The GLEaMviz computational tool, a publicly available software to explore realistic epidemic spreading scenarios at the global scale

Effective distances for epidemics spreading on complex networks

We show that the recently introduced logarithmic metrics used to predict disease arrival times on complex networks are approximations of more general network-based measures derived from random walks theory. Using the daily air-traffic transportation data we perform numerical experiments to compare the infection arrival time with this alternative metric that is obtained by accounting for multiple walks instead of only the most probable path. The comparison with direct simulations reveals a higher correlation compared to the shortest-path approach used previously. In addition our method allows to connect fundamental observables in epidemic spreading with the cumulant-generating function of the hitting time for a Markov chain. Our results provides a general and computationally efficient approach using only algebraic methods.

Toward a Realistic Modeling of Epidemic Spreading with Activity Driven Networks

Models of epidemic spreading are widely used to predict the evolution of an outbreak, test specific intervention scenarios, and steer interventions in the field. Compartmental models are the most common class of models. They are very effective for qualitative analysis, but they rely on simplifying assumptions, such as homogeneous mixing and time scale separation. On the other end of the spectrum, detailed agent-based models, based on realistic mobility pattern models, provide extremely accurate predictions. However, these models require significant computing power and are not suitable for analytical treatment. Our research aims at bridging the gap between these two approaches, toward time-varying network models that are sufficiently accurate to make predictions for real-world applications, while being computationally affordable and amenable to analytical treatment. We leverage the novel paradigm of activity driven networks (ADNs), a particular type of time-varying network that accounts for inherent inhomogeinities within a population. Starting from the basic incarnation of ADNs, we expand on the framework to include behavioral factors triggered by health status and spreading awareness. The enriched paradigm is then utilized to model the 2014–2015 Ebola Virus Disease (EVD) spreading in Liberia, and perform a what-if analysis on the timely application of sanitary interventions in the field. Finally, we propose a new formulation, which is amenable to analytical treatment, beyond the mere computation of the epidemic threshold.

Data-driven outbreak forecasting with a simple nonlinear growth model

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We present EpiGro, a simple data-driven method to forecast the scope of an ongoing outbreak.

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We provide general hypotheses for expected model validity and also discuss model limitations.

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We propose an automated parameter estimation method that can be used for forecasting.

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We test our approach on 9 different outbreaks and show robustness over multiple systems and over noisy data sets.

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In the absence of other information or in conjunction with other models, EpiGro may be useful to public health responders.

Recent events have thrown the spotlight on infectious disease outbreak response. We developed a data-driven method, EpiGro, which can be applied to cumulative case reports to estimate the order of magnitude of the duration, peak and ultimate size of an ongoing outbreak. It is based on a surprisingly simple mathematical property of many epidemiological data sets, does not require knowledge or estimation of disease transmission parameters, is robust to noise and to small data sets, and runs quickly due to its mathematical simplicity. Using data from historic and ongoing epidemics, we present the model. We also provide modeling considerations that justify this approach and discuss its limitations. In the absence of other information or in conjunction with other models, EpiGro may be useful to public health responders.

Distress Propagation in Complex Networks: The Case of Non-Linear DebtRank

We consider a dynamical model of distress propagation on complex networks, which we apply to the study of financial contagion in networks of banks connected to each other by direct exposures. The model that we consider is an extension of the DebtRank algorithm, recently introduced in the literature. The mechanics of distress propagation is very simple: When a bank suffers a loss, distress propagates to its creditors, who in turn suffer losses, and so on. The original DebtRank assumes that losses are propagated linearly between connected banks. Here we relax this assumption and introduce a one-parameter family of non-linear propagation functions. As a case study, we apply this algorithm to a data-set of 183 European banks, and we study how the stability of the system depends on the non-linearity parameter under different stress-test scenarios. We find that the system is characterized by a transition between a regime where small shocks can be amplified and a regime where shocks do not propagate, and that the overall stability of the system increases between 2008 and 2013.

Rich do not rise early: spatio-temporal patterns in the mobility networks of different socio-economic classes

We analyse the urban mobility in the cities of Medellín and Manizales (Colombia). Each city is represented by six mobility networks, each one encoding the origin-destination trips performed by a subset of the population corresponding to a particular socio-economic status. The nodes of each network are the different urban locations whereas links account for the existence of a trip between two different areas of the city. We study the main structural properties of these mobility networks by focusing on their spatio-temporal patterns. Our goal is to relate these patterns with the partition into six socio-economic compartments of these two societies. Our results show that spatial and temporal patterns vary across these socio-economic groups. In particular, the two datasets show that as wealth increases the early-morning activity is delayed, the midday peak becomes smoother and the spatial distribution of trips becomes more localized.

Mathematical models to characterize early epidemic growth: A review

There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014-2015 Ebola epidemic in West Africa.

