we show that environmental transmission likely contributes a majority of infections within a herd during an outbreak, although there is a lot of variation between simulated outbreaks. The accumulation of environmental contamination not only causes infections within a farm, but also has the potential to spread between farms via fomites. We also demonstrate the importance and effectiveness of rapid detection of infected farms in reducing transmission between farms, whether via direct contact or the environment.

A Bayesian inference method to estimate transmission trees with multiple introductions; applied to SARS-CoV-2 in Dutch mink farms

Knowledge of who infected whom during an outbreak of an infectious disease is important to determine risk factors for transmission and to design effective control measures. Both whole-genome sequencing of pathogens and epidemiological data provide useful information about the transmission events and underlying processes. Existing models to infer transmission trees usually assume that the pathogen is introduced only once from outside into the population of interest. However, this is not always true. For instance, SARS-CoV-2 is suggested to be introduced multiple times in mink farms in the Netherlands from the SARS-CoV-2 pandemic among humans. Here, we developed a Bayesian inference method combining whole-genome sequencing data and epidemiological data, allowing for multiple introductions of the pathogen in the population. Our method does not a priori split the outbreak into multiple phylogenetic clusters, nor does it break the dependency between the processes of mutation, within-host dynamics, transmission, and observation. We implemented our method as an additional feature in the R-package phybreak. On simulated data, our method correctly identifies the number of introductions, with an accuracy depending on the proportion of all observed cases that are introductions. Moreover, when a single introduction was simulated, our method produced similar estimates of parameters and transmission trees as the existing package. When applied to data from a SARS-CoV-2 outbreak in Dutch mink farms, the method provides strong evidence for independent introductions of the pathogen at 13 farms, infecting a total of 63 farms. Using the new feature of the phybreak package, transmission routes of a more complex class of infectious disease outbreaks can be inferred which will aid infection control in future outbreaks.

Assessing the effectiveness of environmental sampling for surveillance of foot-and-mouth disease virus in a cattle herd

The survival of foot-and-mouth disease virus (FMDV) in the environment provides an opportunity for indirect transmission, both within and between farms. However it also presents the possibility of surveillance and detection via environmental sampling. This study assesses the effectiveness of environmental sampling strategies in the event of an outbreak, using a previous model for transmission of FMDV in a cattle herd that had been parameterized using data from transmission experiments and outbreaks. We show that environmental sampling can be an effective means of detecting FMDV in a herd, but it requires multiple samples to be taken on multiple occasions. In addition, environmental sampling can potentially detect FMDV in a herd more quickly than clinical inspection. For example, taking 10 samples every 3 days results in a mean time to detection of 6 days, which is lower than the mean time to detection estimated for the 2001 UK epidemic (8 days). We also show how environmental sampling could be used in a herd considered to be at risk as an alternative to pre-emptive culling. However, because of the time taken for virus to accumulate at the start of an outbreak, a reasonable level of confidence (> 99%) that an at-risk herd is indeed free from infection is unlikely to be achieved in less than 1 week.

Modelling effectiveness of COVID-19 pandemic control policies using an Area-based SEIR model with consideration of infection during interzonal travel

This paper studies the effectiveness of several pandemic restriction measures adopted in Singapore during the COVID-19 outbreak. To this end, the classical Susceptible-Exposed-Infectious-Recovered (SEIR) model widely used to describe the dynamic process of epidemic propagation is extended to an area-based SEIR model with the consideration of exposure to infections during commute and quarantine. The proposed model considers infections within areas and infections occurred during the commute of individuals. A case study of the Singapore MRT system is presented to show the effectiveness of pandemic restriction policies implemented in Singapore, namely social distancing, work shift and Circuit Breaker (CB) and phase advisories. A long-term investigation of COVID-19 pandemic in Singapore is performed, and the disease transmission dynamics in 2020-2021 (which covers the first wave and second wave of COVID-19 pandemic in Singapore) is modelled.

Inference of malaria reproduction numbers in three elimination settings by combining temporal data and distance metrics

Individual-level geographic information about malaria cases, such as the GPS coordinates of residence or health facility, is often collected as part of surveillance in near-elimination settings, but could be more effectively utilised to infer transmission dynamics, in conjunction with additional information such as symptom onset time and genetic distance. However, in the absence of data about the flow of parasites between populations, the spatial scale of malaria transmission is often not clear. As a result, it is important to understand the impact of varying assumptions about the spatial scale of transmission on key metrics of malaria transmission, such as reproduction numbers. We developed a method which allows the flexible integration of distance metrics (such as Euclidian distance, genetic distance or accessibility matrices) with temporal information into a single inference framework to infer malaria reproduction numbers. Twelve scenarios were defined, representing different assumptions about the likelihood of transmission occurring over different geographic distances and likelihood of missing infections (as well as high and low amounts of uncertainty in this estimate). These scenarios were applied to four individual level datasets from malaria eliminating contexts to estimate individual reproduction numbers and how they varied over space and time. Model comparison suggested that including spatial information improved models as measured by second order AIC (ΔAICc), compared to time only results. Across scenarios and across datasets, including spatial information tended to increase the seasonality of temporal patterns in reproduction numbers and reduced noise in the temporal distribution of reproduction numbers. The best performing parameterisations assumed long-range transmission (> 200 km) was possible. Our approach is flexible and provides the potential to incorporate other sources of information which can be converted into distance or adjacency matrices such as travel times or molecular markers.

Estimated Dissemination Ratio-A Practical Alternative to the Reproduction Number for Infectious Diseases

Policymakers require consistent and accessible tools to monitor the progress of an epidemic and the impact of control measures in real time. One such measure is the Estimated Dissemination Ratio (EDR), a straightforward, easily replicable, and robust measure of the trajectory of an outbreak that has been used for many years in the control of infectious disease in livestock. It is simple to calculate and explain. Its calculation and use are discussed below together with examples from the current COVID-19 outbreak in the UK. These applications illustrate that EDR can demonstrate changes in transmission rate before they may be clear from the epidemic curve. Thus, EDR can provide an early warning that an epidemic is resuming growth, allowing earlier intervention. A conceptual comparison between EDR and the commonly used reproduction number is also provided.

What can phylodynamics bring to animal health research?

Infectious diseases are a major burden to global economies, and public and animal health. To date, quantifying the spread of infectious diseases to inform policy making has traditionally relied on epidemiological data collected during epidemics. However, interest has grown in recent phylodynamic techniques to infer pathogen transmission dynamics from genetic data. Here, we provide examples of where this new discipline has enhanced disease management in public health and illustrate how it could be further applied in animal health. In particular, we describe how phylodynamics can address fundamental epidemiological questions, such as inferring key transmission parameters in animal populations and quantifying spillover events at the wildlife-livestock interface, and generate important insights for the design of more effective control strategies.

Causes of delayed outbreak responses and their impacts on epidemic spread

Livestock diseases have devastating consequences economically, socially and politically across the globe. In certain systems, pathogens remain viable after host death, which enables residual transmissions from infected carcasses. Rapid culling and carcass disposal are well-established strategies for stamping out an outbreak and limiting its impact; however, wait-times for these procedures, i.e. response delays, are typically farm-specific and time-varying due to logistical constraints. Failing to incorporate variable response delays in epidemiological models may understate outbreak projections and mislead management decisions. We revisited the 2001 foot-and-mouth epidemic in the United Kingdom and sought to understand how misrepresented response delays can influence model predictions. Survival analysis identified farm size and control demand as key factors that impeded timely culling and disposal activities on individual farms. Using these factors in the context of an existing policy to predict local variation in response times significantly affected predictions at the national scale. Models that assumed fixed, timely responses grossly underestimated epidemic severity and its long-term consequences. As a result, this study demonstrates how general inclusion of response dynamics and recognition of partial controllability of interventions can help inform management priorities during epidemics of livestock diseases.