Visual analytics of geo-social interaction patterns for epidemic control

BACKGROUND

Human interaction and population mobility determine the spatio-temporal course of the spread of an airborne disease. This research views such spreads as geo-social interaction problems, because population mobility connects different groups of people over geographical locations via which the viruses transmit. Previous research argued that geo-social interaction patterns identified from population movement data can provide great potential in designing effective pandemic mitigation. However, little work has been done to examine the effectiveness of designing control strategies taking into account geo-social interaction patterns.

METHODS

To address this gap, this research proposes a new framework for effective disease control; specifically this framework proposes that disease control strategies should start from identifying geo-social interaction patterns, designing effective control measures accordingly, and evaluating the efficacy of different control measures. This framework is used to structure design of a new visual analytic tool that consists of three components: a reorderable matrix for geo-social mixing patterns, agent-based epidemic models, and combined visualization methods.

RESULTS

With real world human interaction data in a French primary school as a proof of concept, this research compares the efficacy of vaccination strategies between the spatial-social interaction patterns and the whole areas. The simulation results show that locally targeted vaccination has the potential to keep infection to a small number and prevent spread to other regions. At some small probability, the local control strategies will fail; in these cases other control strategies will be needed. This research further explores the impact of varying spatial-social scales on the success of local vaccination strategies. The results show that a proper spatial-social scale can help achieve the best control efficacy with a limited number of vaccines.

CONCLUSIONS

The case study shows how GS-EpiViz does support the design and testing of advanced control scenarios in airborne disease (e.g., influenza). The geo-social patterns identified through exploring human interaction data can help target critical individuals, locations, and clusters of locations for disease control purposes. The varying spatial-social scales can help geographically and socially prioritize limited resources (e.g., vaccines).

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.

Using numeric simulation in an online e-learning environment to teach functional physiological contexts

BACKGROUND AND OBJECTIVES

Mathematical models are suitable to simulate complex biological processes by a set of non-linear differential equations. These simulation models can be used as an e-learning tool in medical education. However, in many cases these mathematical systems have to be treated numerically which is computationally intensive. The aim of the study was to develop a system for numerical simulation to be used in an online e-learning environment.

METHODS

In the software system the simulation is located on the server as a CGI application. The user (student) selects the boundary conditions for the simulation (e.g., properties of a simulated patient) on the browser. With these parameters the simulation on the server is started and the simulation result is re-transferred to the browser.

RESULTS

With this system two examples of e-learning units were realized. The first one uses a multi-compartment model of the glucose-insulin control loop for the simulation of the plasma glucose level after a simulated meal or during diabetes (including treatment by subcutaneous insulin application). The second one simulates the ion transport leading to the resting and action potential in nerves. The student can vary parameters systematically to explore the biological behavior of the system.

CONCLUSIONS

The described system is able to simulate complex biological processes and offers the possibility to use these models in an online e-learning environment. As far as the underlying principles can be described mathematically, this type of system can be applied to a broad spectrum of biomedical or natural scientific topics.

Measuring the potential of individual airports for pandemic spread over the world airline network

Background

Massive growth in human mobility has dramatically increased the risk and rate of pandemic spread. Macro-level descriptors of the topology of the World Airline Network (WAN) explains middle and late stage dynamics of pandemic spread mediated by this network, but necessarily regard early stage variation as stochastic. We propose that much of this early stage variation can be explained by appropriately characterizing the local network topology surrounding an outbreak’s debut location.

Methods

Based on a model of the WAN derived from public data, we measure for each airport the expected force of infection (AEF) which a pandemic originating at that airport would generate, assuming an epidemic process which transmits from airport to airport via scheduled commercial flights. We observe, for a subset of world airports, the minimum transmission rate at which a disease becomes pandemically competent at each airport. We also observe, for a larger subset, the time until a pandemically competent outbreak achieves pandemic status given its debut location. Observations are generated using a highly sophisticated metapopulation reaction-diffusion simulator under a disease model known to well replicate the 2009 influenza pandemic. The robustness of the AEF measure to model misspecification is examined by degrading the underlying model WAN.

Results

AEF powerfully explains pandemic risk, showing correlation of 0.90 to the transmission level needed to give a disease pandemic competence, and correlation of 0.85 to the delay until an outbreak becomes a pandemic. The AEF is robust to model misspecification. For 97 % of airports, removing 15 % of airports from the model changes their AEF metric by less than 1 %.

Conclusions

Appropriately summarizing the size, shape, and diversity of an airport’s local neighborhood in the WAN accurately explains much of the macro-level stochasticity in pandemic outcomes.

Electronic supplementary material

The online version of this article (doi:10.1186/s12879-016-1350-4) contains supplementary material, which is available to authorized users.

A network model for Ebola spreading

The availability of accurate models for the spreading of infectious diseases has opened a new era in management and containment of epidemics. Models are extensively used to plan for and execute vaccination campaigns, to evaluate the risk of international spreadings and the feasibility of travel bans, and to inform prophylaxis campaigns. Even when no specific therapeutical protocol is available, as for the Ebola Virus Disease (EVD), models of epidemic spreading can provide useful insight to steer interventions in the field and to forecast the trend of the epidemic. Here, we propose a novel mathematical model to describe EVD spreading based on activity driven networks (ADNs). Our approach overcomes the simplifying assumption of homogeneous mixing, which is central to most of the mathematically tractable models of EVD spreading. In our ADN-based model, each individual is not bound to contact every other, and its network of contacts varies in time as a function of an activity potential. Our model contemplates the possibility of non-ideal and time-varying intervention policies, which are critical to accurately describe EVD spreading in afflicted countries. The model is calibrated from field data of the 2014 April-to-December spreading in Liberia. We use the model as a predictive tool, to emulate the dynamics of EVD in Liberia and offer a one-year projection, until December 2015. Our predictions agree with the current vision expressed by professionals in the field, who consider EVD in Liberia at its final stage. The model is also used to perform a what-if analysis to assess the efficacy of timely intervention policies. In particular, we show that an earlier application of the same intervention policy would have greatly reduced the number of EVD cases, the duration of the outbreak, and the infrastructures needed for the implementation of the intervention.

Smart monitoring and controlling of Pandemic Influenza A (H1N1) using Social Network Analysis and cloud computing

H1N1 is an infectious virus which, when spread affects a large volume of the population. It is an airborne disease that spreads easily and has a high death rate. Development of healthcare support systems using cloud computing is emerging as an effective solution with the benefits of better quality of service, reduced costs and flexibility. In this paper, an effective cloud computing architecture is proposed which predicts H1N1 infected patients and provides preventions to control infection rate. It consists of four processing components along with secure cloud storage medical database. The random decision tree is used to initially assess the infection in any patient depending on his/her symptoms. Social Network Analysis (SNA) is used to present the state of the outbreak. The proposed architecture is tested on synthetic data generated for two million users. The system provided 94% accuracy for the classification and around 81% of the resource utilization on Amazon EC2 cloud. The key point of the paper is the use of SNA graphs to calculate role of an infected user in spreading the outbreak known as Outbreak Role Index (ORI). It will help government agencies and healthcare departments to present, analyze and prevent outbreak effectively.

Disease-induced resource constraints can trigger explosive epidemics

Advances in mathematical epidemiology have led to a better understanding of the risks posed by epidemic spreading and informed strategies to contain disease spread. However, a challenge that has been overlooked is that, as a disease becomes more prevalent, it can limit the availability of the capital needed to effectively treat those who have fallen ill. Here we use a simple mathematical model to gain insight into the dynamics of an epidemic when the recovery of sick individuals depends on the availability of healing resources that are generated by the healthy population. We find that epidemics spiral out of control into "explosive" spread if the cost of recovery is above a critical cost. This can occur even when the disease would die out without the resource constraint. The onset of explosive epidemics is very sudden, exhibiting a discontinuous transition under very general assumptions. We find analytical expressions for the critical cost and the size of the explosive jump in infection levels in terms of the parameters that characterize the spreading process. Our model and results apply beyond epidemics to contagion dynamics that self-induce constraints on recovery, thereby amplifying the spreading process.

A Flexible Simulation Architecture for Pandemic Influenza Simulation

Simulation is an important resource for studying the dynamics of pandemic influenza and predicting the potential impact of interventions. However, there are several challenges for the design of such simulator architectures. Specifically, it is difficult to develop simulators that combine flexibility with run-time performance. This tradeoff is problematic in the pandemic-response setting because it makes it challenging to extend and adapt simulators for ongoing situations where rapid results are indispensable. Simulation architectures based on aspect-oriented programming can model specific concerns of the simulator and can allow developers to rapidly extend the simulator in new ways without sacrificing run-time performance. It is possible to use such aspects in conjunction with separate simulation models, which define community, disease, and intervention properties. The implication of this research for pandemic response is that aspects can add a novel layer of flexibility to simulation environments, which enables modelers to extend the simulator run-time component to new requirements that go beyond the original modeling framework.

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.

New technologies in predicting, preventing and controlling emerging infectious diseases

Surveillance of emerging infectious diseases is vital for the early identification of public health threats. Emergence of novel infections is linked to human factors such as population density, travel and trade and ecological factors like climate change and agricultural practices. A wealth of new technologies is becoming increasingly available for the rapid molecular identification of pathogens but also for the more accurate monitoring of infectious disease activity. Web-based surveillance tools and epidemic intelligence methods, used by all major public health institutions, are intended to facilitate risk assessment and timely outbreak detection. In this review, we present new methods for regional and global infectious disease surveillance and advances in epidemic modeling aimed to predict and prevent future infectious diseases threats.