Understanding the Importance of Contact Heterogeneity and Variable Infectiousness in the Dynamics of a Large Norovirus Outbreak

BACKGROUND

Large norovirus (NoV) outbreaks are explosive in nature and vary widely in final size and duration, suggesting that superspreading combined with heterogeneous contact may explain these dynamics. Modeling tools that can capture heterogeneity in infectiousness and contact are important for NoV outbreak prevention and control, yet they remain limited.

METHODS

Data from a large NoV outbreak at a Dutch scout jamboree, which resulted in illness among 326 (of 4500 total) individuals from 7 separate camps, were used to examine the contributions of individual variation in infectiousness and clustered contact patterns to the transmission dynamics. A Bayesian hierarchical model of heterogeneous, clustered outbreak transmission was applied to represent (1) between-individual heterogeneity in infectiousness and (2) heterogeneous patterns of contact.

RESULTS

We found wide heterogeneity in infectiousness across individuals, suggestive of superspreading. Nearly 50% of individual infectiousness was concentrated in the individual's subcamp of residence, with the remainder distributed over other subcamps. This suggests a source-and-sink dynamic in which subcamps with greater average infectiousness fed cases to those with a lower transmission rate. Although the per capita transmission rate within camps was significantly greater than that between camps, the large pool of susceptible individuals across camps enabled similar numbers of secondary cases generated between versus within camps.

CONCLUSIONS

The consideration of clustered transmission and heterogeneous infectiousness is important for understanding NoV transmission dynamics. Models including these mechanisms may be useful for providing early warning and guiding outbreak response.

Data-Driven Approach to Understand the Mobility Patterns of the Portuguese Population during the COVID-19 Pandemic

SARS-CoV-2 emerged in late 2019. Since then, it has spread to several countries, becoming classified as a pandemic. So far, there is no definitive treatment or vaccine, so the best solution is to prevent transmission between individuals through social distancing. However, it is not easy to measure the effectiveness of these distance measures. Therefore, this study uses data from Google COVID-19 Community Mobility Reports to understand the Portuguese population’s mobility patterns during the COVID-19 pandemic. In this study, the Rt value was modeled for Portugal. In addition, the changepoint was calculated for the population mobility patterns. Thus, the mobility pattern change was used to understand the impact of social distance measures on the dissemination of COVID-19. As a result, it can be stated that the initial Rt value in Portugal was very close to 3, falling to values close to 1 after 25 days. Social isolation measures were adopted quickly. Furthermore, it was observed that public transport was avoided during the pandemic. Finally, until the emergence of a vaccine or an effective treatment, this is the new normal, and it must be understood that new patterns of mobility, social interaction, and hygiene must be adapted to this reality.

Key questions for modelling COVID-19 exit strategies

Combinations of intense non-pharmaceutical interventions (lockdowns) were introduced worldwide to reduce SARS-CoV-2 transmission. Many governments have begun to implement exit strategies that relax restrictions while attempting to control the risk of a surge in cases. Mathematical modelling has played a central role in guiding interventions, but the challenge of designing optimal exit strategies in the face of ongoing transmission is unprecedented. Here, we report discussions from the Isaac Newton Institute 'Models for an exit strategy' workshop (11-15 May 2020). A diverse community of modellers who are providing evidence to governments worldwide were asked to identify the main questions that, if answered, would allow for more accurate predictions of the effects of different exit strategies. Based on these questions, we propose a roadmap to facilitate the development of reliable models to guide exit strategies. This roadmap requires a global collaborative effort from the scientific community and policymakers, and has three parts: (i) improve estimation of key epidemiological parameters; (ii) understand sources of heterogeneity in populations; and (iii) focus on requirements for data collection, particularly in low-to-middle-income countries. This will provide important information for planning exit strategies that balance socio-economic benefits with public health.

Probabilistic reconstruction of measles transmission clusters from routinely collected surveillance data

Pockets of susceptibility resulting from spatial or social heterogeneity in vaccine coverage can drive measles outbreaks, as cases imported into such pockets are likely to cause further transmission and lead to large transmission clusters. Characterizing the dynamics of transmission is essential for identifying which individuals and regions might be most at risk. As data from detailed contact-tracing investigations are not available in many settings, we developed an R package called o2geosocial to reconstruct the transmission clusters and the importation status of the cases from their age, location, genotype and onset date. We compared our inferred cluster size distributions to 737 transmission clusters identified through detailed contact-tracing in the USA between 2001 and 2016. We were able to reconstruct the importation status of the cases and found good agreement between the inferred and reference clusters. The results were improved when the contact-tracing investigations were used to set the importation status before running the model. Spatial heterogeneity in vaccine coverage is difficult to measure directly. Our approach was able to highlight areas with potential for local transmission using a minimal number of variables and could be applied to assess the intensity of ongoing transmission in a region.

Perfect counterfactuals for epidemic simulations

Simulation studies are often used to predict the expected impact of control measures in infectious disease outbreaks. Typically, two independent sets of simulations are conducted, one with the intervention, and one without, and epidemic sizes (or some related metric) are compared to estimate the effect of the intervention. Since it is possible that controlled epidemics are larger than uncontrolled ones if there is substantial stochastic variation between epidemics, uncertainty intervals from this approach can include a negative effect even for an effective intervention. To more precisely estimate the number of cases an intervention will prevent within a single epidemic, here we develop a 'single-world' approach to matching simulations of controlled epidemics to their exact uncontrolled counterfactual. Our method borrows concepts from percolation approaches, prunes out possible epidemic histories and creates potential epidemic graphs (i.e. a mathematical representation of all consistent epidemics) that can be 'realized' to create perfectly matched controlled and uncontrolled epidemics. We present an implementation of this method for a common class of compartmental models (e.g. SIR models), and its application in a simple SIR model. Results illustrate how, at the cost of some computation time, this method substantially narrows confidence intervals and avoids nonsensical inferences. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'. This theme issue is linked with the earlier issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'.

Phase-adjusted estimation of the number of Coronavirus Disease 2019 cases in Wuhan, China

An outbreak of clusters of viral pneumonia due to a novel coronavirus (2019-nCoV/SARS-CoV-2) happened in Wuhan, Hubei Province in China in December 2019. Since the outbreak, several groups reported estimated R0 of Coronavirus Disease 2019 (COVID-19) and generated valuable prediction for the early phase of this outbreak. After implementation of strict prevention and control measures in China, new estimation is needed. An infectious disease dynamics SEIR (Susceptible, Exposed, Infectious, and Removed) model was applied to estimate the epidemic trend in Wuhan, China under two assumptions of Rt . In the first assumption, Rt was assumed to maintain over 1. The estimated number of infections would continue to increase throughout February without any indication of dropping with Rt  = 1.9, 2.6, or 3.1. The number of infections would reach 11,044, 70,258, and 227,989, respectively, by 29 February 2020. In the second assumption, Rt was assumed to gradually decrease at different phases from high level of transmission (Rt  = 3.1, 2.6, and 1.9) to below 1 (Rt  = 0.9 or 0.5) owing to increasingly implemented public health intervention. Several phases were divided by the dates when various levels of prevention and control measures were taken in effect in Wuhan. The estimated number of infections would reach the peak in late February, which is 58,077-84,520 or 55,869-81,393. Whether or not the peak of the number of infections would occur in February 2020 may be an important index for evaluating the sufficiency of the current measures taken in China. Regardless of the occurrence of the peak, the currently strict measures in Wuhan should be continuously implemented and necessary strict public health measures should be applied in other locations in China with high number of COVID-19 cases, in order to reduce Rt to an ideal level and control the infection.