Saving Human Lives: What Complexity Science and Information Systems can Contribute

We discuss models and data of crowd disasters, crime, terrorism, war and disease spreading to show that conventional recipes, such as deterrence strategies, are often not effective and sufficient to contain them. Many common approaches do not provide a good picture of the actual system behavior, because they neglect feedback loops, instabilities and cascade effects. The complex and often counter-intuitive behavior of social systems and their macro-level collective dynamics can be better understood by means of complexity science. We highlight that a suitable system design and management can help to stop undesirable cascade effects and to enable favorable kinds of self-organization in the system. In such a way, complexity science can help to save human lives.

An Interactive, Web-based High Performance Modeling Environment for Computational Epidemiology

We present an integrated interactive modeling environment to support public health epidemiology. The environment combines a high resolution individual-based model with a user-friendly web-based interface that allows analysts to access the models and the analytics back-end remotely from a desktop or a mobile device. The environment is based on a loosely-coupled service-oriented-architecture that allows analysts to explore various counter factual scenarios. As the modeling tools for public health epidemiology are getting more sophisticated, it is becoming increasingly hard for non-computational scientists to effectively use the systems that incorporate such models. Thus an important design consideration for an integrated modeling environment is to improve ease of use such that experimental simulations can be driven by the users. This is achieved by designing intuitive and user-friendly interfaces that allow users to design and analyze a computational experiment and steer the experiment based on the state of the system. A key feature of a system that supports this design goal is the ability to start, stop, pause and roll-back the disease propagation and intervention application process interactively. An analyst can access the state of the system at any point in time and formulate dynamic interventions based on additional information obtained through state assessment. In addition, the environment provides automated services for experiment set-up and management, thus reducing the overall time for conducting end-to-end experimental studies. We illustrate the applicability of the system by describing computational experiments based on realistic pandemic planning scenarios. The experiments are designed to demonstrate the system's capability and enhanced user productivity.

Optimal surveillance network design: a value of information model

Purpose

Infectious diseases are the second leading cause of deaths worldwide, accounting for 15 million deaths – that is more than 25% of all deaths – each year. Food plays a crucial role, contributing to 1.5 million deaths, most of which are children, through foodborne diarrheal disease alone. Thus, the ability to timely detect outbreak pathways via high-efficiency surveillance system is essential to the physical and social well being of populations. For this purpose, a traceability model inspired by wavepattern recognition models to detect “zero-patient” areas based on outbreak spread is proposed.

Methods

Model effectiveness is assessed for data from the 2010 Cholera epidemic in Cameroon, the 2012 foodborne Salmonella epidemic in USA, and the 2004-2007 H5N1 avian influenza pandemic. Previous models are complemented by the introduction of an optimal selection algorithm of surveillance networks based on the Value of Information (VoI) of reporting nodes that are subnetworks of mobility networks in which people, food, and species move. The surveillance network is considered the response variable to be determined in maximizing the accuracy of outbreak source detections while minimizing detection error. Surveillance network topologies are selected by considering their integrated network resilience expressing the rewiring probability that is related to the ability to report outbreak information even in case of network destruction or missing information.

Results

Independently of the outbreak epidemiology, the maximization of the VoI leads to a minimum increase in accuracy of 40% compared to the random surveillance model. Such accuracy is accompanied by an average reduction of 25% in required surveillance nodes with respect to random surveillance. Accuracy in systems diagnosis increases when system syndromic signs are the most informative in a way they reveal linkages between outbreak patterns and network transmission processes.

Conclusions

The model developed is extremely useful for the optimization of surveillance networks to drastically reduce the burden of food-borne and other infectious diseases. The model can be the framework of a cyber-technology that governments and industries can utilize in a real-time manner to avoid catastrophic and costly health and economic outcomes. Further applications are envisioned for chronic diseases, socially communicable diseases, biodefense and other detection related problems at different scales.

Understanding and predicting the global spread of emergent infectious diseases

The emergence and global spread of human infectious diseases has become one of the most serious public health threats of the 21st century. Sophisticated computer simulations have become a key tool for understanding and predicting disease spread on a global scale. Combining theoretical insights from nonlinear dynamics, stochastic processes and complex network theory these computational models are becoming increasingly important in the design of efficient mitigation and control strategies and for public health in general.

Six challenges in measuring contact networks for use in modelling

Contact networks are playing an increasingly important role in epidemiology. A contact network represents individuals in a host population as nodes and the interactions among them that may lead to the transmission of infection as edges. New avenues for data collection in recent years have afforded us the opportunity to collect individual- and population-scale information to empirically describe the patterns of contact within host populations. Here, we present some of the current challenges in measuring empirical contact networks. We address fundamental questions such as defining contact; measurement of non-trivial contact properties; practical issues of bounding measurement of contact networks in space, time and scope; exploiting proxy information about contacts; dealing with missing data. Finally, we consider the privacy and ethical issues surrounding the collection of contact network data.