Spatially Adjusted Time-varying Reproductive Numbers: Understanding the Geographical Expansion of Urban Dengue Outbreaks

The basic reproductive number (R₀) is a fundamental measure used to quantify the transmission potential of an epidemic in public health practice. However, R₀ cannot reflect the time-varying nature of an epidemic. A time-varying effective reproductive number R_t can provide more information because it tracks the subsequent evolution of transmission. However, since it neglects individual-level geographical variations in exposure risk, R_t may smooth out interpersonal heterogeneous transmission potential, obscure high-risk spreaders, and hence hamper the effectiveness of control measures in spatial dimension. Therefore, this study proposes a new method for quantifying spatially adjusted (time-varying) reproductive numbers that reflects spatial heterogeneity in transmission potential among individuals. This new method estimates individual-level effective reproductive numbers (R^j) and a summarized indicator for population-level time-varying reproductive number (R_t). Data from the five most severe dengue outbreaks in southern Taiwan from 1998-2015 were used to demonstrate the ability of the method to highlight early spreaders contributing to the geographic expansion of dengue transmission. Our results show spatial heterogeneity in the transmission potential of dengue among individuals and identify the spreaders with the highest R^j during the epidemic period. The results also reveal that super-spreaders are usually early spreaders that locate at the edges of the epidemic foci, which means that these cases could be the drivers of the expansion of the outbreak. Therefore, our proposed method depicts a more detailed spatial-temporal dengue transmission process and identifies the significant role of the edges of the epidemic foci, which could be weak spots in disease control and prevention.

The Risk of Foot and Mouth Disease Transmission Posed by Public Access to the Countryside During an Outbreak

During the 2001 UK FMD outbreak, local authorities restricted rural access to try to prevent further disease spread by people and animals, which had major socio-economic consequences for rural communities. This study describes the results of qualitative veterinary risk assessments to assess the likelihood of different recreational activities causing new outbreaks of foot and mouth disease, as part of contingency planning for future outbreaks. For most activities, the likelihood of causing new outbreaks of foot and mouth disease is considered to vary from very low to medium depending on the control zone (which is based on distance to the nearest infected premises), assuming compliance with specified mitigation strategies. The likelihood of new outbreaks associated with hunting, shooting, stalking, and equestrian activities is considered to be greater. There are areas of significant uncertainty associated with data paucity, particularly regarding the likelihood of transmission via fomites. This study provides scientific evidence to underpin refinement of rural access management plans and inform decision-making in future disease outbreaks.

Bayesian inference of transmission chains using timing of symptoms, pathogen genomes and contact data

There exists significant interest in developing statistical and computational tools for inferring 'who infected whom' in an infectious disease outbreak from densely sampled case data, with most recent studies focusing on the analysis of whole genome sequence data. However, genomic data can be poorly informative of transmission events if mutations accumulate too slowly to resolve individual transmission pairs or if there exist multiple pathogens lineages within-host, and there has been little focus on incorporating other types of outbreak data. We present here a methodology that uses contact data for the inference of transmission trees in a statistically rigorous manner, alongside genomic data and temporal data. Contact data is frequently collected in outbreaks of pathogens spread by close contact, including Ebola virus (EBOV), severe acute respiratory syndrome coronavirus (SARS-CoV) and Mycobacterium tuberculosis (TB), and routinely used to reconstruct transmission chains. As an improvement over previous, ad-hoc approaches, we developed a probabilistic model that relates a set of contact data to an underlying transmission tree and integrated this in the outbreaker2 inference framework. By analyzing simulated outbreaks under various contact tracing scenarios, we demonstrate that contact data significantly improves our ability to reconstruct transmission trees, even under realistic limitations on the coverage of the contact tracing effort and the amount of non-infectious mixing between cases. Indeed, contact data is equally or more informative than fully sampled whole genome sequence data in certain scenarios. We then use our method to analyze the early stages of the 2003 SARS outbreak in Singapore and describe the range of transmission scenarios consistent with contact data and genetic sequence in a probabilistic manner for the first time. This simple yet flexible model can easily be incorporated into existing tools for outbreak reconstruction and should permit a better integration of genomic and epidemiological data for inferring transmission chains.

Unraveling the Complexity of Wildland Urban Interface Fires

Recent wildland urban interface fires have demonstrated the unrelenting destructive nature of these events and have called for an urgent need to address the problem. The Wildfire paradox reinforces the ideology that forest fires are inevitable and are actually beneficial; therefore focus should to be shifted towards minimizing potential losses to communities. This requires the development of vulnerability-based frameworks that can be used to provide holistic understanding of risk. In this study, we devise a probabilistic approach for quantifying community vulnerability to wildfires by applying concepts of graph theory. A directed graph for community in question is developed to model wildfire inside a community by incorporating different fire propagation modes. The model accounts for relevant community-specific characteristics including wind conditions, community layout, individual structural features, and the surrounding wildland vegetation. We calibrate the framework to study the infamous 1991 Oakland fire in an attempt to unravel the complexity of community fires. We use traditional centrality measures to identify critical behavior patterns and to evaluate the effect of fire mitigation strategies. Unlike current practice, the results are shown to be community-specific with substantial dependency of risk on meteorological conditions, environmental factors, and community characteristics and layout.

Quantifying Transmission

Transmissibility is the defining characteristic of infectious diseases. Quantifying transmission matters for understanding infectious disease epidemiology and designing evidence-based disease control programs. Tracing individual transmission events can be achieved by epidemiological investigation coupled with pathogen typing or genome sequencing. Individual infectiousness can be estimated by measuring pathogen loads, but few studies have directly estimated the ability of infected hosts to transmit to uninfected hosts. Individuals' opportunities to transmit infection are dependent on behavioral and other risk factors relevant given the transmission route of the pathogen concerned. Transmission at the population level can be quantified through knowledge of risk factors in the population or phylogeographic analysis of pathogen sequence data. Mathematical model-based approaches require estimation of the per capita transmission rate and basic reproduction number, obtained by fitting models to case data and/or analysis of pathogen sequence data. Heterogeneities in infectiousness, contact behavior, and susceptibility can have substantial effects on the epidemiology of an infectious disease, so estimates of only mean values may be insufficient. For some pathogens, super-shedders (infected individuals who are highly infectious) and super-spreaders (individuals with more opportunities to transmit infection) may be important. Future work on quantifying transmission should involve integrated analyses of multiple data sources.

The primary case is not enough: Variation among individuals, groups and social networks modify bacterial transmission dynamics

The traits of the primary case of an infectious disease outbreak, and the circumstances for their aetiology, potentially influence the trajectory of transmission dynamics. However, these dynamics likely also depend on the traits of the individuals with whom the primary case interacts. We used the social spider Stegodyphus dumicola to test how the traits of the primary case, group phenotypic composition and group size interact to facilitate the transmission of a GFP-labelled cuticular bacterium. We also compared bacterial transmission across experimentally generated "daisy-chain" vs. "star" networks of social interactions. Finally, we compared social network structure across groups of different sizes. Groups of 10 spiders experienced more bacterial transmission events compared to groups of 30 spiders, regardless of groups' behavioural composition. Groups containing only one bold spider experienced the lowest levels of bacterial transmission regardless of group size. We found no evidence for the traits of the primary case influencing any transmission dynamics. In a second experiment, bacteria were transmitted to more individuals in experimentally induced star networks than in daisy-chains, on which transmission never exceeded three steps. In both experimental network types, transmission success depended jointly on the behavioural traits of the interacting individuals; however, the behavioural traits of the primary case were only important for transmission on star networks. Larger social groups exhibited lower interaction density (i.e. had a low ratio of observed to possible connections) and were more modular, i.e. they had more connections between nodes within a subgroup and fewer connections across subgroups. Thus, larger groups may restrict transmission by forming fewer interactions and by isolating subgroups that interacted with the primary case. These findings suggest that accounting for the traits of single exposed hosts has less power in predicting transmission dynamics compared to the larger scale factors of the social groups in which they reside. Factors like group size and phenotypic composition appear to alter social interaction patterns, which leads to differential transmission of microbes.

A mechanistic spatio-temporal framework for modelling individual-to-individual transmission-With an application to the 2014-2015 West Africa Ebola outbreak

In recent years there has been growing availability of individual-level spatio-temporal disease data, particularly due to the use of modern communicating devices with GPS tracking functionality. These detailed data have been proven useful for inferring disease transmission to a more refined level than previously. However, there remains a lack of statistically sound frameworks to model the underlying transmission dynamic in a mechanistic manner. Such a development is particularly crucial for enabling a general epidemic predictive framework at the individual level. In this paper we propose a new statistical framework for mechanistically modelling individual-to-individual disease transmission in a landscape with heterogeneous population density. Our methodology is first tested using simulated datasets, validating our inferential machinery. The methodology is subsequently applied to data that describes a regional Ebola outbreak in Western Africa (2014-2015). Our results show that the methods are able to obtain estimates of key epidemiological parameters that are broadly consistent with the literature, while revealing a significantly shorter distance of transmission. More importantly, in contrast to existing approaches, we are able to perform a more general model prediction that takes into account the susceptible population. Finally, our results show that, given reasonable scenarios, the framework can be an effective surrogate for susceptible-explicit individual models which are often computationally challenging.

Availability of individual-level, spatio-temporal disease data (e.g. GPS locations of infected individuals) has been increasing in recent years, primarily due to the increased use of modern communication devices such as mobile phones. Such data create invaluable opportunities for researchers to study disease transmission on a more refined individual-to-individual level, facilitating the designs of potentially more effective control measures. However, the growing availability of such precise data has not been accompanied by development of statistically sound mechanistic frameworks. Developing such frameworks is an essential step for systematically extracting maximal information from data, in particular, evaluating the efficacy of individually-targeted control strategies and enabling forward epidemic prediction at the individual level. In this paper we develop a novel statistical framework that overcomes a few key limitations of existing approaches, enabling a machinery that can be used to infer the history of partially observed outbreaks and, more importantly, to produce a more comprehensive epidemic prediction. Our framework may also be a good surrogate for more computationally challenging individual-based models.

Exploiting Genetic Information to Trace Plant Virus Dispersal in Landscapes

During the past decade, knowledge of pathogen life history has greatly benefited from the advent and development of molecular epidemiology. This branch of epidemiology uses information on pathogen variation at the molecular level to gain insights into a pathogen's niche and evolution and to characterize pathogen dispersal within and between host populations. Here, we review molecular epidemiology approaches that have been developed to trace plant virus dispersal in landscapes. In particular, we highlight how virus molecular epidemiology, nourished with powerful sequencing technologies, can provide novel insights at the crossroads between the blooming fields of landscape genetics, phylogeography, and evolutionary epidemiology. We present existing approaches and their limitations and contributions to the understanding of plant virus epidemiology.

Predicting the Ability of Preclinical Diagnosis To Improve Control of Farm-to-Farm Foot-and-Mouth Disease Transmission in Cattle

Foot-and-mouth disease (FMD) can cause large disruptive epidemics in livestock. Current eradication measures rely on the rapid clinical detection and removal of infected herds. Here, we evaluated the potential for preclinical diagnosis during reactive surveillance to reduce the risk of between-farm transmission. We used data from transmission experiments in cattle where both samples from individual animals, such as blood, probang samples, and saliva and nasal swabs, and herd-level samples, such as air samples, were taken daily during the course of infection. The sensitivity of each of these sample types for the detection of infected cattle during different phases of the early infection period was quantified. The results were incorporated into a mathematical model for FMD, in a cattle herd, to evaluate the impact of the early detection and culling of an infected herd on the infectious output. The latter was expressed as the between-herd reproduction ratio, R_h, where an effective surveillance approach would lead to a reduction in the R_h value to <1. Applying weekly surveillance, clinical inspection alone was found to be ineffective at blocking transmission. This was in contrast to the impact of weekly random sampling (i.e., using saliva swabs) of at least 10 animals per farm or daily air sampling (housed cattle), both of which were shown to reduce the R_h to <1. In conclusion, preclinical detection during outbreaks has the potential to allow earlier culling of infected herds and thereby reduce transmission and aid the control of epidemics.

Spatial and temporal dynamics of superspreading events in the 2014-2015 West Africa Ebola epidemic

The unprecedented scale of the Ebola outbreak in Western Africa (2014-2015) has prompted an explosion of efforts to understand the transmission dynamics of the virus and to analyze the performance of possible containment strategies. Models have focused primarily on the reproductive numbers of the disease that represent the average number of secondary infections produced by a random infectious individual. However, these population-level estimates may conflate important systematic variation in the number of cases generated by infected individuals, particularly found in spatially localized transmission and superspreading events. Although superspreading features prominently in first-hand narratives of Ebola transmission, its dynamics have not been systematically characterized, hindering refinements of future epidemic predictions and explorations of targeted interventions. We used Bayesian model inference to integrate individual-level spatial information with other epidemiological data of community-based (undetected within clinical-care systems) cases and to explicitly infer distribution of the cases generated by each infected individual. Our results show that superspreaders play a key role in sustaining onward transmission of the epidemic, and they are responsible for a significant proportion ([Formula: see text]61%) of the infections. Our results also suggest age as a key demographic predictor for superspreading. We also show that community-based cases may have progressed more rapidly than those notified within clinical-care systems, and most transmission events occurred in a relatively short distance (with median value of 2.51 km). Our results stress the importance of characterizing superspreading of Ebola, enhance our current understanding of its spatiotemporal dynamics, and highlight the potential importance of targeted control measures.

Potential impact of a ventilation intervention for influenza in the context of a dense indoor contact network in Hong Kong

Emerging diseases may spread rapidly through dense and large urban contact networks. We constructed a simple but novel dual-contact network model to account for both airborne contact and close contact of individuals in the densely populated city of Hong Kong. The model was then integrated with an existing epidemiological susceptible-exposed-infectious-recovered (SEIR) model, and we used a revised Wells-Riley model to estimate infection risks by the airborne route and an exponential dose-response model for risks by the contact and droplet routes. A potential outbreak of partially airborne influenza was examined, assuming different proportions of transmission through the airborne route. Our results show that building ventilation can have significant effects in airborne transmission-dominated conditions. Moreover, even when the airborne route only contributes 20% to the total infection risk, increasing the ventilation rate has a strong influence on transmission dynamics, and it also can achieve control effects similar to those of wearing masks for patients, isolation and vaccination.