A generic open-source software framework supporting scenario simulations in bioterrorist crises

Since the 2001 anthrax attack in the United States, awareness of threats originating from bioterrorism has grown. This led internationally to increased research efforts to improve knowledge of and approaches to protecting human and animal populations against the threat from such attacks. A collaborative effort in this context is the extension of the open-source Spatiotemporal Epidemiological Modeler (STEM) simulation and modeling software for agro- or bioterrorist crisis scenarios. STEM, originally designed to enable community-driven public health disease models and simulations, was extended with new features that enable integration of proprietary data as well as visualization of agent spread along supply and production chains. STEM now provides a fully developed open-source software infrastructure supporting critical modeling tasks such as ad hoc model generation, parameter estimation, simulation of scenario evolution, estimation of effects of mitigation or management measures, and documentation. This open-source software resource can be used free of charge. Additionally, STEM provides critical features like built-in worldwide data on administrative boundaries, transportation networks, or environmental conditions (eg, rainfall, temperature, elevation, vegetation). Users can easily combine their own confidential data with built-in public data to create customized models of desired resolution. STEM also supports collaborative and joint efforts in crisis situations by extended import and export functionalities. In this article we demonstrate specifically those new software features implemented to accomplish STEM application in agro- or bioterrorist crisis scenarios.

Disease prediction models and operational readiness

The objective of this manuscript is to present a systematic review of biosurveillance models that operate on select agents and can forecast the occurrence of a disease event. We define a disease event to be a biological event with focus on the One Health paradigm. These events are characterized by evidence of infection and or disease condition. We reviewed models that attempted to predict a disease event, not merely its transmission dynamics and we considered models involving pathogens of concern as determined by the US National Select Agent Registry (as of June 2011). We searched commercial and government databases and harvested Google search results for eligible models, using terms and phrases provided by public health analysts relating to biosurveillance, remote sensing, risk assessments, spatial epidemiology, and ecological niche modeling. After removal of duplications and extraneous material, a core collection of 6,524 items was established, and these publications along with their abstracts are presented in a semantic wiki at http://BioCat.pnnl.gov. As a result, we systematically reviewed 44 papers, and the results are presented in this analysis. We identified 44 models, classified as one or more of the following: event prediction (4), spatial (26), ecological niche (28), diagnostic or clinical (6), spread or response (9), and reviews (3). The model parameters (e.g., etiology, climatic, spatial, cultural) and data sources (e.g., remote sensing, non-governmental organizations, expert opinion, epidemiological) were recorded and reviewed. A component of this review is the identification of verification and validation (V&V) methods applied to each model, if any V&V method was reported. All models were classified as either having undergone Some Verification or Validation method, or No Verification or Validation. We close by outlining an initial set of operational readiness level guidelines for disease prediction models based upon established Technology Readiness Level definitions.

Human mobility and the worldwide impact of intentional localized highly pathogenic virus release

The threat of bioterrorism and the possibility of accidental release have spawned a growth of interest in modeling the course of the release of a highly pathogenic agent. Studies focused on strategies to contain local outbreaks after their detection show that timely interventions with vaccination and contact tracing are able to halt transmission. However, such studies do not consider the effects of human mobility patterns. Using a large-scale structured metapopulation model to simulate the global spread of smallpox after an intentional release event, we show that index cases and potential outbreaks can occur in different continents even before the detection of the pathogen release. These results have two major implications: i) intentional release of a highly pathogenic agent within a country will have global effects; ii) the release event may trigger outbreaks in countries lacking the health infrastructure necessary for effective containment. The presented study provides data with potential uses in defining contingency plans at the National and International level.

Unifying viral genetics and human transportation data to predict the global transmission dynamics of human influenza H3N2

Information on global human movement patterns is central to spatial epidemiological models used to predict the behavior of influenza and other infectious diseases. Yet it remains difficult to test which modes of dispersal drive pathogen spread at various geographic scales using standard epidemiological data alone. Evolutionary analyses of pathogen genome sequences increasingly provide insights into the spatial dynamics of influenza viruses, but to date they have largely neglected the wealth of information on human mobility, mainly because no statistical framework exists within which viral gene sequences and empirical data on host movement can be combined. Here, we address this problem by applying a phylogeographic approach to elucidate the global spread of human influenza subtype H3N2 and assess its ability to predict the spatial spread of human influenza A viruses worldwide. Using a framework that estimates the migration history of human influenza while simultaneously testing and quantifying a range of potential predictive variables of spatial spread, we show that the global dynamics of influenza H3N2 are driven by air passenger flows, whereas at more local scales spread is also determined by processes that correlate with geographic distance. Our analyses further confirm a central role for mainland China and Southeast Asia in maintaining a source population for global influenza diversity. By comparing model output with the known pandemic expansion of H1N1 during 2009, we demonstrate that predictions of influenza spatial spread are most accurate when data on human mobility and viral evolution are integrated. In conclusion, the global dynamics of influenza viruses are best explained by combining human mobility data with the spatial information inherent in sampled viral genomes. The integrated approach introduced here offers great potential for epidemiological surveillance through phylogeographic reconstructions and for improving predictive models of disease control.