Estimating infectious disease transmission distances using the overall distribution of cases

The average spatial distance between transmission-linked cases is a fundamental property of infectious disease dispersal. However, the distance between a case and their infector is rarely measurable. Contact-tracing investigations are resource intensive or even impossible, particularly when only a subset of cases are detected. Here, we developed an approach that uses onset dates, the generation time distribution and location information to estimate the mean transmission distance. We tested our method using outbreak simulations. We then applied it to the 2001 foot-and-mouth outbreak in Cumbria, UK, and compared our results to contact-tracing activities. In simulations with a true mean distance of 106m, the average mean distance estimated was 109m when cases were fully observed (95% range of 71-142). Estimates remained consistent with the true mean distance when only five percent of cases were observed, (average estimate of 128m, 95% range 87-165). Estimates were robust to spatial heterogeneity in the underlying population. We estimated that both the mean and the standard deviation of the transmission distance during the 2001 foot-and-mouth outbreak was 8.9km (95% CI: 8.4km-9.7km). Contact-tracing activities found similar values of 6.3km (5.2km-7.4km) and 11.2km (9.5km-12.8km), respectively. We were also able to capture the drop in mean transmission distance over the course of the outbreak. Our approach is applicable across diseases, robust to under-reporting and can inform interventions and surveillance.

The transmission process: A combinatorial stochastic process for the evolution of transmission trees over networks

We derive a combinatorial stochastic process for the evolution of the transmission tree over the infected vertices of a host contact network in a susceptible-infected (SI) model of an epidemic. Models of transmission trees are crucial to understanding the evolution of pathogen populations. We provide an explicit description of the transmission process on the product state space of (rooted planar ranked labelled) binary transmission trees and labelled host contact networks with SI-tags as a discrete-state continuous-time Markov chain. We give the exact probability of any transmission tree when the host contact network is a complete, star or path network - three illustrative examples. We then develop a biparametric Beta-splitting model that directly generates transmission trees with exact probabilities as a function of the model parameters, but without explicitly modelling the underlying contact network, and show that for specific values of the parameters we can recover the exact probabilities for our three example networks through the Markov chain construction that explicitly models the underlying contact network. We use the maximum likelihood estimator (MLE) to consistently infer the two parameters driving the transmission process based on observations of the transmission trees and use the exact MLE to characterize equivalence classes over the space of contact networks with a single initial infection. An exploratory simulation study of the MLEs from transmission trees sampled from three other deterministic and four random families of classical contact networks is conducted to shed light on the relation between the MLEs of these families with some implications for statistical inference along with pointers to further extensions of our models. The insights developed here are also applicable to the simplest models of "meme" evolution in online social media networks through transmission events that can be distilled from observable actions such as "likes", "mentions", "retweets" and "+1s" along with any concomitant comments.

Using Combined Diagnostic Test Results to Hindcast Trends of Infection from Cross-Sectional Data

Infectious disease surveillance is key to limiting the consequences from infectious pathogens and maintaining animal and public health. Following the detection of a disease outbreak, a response in proportion to the severity of the outbreak is required. It is thus critical to obtain accurate information concerning the origin of the outbreak and its forward trajectory. However, there is often a lack of situational awareness that may lead to over- or under-reaction. There is a widening range of tests available for detecting pathogens, with typically different temporal characteristics, e.g. in terms of when peak test response occurs relative to time of exposure. We have developed a statistical framework that combines response level data from multiple diagnostic tests and is able to 'hindcast' (infer the historical trend of) an infectious disease epidemic. Assuming diagnostic test data from a cross-sectional sample of individuals infected with a pathogen during an outbreak, we use a Bayesian Markov Chain Monte Carlo (MCMC) approach to estimate time of exposure, and the overall epidemic trend in the population prior to the time of sampling. We evaluate the performance of this statistical framework on simulated data from epidemic trend curves and show that we can recover the parameter values of those trends. We also apply the framework to epidemic trend curves taken from two historical outbreaks: a bluetongue outbreak in cattle, and a whooping cough outbreak in humans. Together, these results show that hindcasting can estimate the time since infection for individuals and provide accurate estimates of epidemic trends, and can be used to distinguish whether an outbreak is increasing or past its peak. We conclude that if temporal characteristics of diagnostics are known, it is possible to recover epidemic trends of both human and animal pathogens from cross-sectional data collected at a single point in time.

Understanding Spatio-Temporal Variability in the Reproduction Ratio of the Bluetongue (BTV-1) Epidemic in Southern Spain (Andalusia) in 2007 Using Epidemic Trees

Andalusia (Southern Spain) is considered one of the main routes of introduction of bluetongue virus (BTV) into Europe, evidenced by a devastating epidemic caused by BTV-1 in 2007. Understanding the pattern and the drivers of BTV-1 spread in Andalusia is critical for effective detection and control of future epidemics. A long-standing metric for quantifying the behaviour of infectious diseases is the case-reproduction ratio (R_t), defined as the average number of secondary cases arising from a single infected case at time t (for t>0). Here we apply a method using epidemic trees to estimate the between-herd case reproduction ratio directly from epidemic data allowing the spatial and temporal variability in transmission to be described. We then relate this variability to predictors describing the hosts, vectors and the environment to better understand why the epidemic spread more quickly in some regions or periods. The R_t value for the BTV-1 epidemic in Andalusia peaked in July at 4.6, at the start of the epidemic, then decreased to 2.2 by August, dropped below 1 by September (0.8), and by October it had decreased to 0.02. BTV spread was the consequence of both local transmission within established disease foci and BTV expansion to distant new areas (i.e. new foci), which resulted in a high variability in BTV transmission, not only among different areas, but particularly through time, which suggests that general control measures applied at broad spatial scales are unlikely to be effective. This high variability through time was probably due to the impact of temperature on BTV transmission, as evidenced by a reduction in the value of R_t by 0.0041 for every unit increase (day) in the extrinsic incubation period (EIP), which is itself directly dependent on temperature. Moreover, within the range of values at which BTV-1 transmission occurred in Andalusia (20.6°C to 29.5°C) there was a positive correlation between temperature and R_t values, although the relationship was not linear, probably as a result of the complex relationship between temperature and the different parameters affecting BTV transmission. R_t values for BTV-1 in Andalusia fell below the threshold of 1 when temperatures dropped below 21°C, a much higher threshold than that reported in other BTV outbreaks, such as the BTV-8 epidemic in Northern Europe. This divergence may be explained by differences in the adaptation to temperature of the main vectors of the BTV-1 epidemic in Andalusia (Culicoides imicola) compared those of the BTV-8 epidemic in Northern Europe (Culicoides obsoletus). Importantly, we found that BTV transmission (R_t value) increased significantly in areas with higher densities of sheep. Our analysis also established that control of BTV-1 in Andalusia was complicated by the simultaneous establishment of several distant foci at the start of the epidemic, which may have been caused by several independent introductions of infected vectors from the North of Africa. We discuss the implications of these findings for BTV surveillance and control in this region of Europe.