What explains the geographic dispersal of emerging pathogens? Reconstructions of evolutionary history from pathogen gene sequences offer qualitative descriptions of spatial spread, but current approaches are poorly equipped to formally test and quantify the contribution of different potential explanatory factors, such as human mobility and demography. Here, we use a novel phylogeographic method to evaluate multiple potential predictors of viral spread in human influenza dynamics. We identify air travel as the predominant driver of global influenza migration, whilst also revealing the contribution of other mobility processes at more local scales. We demonstrate the power of our inter-disciplinary approach by using it to predict the global pandemic expansion of H1N1 influenza in 2009. Our study highlights the importance of integrating evolutionary and ecological information when studying the dynamics of infectious disease.

The epidemiology ontology: an ontology for the semantic annotation of epidemiological resources

Background

Epidemiology is a data-intensive and multi-disciplinary subject, where data integration, curation and sharing are becoming increasingly relevant, given its global context and time constraints. The semantic annotation of epidemiology resources is a cornerstone to effectively support such activities. Although several ontologies cover some of the subdomains of epidemiology, we identified a lack of semantic resources for epidemiology-specific terms. This paper addresses this need by proposing the Epidemiology Ontology (EPO) and by describing its integration with other related ontologies into a semantic enabled platform for sharing epidemiology resources.

Results

The EPO follows the OBO Foundry guidelines and uses the Basic Formal Ontology (BFO) as an upper ontology. The first version of EPO models several epidemiology and demography parameters as well as transmission of infection processes, participants and related procedures. It currently has nearly 200 classes and is designed to support the semantic annotation of epidemiology resources and data integration, as well as information retrieval and knowledge discovery activities.

Conclusions

EPO is under active development and is freely available at https://code.google.com/p/epidemiology-ontology/. We believe that the annotation of epidemiology resources with EPO will help researchers to gain a better understanding of global epidemiological events by enhancing data integration and sharing.

Spreading dynamics on complex networks: a general stochastic approach

Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach is especially well adapted for modelling spreading processes and/or population dynamics. In particular, the generality of our framework and the fact that its assumptions are explicitly stated suggests that it could be used as a common ground for comparing existing epidemics models too complex for direct comparison, such as agent-based computer simulations. We provide many examples for the special cases of susceptible-infectious-susceptible and susceptible-infectious-removed dynamics (e.g., epidemics propagation) and we observe multiple situations where accurate results may be obtained at low computational cost. Our perspective reveals a subtle balance between the complex requirements of a realistic model and its basic assumptions.

A lattice model for influenza spreading

We construct a stochastic SIR model for influenza spreading on a D-dimensional lattice, which represents the dynamic contact network of individuals. An age distributed population is placed on the lattice and moves on it. The displacement from a site to a nearest neighbor empty site, allows individuals to change the number and identities of their contacts. The dynamics on the lattice is governed by an attractive interaction between individuals belonging to the same age-class. The parameters, which regulate the pattern dynamics, are fixed fitting the data on the age-dependent daily contact numbers, furnished by the Polymod survey. A simple SIR transmission model with a nearest neighbors interaction and some very basic adaptive mobility restrictions complete the model. The model is validated against the age-distributed Italian epidemiological data for the influenza A(H1N1) during the [Formula: see text] season, with sensible predictions for the epidemiological parameters. For an appropriate topology of the lattice, we find that, whenever the accordance between the contact patterns of the model and the Polymod data is satisfactory, there is a good agreement between the numerical and the experimental epidemiological data. This result shows how rich is the information encoded in the average contact patterns of individuals, with respect to the analysis of the epidemic spreading of an infectious disease.

An infectious disease model on empirical networks of human contact: bridging the gap between dynamic network data and contact matrices

BACKGROUND

The integration of empirical data in computational frameworks designed to model the spread of infectious diseases poses a number of challenges that are becoming more pressing with the increasing availability of high-resolution information on human mobility and contacts. This deluge of data has the potential to revolutionize the computational efforts aimed at simulating scenarios, designing containment strategies, and evaluating outcomes. However, the integration of highly detailed data sources yields models that are less transparent and general in their applicability. Hence, given a specific disease model, it is crucial to assess which representations of the raw data work best to inform the model, striking a balance between simplicity and detail.