Integrating serological and genetic data to quantify cross-species transmission: brucellosis as a case study

Epidemiological data are often fragmented, partial, and/or ambiguous and unable to yield the desired level of understanding of infectious disease dynamics to adequately inform control measures. Here, we show how the information contained in widely available serology data can be enhanced by integration with less common type-specific data, to improve the understanding of the transmission dynamics of complex multi-species pathogens and host communities. Using brucellosis in northern Tanzania as a case study, we developed a latent process model based on serology data obtained from the field, to reconstruct Brucella transmission dynamics. We were able to identify sheep and goats as a more likely source of human and animal infection than cattle; however, the highly cross-reactive nature of Brucella spp. meant that it was not possible to determine which Brucella species (B. abortus or B. melitensis) is responsible for human infection. We extended our model to integrate simulated serology and typing data, and show that although serology alone can identify the host source of human infection under certain restrictive conditions, the integration of even small amounts (5%) of typing data can improve understanding of complex epidemiological dynamics. We show that data integration will often be essential when more than one pathogen is present and when the distinction between exposed and infectious individuals is not clear from serology data. With increasing epidemiological complexity, serology data become less informative. However, we show how this weakness can be mitigated by integrating such data with typing data, thereby enhancing the inference from these data and improving understanding of the underlying dynamics.

Biothreat Reduction and Economic Development: The Case of Animal Husbandry in Central Asia

Improving human welfare is a critical global concern, but not always easy to achieve. Complications in this regard have been faced by the states of the Former Soviet Union, where socialist-style economic institutions have disappeared, and the transition to a market economy has been slow in coming. Lack of capital, ethnic conflict, and political instability have at times undermined the institutional reform that would be necessary to enable economic efficiency and development. Nowhere are such challenges more pronounced than in the new nation states of central Asia, including Kazakhstan, Kyrgyzstan, Tajikistan, Turkmenistan, and Uzbekistan. Here, a severe climate limits agriculture, and industrialization has been inhibited by lack of infrastructure, low levels of human capital, and a scarcity of financial resources. These conditions are aggravated by the fact that the central Asian states are landlocked, far from centers of market demand and capital availability. Despite these daunting barriers, development potential does exist, and the goal of the paper is to consider central Asia's pastoral economy, with a focus on Kazakhstan, which stands poised to become a regional growth pole. The article pursues its goal as follows. It first addresses the biothreat situation to central Asian livestock herds, the most significant existing impediment to realizing the full market potential of the region's animal products. Next, it provides an outline of interventions that can reduce risk levels for key biothreats impacting central Asia, namely foot and mouth disease (FMD), which greatly impacts livestock and prohibits export, and Brucellosis, a bacterial zoonosis with high incidence in both humans and livestock in the region. Included is an important success story involving the FMD eradication programs in Brazil, which enabled an export boom in beef. After this comes a description of the epidemiological situation in Kazakhstan; here, the article considers the role of wildlife in acting as a possible disease reservoir, which presents a conservation issue for the Kazakhstani case. This is followed by a discussion of the role of science in threat reduction, particularly with respect to the potential offered by geospatial technologies to improve our epidemiological knowledge base. The article concludes with an assessment of the research that would be necessary to identify feasible pathways to develop the economic potential of central Asian livestock production as changes in policy are implemented and livestock health improves.

Infectious disease modeling methods as tools for informing response to novel influenza viruses of unknown pandemic potential

The rising importance of infectious disease modeling makes this an appropriate time for a guide for public health practitioners tasked with preparing for, and responding to, an influenza pandemic. We list several questions that public health practitioners commonly ask about pandemic influenza and match these with analytical methods, giving details on when during a pandemic the methods can be used, how long it might take to implement them, and what data are required. Although software to perform these tasks is available, care needs to be taken to understand: (1) the type of data needed, (2) the implementation of the methods, and (3) the interpretation of results in terms of model uncertainty and sensitivity. Public health leaders can use this article to evaluate the modeling literature, determine which methods can provide appropriate evidence for decision-making, and to help them request modeling work from in-house teams or academic groups.

A Bayesian inferential approach to quantify the transmission intensity of disease outbreak

BACKGROUND

Emergence of infectious diseases like influenza pandemic (H1N1) 2009 has become great concern, which posed new challenges to the health authorities worldwide. To control these diseases various studies have been developed in the field of mathematical modelling, which is useful tool for understanding the epidemiological dynamics and their dependence on social mixing patterns.

METHOD

We have used Bayesian approach to quantify the disease outbreak through key epidemiological parameter basic reproduction number (R0), using effective contacts, defined as sum of the product of incidence cases and probability of generation time distribution. We have estimated R0 from daily case incidence data for pandemic influenza A/H1N1 2009 in India, for the initial phase.

RESULT

The estimated R0 with 95% credible interval is consistent with several other studies on the same strain. Through sensitivity analysis our study indicates that infectiousness affects the estimate of R0.

CONCLUSION

Basic reproduction number R0 provides the useful information to the public health system to do some effort in controlling the disease by using mitigation strategies like vaccination, quarantine, and so forth.

Supersize me: how whole-genome sequencing and big data are transforming epidemiology

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Whole-genome sequencing is used for forensic epidemiology.

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Big data can transform forensic epidemiology.

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Clustering, biases, wildlife reservoirs, and emerging infections can all be addressed.

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Phylodynamics approaches to integrate epidemiological and evolutionary data have been highly successful but still face scientific challenges.

In epidemiology, the identification of ‘who infected whom’ allows us to quantify key characteristics such as incubation periods, heterogeneity in transmission rates, duration of infectiousness, and the existence of high-risk groups. Although invaluable, the existence of many plausible infection pathways makes this difficult, and epidemiological contact tracing either uncertain, logistically prohibitive, or both. The recent advent of next-generation sequencing technology allows the identification of traceable differences in the pathogen genome that are transforming our ability to understand high-resolution disease transmission, sometimes even down to the host-to-host scale. We review recent examples of the use of pathogen whole-genome sequencing for the purpose of forensic tracing of transmission pathways, focusing on the particular problems where evolutionary dynamics must be supplemented by epidemiological information on the most likely timing of events as well as possible transmission pathways. We also discuss potential pitfalls in the over-interpretation of these data, and highlight the manner in which a confluence of this technology with sophisticated mathematical and statistical approaches has the potential to produce a paradigm shift in our understanding of infectious disease transmission and control.

Bayesian reconstruction of disease outbreaks by combining epidemiologic and genomic data

Recent years have seen progress in the development of statistically rigorous frameworks to infer outbreak transmission trees ("who infected whom") from epidemiological and genetic data. Making use of pathogen genome sequences in such analyses remains a challenge, however, with a variety of heuristic approaches having been explored to date. We introduce a statistical method exploiting both pathogen sequences and collection dates to unravel the dynamics of densely sampled outbreaks. Our approach identifies likely transmission events and infers dates of infections, unobserved cases and separate introductions of the disease. It also proves useful for inferring numbers of secondary infections and identifying heterogeneous infectivity and super-spreaders. After testing our approach using simulations, we illustrate the method with the analysis of the beginning of the 2003 Singaporean outbreak of Severe Acute Respiratory Syndrome (SARS), providing new insights into the early stage of this epidemic. Our approach is the first tool for disease outbreak reconstruction from genetic data widely available as free software, the R package outbreaker. It is applicable to various densely sampled epidemics, and improves previous approaches by detecting unobserved and imported cases, as well as allowing multiple introductions of the pathogen. Because of its generality, we believe this method will become a tool of choice for the analysis of densely sampled disease outbreaks, and will form a rigorous framework for subsequent methodological developments.

"Wrong, but useful": negotiating uncertainty in infectious disease modelling

For infectious disease dynamical models to inform policy for containment of infectious diseases the models must be able to predict; however, it is well recognised that such prediction will never be perfect. Nevertheless, the consensus is that although models are uncertain, some may yet inform effective action. This assumes that the quality of a model can be ascertained in order to evaluate sufficiently model uncertainties, and to decide whether or not, or in what ways or under what conditions, the model should be 'used'. We examined uncertainty in modelling, utilising a range of data: interviews with scientists, policy-makers and advisors, and analysis of policy documents, scientific publications and reports of major inquiries into key livestock epidemics. We show that the discourse of uncertainty in infectious disease models is multi-layered, flexible, contingent, embedded in context and plays a critical role in negotiating model credibility. We argue that usability and stability of a model is an outcome of the negotiation that occurs within the networks and discourses surrounding it. This negotiation employs a range of discursive devices that renders uncertainty in infectious disease modelling a plastic quality that is amenable to 'interpretive flexibility'. The utility of models in the face of uncertainty is a function of this flexibility, the negotiation this allows, and the contexts in which model outputs are framed and interpreted in the decision making process. We contend that rather than being based predominantly on beliefs about quality, the usefulness and authority of a model may at times be primarily based on its functional status within the broad social and political environment in which it acts.

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.

Estimating the probability of a major outbreak from the timing of early cases: an indeterminate problem?

Conservation biologists, as well as veterinary and public health officials, would benefit greatly from being able to forecast whether outbreaks of infectious disease will be major. For values of the basic reproductive number (R₀) between one and two, infectious disease outbreaks have a reasonable chance of either fading out at an early stage or, in the absence of intervention, spreading widely within the population. If it were possible to predict when fadeout was likely to occur, the need for costly precautionary control strategies could be minimized. However, the predictability of even simple epidemic processes remains largely unexplored. Here we conduct an examination of simulated data from the early stages of a fatal disease outbreak and explore how observable information might be useful for predicting major outbreaks. Specifically, would knowing the time of deaths for the first few cases allow us to predict whether an outbreak will be major? Using two approaches, trajectory matching and discriminant function analysis, we find that even in our best-case scenario (with accurate knowledge of epidemiological parameters, and precise times of death), it was not possible to reliably predict the outcome of a stochastic Susceptible-Exposed–Infectious-Recovered (SEIR) process.

Inferring Contagion Patterns in Social Contact Networks with Limited Infection Data

The spread of infectious disease is an inherently stochastic process. As such, real time control and prediction methods present a significant challenge. For diseases which spread through direct human interaction, (e.g., transferred from infected to susceptible individuals) the contagion process can be modeled on a social-contact network where individuals are represented as nodes, and contacts between individuals are represented as links. The model presented in this paper seeks to identify the infection pattern which depicts the current state of an ongoing outbreak. This is accomplished by inferring the most likely paths of infection through a contact network under the assumption of partially available infection data. The problem is formulated as a bi-linear integer program, and heuristic solution methods are developed based on sub-problems which can be solved much more efficiently. The heuristic performance is presented for a range of randomly generated networks and different levels of information. The model results, which include the most likely set of infection spreading contacts, can be used to provide insight into future epidemic outbreak patterns, and aid in the development of intervention strategies.

Transmission of equine influenza virus during an outbreak is characterized by frequent mixed infections and loose transmission bottlenecks

The ability of influenza A viruses (IAVs) to cross species barriers and evade host immunity is a major public health concern. Studies on the phylodynamics of IAVs across different scales – from the individual to the population – are essential for devising effective measures to predict, prevent or contain influenza emergence. Understanding how IAVs spread and evolve during outbreaks is critical for the management of epidemics. Reconstructing the transmission network during a single outbreak by sampling viral genetic data in time and space can generate insights about these processes. Here, we obtained intra-host viral sequence data from horses infected with equine influenza virus (EIV) to reconstruct the spread of EIV during a large outbreak. To this end, we analyzed within-host viral populations from sequences covering 90% of the infected yards. By combining gene sequence analyses with epidemiological data, we inferred a plausible transmission network, in turn enabling the comparison of transmission patterns during the course of the outbreak and revealing important epidemiological features that were not apparent using either approach alone. The EIV populations displayed high levels of genetic diversity, and in many cases we observed distinct viral populations containing a dominant variant and a number of related minor variants that were transmitted between infectious horses. In addition, we found evidence of frequent mixed infections and loose transmission bottlenecks in these naturally occurring populations. These frequent mixed infections likely influence the size of epidemics.

Influenza A viruses (IAVs) are major pathogens of humans and animals. Understanding how IAVs spread and evolve at different scales (individual, regional, global) in natural conditions is critical for preventing or managing influenza epidemics. A vast body of knowledge has been generated on the evolution of IAVs at the global scale. Additionally, recent experimental transmission studies have examined the diversity and transmission of influenza viruses within and between hosts. However, most studies on the spread of IAVs during epidemics have been based on consensus viral sequences, an approach that does not have enough discriminatory power to reveal exact transmission pathways. Here, we analyzed multiple within-host viral populations from different horses infected with equine influenza virus (EIV) during the course of an outbreak in a population within a confined area. This provided an opportunity to examine the genetic diversity of the viruses within single animals, the transmission of the viruses between each closely confined population within a yard, and the transmission between horses in different yards. We show that individual horses can be infected by viruses from more than one other horse, which has important implications for facilitating segment reassortment and the evolution of EIV. Additionally, by combining viral sequencing data and epidemiological data we show that the high levels of mixed infections can reveal the underlying epidemiological dynamics of the outbreak, and that epidemic size could be underestimated if only epidemiological data is considered. As sequencing technologies become cheaper and faster, these analyses could be undertaken almost in real-time and help control future outbreaks.

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.

In order to most effectively control the spread of an infectious disease, we need to better understand how pathogens spread within a host population, yet this is something we know remarkably little about. Cases close together in their locations and timing are often thought to be linked, but timings and locations alone are usually consistent with many different scenarios of who-infected-who. The genome of many pathogens evolves so quickly relative to the rate that they are transmitted, that even over single short epidemics we can identify which hosts contain pathogens that are most closely related to each other. This information is valuable because when combined with the spatial and timing data it should help us infer more reliably who-transmitted-to-who over the course of a disease outbreak. However, doing this so that these three different lines of evidence are appropriately weighted and interpreted remains a major statistical challenge. In our paper we present a new statistical method for combining these different types of data and estimating trees that show how infection was most likely transmitted between individuals in a host population. Because sequencing genetic material has become so affordable, we think methods like ours will become very important for future epidemiology.

Countering the livestock-targeted bioterrorism threat and responding with an animal health safeguarding system

Attacks against livestock and poultry using biological agents constitute a subtype of agroterrorism. These attacks are defined as the intentional introduction of an animal infectious disease to strike fear in people, damage a nation's economy and/or threaten social stability. Livestock bioterrorism is considered attractive to terrorists because biological agents for use against livestock or poultry are more readily available and difficult to monitor than biological agents for use against humans. In addition, an attack on animal husbandry can have enormous economic consequences, even without human casualties. Animal husbandry is vulnerable to livestock-targeted bioterrorism because it is nearly impossible to secure all livestock animals, and compared with humans, livestock are less well-guarded targets. Furthermore, anti-livestock biological weapons are relatively easy to employ, and a significant effect can be produced with only a small amount of infectious material. The livestock sector is presently very vulnerable to bioterrorism as a result of large-scale husbandry methods and weaknesses in the systems used to detect disease outbreaks, which could aggravate the consequences of livestock-targeted bioterrorism. Thus, terrorism against livestock and poultry cannot be thought of as either a 'low-probability' or 'low-consequence' incident. This review provides an overview of methods to prevent livestock-targeted bioterrorism and respond to terrorism involving the deliberate introduction of a pathogen-targeting livestock and poultry.