METHODS

We consider high-resolution data on the face-to-face interactions of individuals in a pediatric hospital ward, obtained by using wearable proximity sensors. We simulate the spread of a disease in this community by using an SEIR model on top of different mathematical representations of the empirical contact patterns. At the most detailed level, we take into account all contacts between individuals and their exact timing and order. Then, we build a hierarchy of coarse-grained representations of the contact patterns that preserve only partially the temporal and structural information available in the data. We compare the dynamics of the SEIR model across these representations.

RESULTS

We show that a contact matrix that only contains average contact durations between role classes fails to reproduce the size of the epidemic obtained using the high-resolution contact data and also fails to identify the most at-risk classes. We introduce a contact matrix of probability distributions that takes into account the heterogeneity of contact durations between (and within) classes of individuals, and we show that, in the case study presented, this representation yields a good approximation of the epidemic spreading properties obtained by using the high-resolution data.

CONCLUSIONS

Our results mark a first step towards the definition of synopses of high-resolution dynamic contact networks, providing a compact representation of contact patterns that can correctly inform computational models designed to discover risk groups and evaluate containment policies. We show in a typical case of a structured population that this novel kind of representation can preserve in simulation quantitative features of the epidemics that are crucial for their study and management.

Predicting and controlling infectious disease epidemics using temporal networks

Infectious diseases can be considered to spread over social networks of people or animals. Mainly owing to the development of data recording and analysis techniques, an increasing amount of social contact data with time stamps has been collected in the last decade. Such temporal data capture the dynamics of social networks on a timescale relevant to epidemic spreading and can potentially lead to better ways to analyze, forecast, and prevent epidemics. However, they also call for extended analysis tools for network epidemiology, which has, to date, mostly viewed networks as static entities. We review recent results of network epidemiology for such temporal network data and discuss future developments.

Real-time numerical forecast of global epidemic spreading: case study of 2009 A/H1N1pdm

BACKGROUND

Mathematical and computational models for infectious diseases are increasingly used to support public-health decisions; however, their reliability is currently under debate. Real-time forecasts of epidemic spread using data-driven models have been hindered by the technical challenges posed by parameter estimation and validation. Data gathered for the 2009 H1N1 influenza crisis represent an unprecedented opportunity to validate real-time model predictions and define the main success criteria for different approaches.

METHODS

We used the Global Epidemic and Mobility Model to generate stochastic simulations of epidemic spread worldwide, yielding (among other measures) the incidence and seeding events at a daily resolution for 3,362 subpopulations in 220 countries. Using a Monte Carlo Maximum Likelihood analysis, the model provided an estimate of the seasonal transmission potential during the early phase of the H1N1 pandemic and generated ensemble forecasts for the activity peaks in the northern hemisphere in the fall/winter wave. These results were validated against the real-life surveillance data collected in 48 countries, and their robustness assessed by focusing on 1) the peak timing of the pandemic; 2) the level of spatial resolution allowed by the model; and 3) the clinical attack rate and the effectiveness of the vaccine. In addition, we studied the effect of data incompleteness on the prediction reliability.

RESULTS

Real-time predictions of the peak timing are found to be in good agreement with the empirical data, showing strong robustness to data that may not be accessible in real time (such as pre-exposure immunity and adherence to vaccination campaigns), but that affect the predictions for the attack rates. The timing and spatial unfolding of the pandemic are critically sensitive to the level of mobility data integrated into the model.

CONCLUSIONS

Our results show that large-scale models can be used to provide valuable real-time forecasts of influenza spreading, but they require high-performance computing. The quality of the forecast depends on the level of data integration, thus stressing the need for high-quality data in population-based models, and of progressive updates of validated available empirical knowledge to inform these models.

Development of a resource modelling tool to support decision makers in pandemic influenza preparedness: The AsiaFluCap Simulator

BACKGROUND

Health care planning for pandemic influenza is a challenging task which requires predictive models by which the impact of different response strategies can be evaluated. However, current preparedness plans and simulations exercises, as well as freely available simulation models previously made for policy makers, do not explicitly address the availability of health care resources or determine the impact of shortages on public health. Nevertheless, the feasibility of health systems to implement response measures or interventions described in plans and trained in exercises depends on the available resource capacity. As part of the AsiaFluCap project, we developed a comprehensive and flexible resource modelling tool to support public health officials in understanding and preparing for surges in resource demand during future pandemics.

RESULTS

The AsiaFluCap Simulator is a combination of a resource model containing 28 health care resources and an epidemiological model. The tool was built in MS Excel© and contains a user-friendly interface which allows users to select mild or severe pandemic scenarios, change resource parameters and run simulations for one or multiple regions. Besides epidemiological estimations, the simulator provides indications on resource gaps or surpluses, and the impact of shortages on public health for each selected region. It allows for a comparative analysis of the effects of resource availability and consequences of different strategies of resource use, which can provide guidance on resource prioritising and/or mobilisation. Simulation results are displayed in various tables and graphs, and can also be easily exported to GIS software to create maps for geographical analysis of the distribution of resources.