Quantifying type-specific reproduction numbers for nosocomial pathogens: evidence for heightened transmission of an Asian sequence type 239 MRSA clone

An important determinant of a pathogen's success is the rate at which it is transmitted from infected to susceptible hosts. Although there are anecdotal reports that methicillin-resistant Staphylococcus aureus (MRSA) clones vary in their transmissibility in hospital settings, attempts to quantify such variation are lacking for common subtypes, as are methods for addressing this question using routinely-collected MRSA screening data in endemic settings. Here we present a method to quantify the time-varying transmissibility of different subtypes of common bacterial nosocomial pathogens using routine surveillance data. The method adapts approaches for estimating reproduction numbers based on the probabilistic reconstruction of epidemic trees, but uses relative hazards rather than serial intervals to assign probabilities to different sources for observed transmission events. The method is applied to data collected as part of a retrospective observational study of a concurrent MRSA outbreak in the United Kingdom with dominant endemic MRSA clones (ST22 and ST36) and an Asian ST239 MRSA strain (ST239-TW) in two linked adult intensive care units, and compared with an approach based on a fully parametric transmission model. The results provide support for the hypothesis that the clones responded differently to an infection control measure based on the use of topical antiseptics, which was more effective at reducing transmission of endemic clones. They also suggest that in one of the two ICUs patients colonized or infected with the ST239-TW MRSA clone had consistently higher risks of transmitting MRSA to patients free of MRSA. These findings represent some of the first quantitative evidence of enhanced transmissibility of a pandemic MRSA lineage, and highlight the potential value of tailoring hospital infection control measures to specific pathogen subtypes.

Epidemic characterization and modeling within herd transmission dynamics of an "emerging trans-boundary" camel disease epidemic in Ethiopia

A highly acute and contagious camel disease, an epidemic wave of unknown etiology, referred to here as camel sudden death syndrome, has plagued camel population in countries in the Horn of Africa. To better understand its epidemic patterns and transmission dynamics, we used epidemiologic parameters and differential equation deterministic modeling (SEIR/D-model) to predict the outcome likelihood following an exposure of susceptible camel population. Our results showed 45.7, 17.6, and 38.6 % overall morbidity, mortality, and case fatality rates of the epidemic, respectively. Pregnant camels had the highest mortality and case fatality rates, followed by breeding males, and lactating females, implying serious socioeconomic consequences. Disease dynamics appeared to be linked to livestock trade route and animal movements. The epidemic exhibited a strong basic reproductive number (R (0)) with an average of 16 camels infected by one infectious case during the entire infectious period. The epidemic curve suggested that the critical moment of the disease development is approximately between 30 and 40 days, where both infected/exposed and infectious camels are at their highest numbers. The lag between infected/infectious curves indicates a time-shift of approximately 3-5 days from when a camel is infected and until it becomes infectious. According to this predictive model, of all animals exposed to the infection, 66.8 % (n = 868) and 33.2 % (n = 431) had recovered and died, respectively, at the end of epidemic period. Hence, if early measures are not taken, such an epidemic could cause a much more devastative effect, within short period of time than the anticipated proportion.

Estimating spatial and temporal variations of the reproduction number for highly pathogenic avian influenza H5N1 epidemic in Thailand

Since 2003, highly pathogenic avian influenza (HPAI) H5N1 virus has spread, causing a pandemic with serious economic consequences and public health implications. Quantitative estimates of the spread of HPAI H5N1 are needed to adapt control measures. This study aimed to estimate the variations of the reproduction number R in space and time for the HPAI H5N1 epidemic in Thailand. Transmission between sub-districts was analyzed using three different and complementary methods. Transmission of HPAI H5N1 was intense (R(t)>1) before October 2004, at which point the epidemic started to progressively fade out (R(t)<1). The spread was mainly local, with 75% of the putative distances of transmission less than 32km. The map of the mean standardized ratio of transmitting the infection (sr) showed sub-districts with a high risk of transmitting infection. Findings from this study can contribute to discussions regarding the efficacy of control measures and help target surveillance programs.

Impact of regulatory perturbations to disease spread through cattle movements in Great Britain

During the past decade the British livestock industry has suffered from several major pathogen outbreaks, and a variety of regulatory and disease control measures have been applied to the movement of livestock with the express aim of mitigating the spread of infection. The Rapid Analysis and Detection of Animal-related Risks (RADAR) project, which has been collecting data on the movement of cattle since 1998, provides a relatively comprehensive record of how these policies have influenced the movement of cattle between animal holdings, markets, and slaughterhouses in Britain. Many previous studies have focused on the properties of the network that can be derived from these movements – treating farms as nodes and movements as directed (and potentially weighted) edges in the network. However, of far greater importance is how these policy changes have influenced the potential spread of infectious diseases. Here we use a stochastic fully individual-based model of cattle in Britain to assess how the epidemic potential has varied from 2000 to 2009 as the pattern of movements has changed in response to legislation and market forces. Our simulations show that the majority of policy changes lead to significant decreases in the epidemic potential (measured in multiple ways), but that this potential then increases through time as cattle farmers modify their behaviour in response. Our results suggest that the cattle industry is likely to experience boom-bust dynamics, with the actions that farmers take during epidemic-free periods to maximise their profitability likely to increase the potential for large-scale epidemics to occur.

Connecting network properties of rapidly disseminating epizoonotics

BACKGROUND

To effectively control the geographical dissemination of infectious diseases, their properties need to be determined. To test that rapid microbial dispersal requires not only susceptible hosts but also a pre-existing, connecting network, we explored constructs meant to reveal the network properties associated with disease spread, which included the road structure.

METHODS

Using geo-temporal data collected from epizoonotics in which all hosts were susceptible (mammals infected by Foot-and-mouth disease virus, Uruguay, 2001; birds infected by Avian Influenza virus H5N1, Nigeria, 2006), two models were compared: 1) 'connectivity', a model that integrated bio-physical concepts (the agent's transmission cycle, road topology) into indicators designed to measure networks ('nodes' or infected sites with short- and long-range links), and 2) 'contacts', which focused on infected individuals but did not assess connectivity.

RESULTS

THE CONNECTIVITY MODEL SHOWED FIVE NETWORK PROPERTIES: 1) spatial aggregation of cases (disease clusters), 2) links among similar 'nodes' (assortativity), 3) simultaneous activation of similar nodes (synchronicity), 4) disease flows moving from highly to poorly connected nodes (directionality), and 5) a few nodes accounting for most cases (a "20:80" pattern). In both epizoonotics, 1) not all primary cases were connected but at least one primary case was connected, 2) highly connected, small areas (nodes) accounted for most cases, 3) several classes of nodes were distinguished, and 4) the contact model, which assumed all primary cases were identical, captured half the number of cases identified by the connectivity model. When assessed together, the synchronicity and directionality properties explained when and where an infectious disease spreads.

CONCLUSIONS

Geo-temporal constructs of Network Theory's nodes and links were retrospectively validated in rapidly disseminating infectious diseases. They distinguished classes of cases, nodes, and networks, generating information usable to revise theory and optimize control measures. Prospective studies that consider pre-outbreak predictors, such as connecting networks, are recommended.