CONCLUSIONS

The AsiaFluCap Simulator is freely available software (http://www.cdprg.org) which can be used by policy makers, policy advisors, donors and other stakeholders involved in preparedness for providing evidence based and illustrative information on health care resource capacities during future pandemics. The tool can inform both preparedness plans and simulation exercises and can help increase the general understanding of dynamics in resource capacities during a pandemic. The combination of a mathematical model with multiple resources and the linkage to GIS for creating maps makes the tool unique compared to other available software.

Inferring the structure of social contacts from demographic data in the analysis of infectious diseases spread

Social contact patterns among individuals encode the transmission route of infectious diseases and are a key ingredient in the realistic characterization and modeling of epidemics. Unfortunately, the gathering of high quality experimental data on contact patterns in human populations is a very difficult task even at the coarse level of mixing patterns among age groups. Here we propose an alternative route to the estimation of mixing patterns that relies on the construction of virtual populations parametrized with highly detailed census and demographic data. We present the modeling of the population of 26 European countries and the generation of the corresponding synthetic contact matrices among the population age groups. The method is validated by a detailed comparison with the matrices obtained in six European countries by the most extensive survey study on mixing patterns. The methodology presented here allows a large scale comparison of mixing patterns in Europe, highlighting general common features as well as country-specific differences. We find clear relations between epidemiologically relevant quantities (reproduction number and attack rate) and socio-demographic characteristics of the populations, such as the average age of the population and the duration of primary school cycle. This study provides a numerical approach for the generation of human mixing patterns that can be used to improve the accuracy of mathematical models in the absence of specific experimental data.

The dynamics of infectious diseases caused by pathogens transmissible from human to human strongly depends on contact patterns between individuals. High quality observational data on contact patterns, usually presented in the form of age-specific contact matrices, are difficult to gather and are currently available only for few countries worldwide. Here we propose a computational approach, based on the simulation of a virtual society of agents, allowing the estimation of contact patterns by age for 26 European countries. We validate the estimated contact matrices against those obtained by the most extensive field study on contact patterns, with data collected in eight European countries. We show that our contact matrices share some common features, e.g. individuals tend to mix preferentially with individuals their own age, and country-specific differences, which can be partly explained by differences in population structures due to different demographic trajectories followed after WWII. Our analysis highlights well defined correlations between epidemiological parameters and socio-demographic features of the populations. This study provides the first estimates of contact matrices for many European countries where specific experimental data are still not available.

Air travel and vector-borne disease movement

Recent decades have seen substantial expansions in the global air travel network and rapid increases in traffic volumes. The effects of this are well studied in terms of the spread of directly transmitted infections, but the role of air travel in the movement of vector-borne diseases is less well understood. Increasingly however, wider reaching surveillance for vector-borne diseases and our improving abilities to map the distributions of vectors and the diseases they carry, are providing opportunities to better our understanding of the impact of increasing air travel. Here we examine global trends in the continued expansion of air transport and its impact upon epidemiology. Novel malaria and chikungunya examples are presented, detailing how geospatial data in combination with information on air traffic can be used to predict the risks of vector-borne disease importation and establishment. Finally, we describe the development of an online tool, the Vector-Borne Disease Airline Importation Risk (VBD-Air) tool, which brings together spatial data on air traffic and vector-borne disease distributions to quantify the seasonally changing risks for importation to non-endemic regions. Such a framework provides the first steps towards an ultimate goal of adaptive management based on near real time flight data and vector-borne disease surveillance.

Evolution of scaling emergence in large-scale spatial epidemic spreading

Background

Zipf's law and Heaps' law are two representatives of the scaling concepts, which play a significant role in the study of complexity science. The coexistence of the Zipf's law and the Heaps' law motivates different understandings on the dependence between these two scalings, which has still hardly been clarified.

Methodology/Principal Findings

In this article, we observe an evolution process of the scalings: the Zipf's law and the Heaps' law are naturally shaped to coexist at the initial time, while the crossover comes with the emergence of their inconsistency at the larger time before reaching a stable state, where the Heaps' law still exists with the disappearance of strict Zipf's law. Such findings are illustrated with a scenario of large-scale spatial epidemic spreading, and the empirical results of pandemic disease support a universal analysis of the relation between the two laws regardless of the biological details of disease. Employing the United States domestic air transportation and demographic data to construct a metapopulation model for simulating the pandemic spread at the U.S. country level, we uncover that the broad heterogeneity of the infrastructure plays a key role in the evolution of scaling emergence.

Conclusions/Significance

The analyses of large-scale spatial epidemic spreading help understand the temporal evolution of scalings, indicating the coexistence of the Zipf's law and the Heaps' law depends on the collective dynamics of epidemic processes, and the heterogeneity of epidemic spread indicates the significance of performing targeted containment strategies at the early time of a pandemic disease.