Nicola Perra

Seasonal transmission potential and activity peaks of the new influenza A(H1N1): a Monte Carlo likelihood analysis based on human mobility

BackgroundOn 11 June the World Health Organization officially raised the phase of pandemic alert (with regard to the new H1N1 influenza strain) to level 6. As of 19 July, 137,232 cases of the H1N1 influenza strain have been officially confirmed in 142 different countries, and the pandemic unfolding in the Southern hemisphere is now under scrutiny to gain insights about the next winter wave in the Northern hemisphere. A major challenge is pre-empted by the need to estimate the transmission potential of the virus and to assess its dependence on seasonality aspects in order to be able to use numerical models capable of projecting the spatiotemporal pattern of the pandemic.MethodsIn the present work, we use a global structured metapopulation model integrating mobility and transportation data worldwide. The model considers data on 3,362 subpopulations in 220 different countries and individual mobility across them. The model generates stochastic realizations of the epidemic evolution worldwide considering 6 billion individuals, from which we can gather information such as prevalence, morbidity, number of secondary cases and number and date of imported cases for each subpopulation, all with a time resolution of 1 day. In order to estimate the transmission potential and the relevant model parameters we used the data on the chronology of the 2009 novel influenza A(H1N1). The method is based on the maximum likelihood analysis of the arrival time distribution generated by the model in 12 countries seeded by Mexico by using 1 million computationally simulated epidemics. An extended chronology including 93 countries worldwide seeded before 18 June was used to ascertain the seasonality effects.ResultsWe found the best estimate R0 = 1.75 (95% confidence interval (CI) 1.64 to 1.88) for the basic reproductive number. Correlation analysis allows the selection of the most probable seasonal behavior based on the observed pattern, leading to the identification of plausible scenarios for the future unfolding of the pandemic and the estimate of pandemic activity peaks in the different hemispheres. We provide estimates for the number of hospitalizations and the attack rate for the next wave as well as an extensive sensitivity analysis on the disease parameter values. We also studied the effect of systematic therapeutic use of antiviral drugs on the epidemic timeline.ConclusionThe analysis shows the potential for an early epidemic peak occurring in October/November in the Northern hemisphere, likely before large-scale vaccination campaigns could be carried out. The baseline results refer to a worst-case scenario in which additional mitigation policies are not considered. We suggest that the planning of additional mitigation policies such as systematic antiviral treatments might be the key to delay the activity peak in order to restore the effectiveness of the vaccination programs.

Statistical physics of vaccination

Historically, infectious diseases caused considerable damage to human societies, and they continue to do so today. To help reduce their impact, mathematical models of disease transmission have been studied to help understand disease dynamics and inform prevention strategies. Vaccination - one of the most important preventive measures of modern times - is of great interest both theoretically and empirically. And in contrast to traditional approaches, recent research increasingly explores the pivotal implications of individual behavior and heterogeneous contact patterns in populations. Our report reviews the developmental arc of theoretical epidemiology with emphasis on vaccination, as it led from classical models assuming homogeneously mixing (mean-field) populations and ignoring human behavior, to recent models that account for behavioral feedback and/or population spatial/social structure. Many of the methods used originated in statistical physics, such as lattice and network models, and their associated analytical frameworks. Similarly, the feedback loop between vaccinating behavior and disease propagation forms a coupled nonlinear system with analogs in physics. We also review the new paradigm of digital epidemiology, wherein sources of digital data such as online social media are mined for high-resolution information on epidemiologically relevant individual behavior. Armed with the tools and concepts of statistical physics, and further assisted by new sources of digital data, models that capture nonlinear interactions between behavior and disease dynamics offer a novel way of modeling real-world phenomena, and can help improve health outcomes. We conclude the review by discussing open problems in the field and promising directions for future research.

Modeling human mobility responses to the large-scale spreading of infectious diseases

Current modeling of infectious diseases allows for the study of realistic scenarios that include population heterogeneity, social structures, and mobility processes down to the individual level. The advances in the realism of epidemic description call for the explicit modeling of individual behavioral responses to the presence of disease within modeling frameworks. Here we formulate and analyze a metapopulation model that incorporates several scenarios of self-initiated behavioral changes into the mobility patterns of individuals. We find that prevalence-based travel limitations do not alter the epidemic invasion threshold. Strikingly, we observe in both synthetic and data-driven numerical simulations that when travelers decide to avoid locations with high levels of prevalence, this self-initiated behavioral change may enhance disease spreading. Our results point out that the real-time availability of information on the disease and the ensuing behavioral changes in the population may produce a negative impact on disease containment and mitigation.

The Twitter of Babel: Mapping World Languages through Microblogging Platforms

Large scale analysis and statistics of socio-technical systems that just a few short years ago would have required the use of consistent economic and human resources can nowadays be conveniently performed by mining the enormous amount of digital data produced by human activities. Although a characterization of several aspects of our societies is emerging from the data revolution, a number of questions concerning the reliability and the biases inherent to the big data “proxies” of social life are still open. Here, we survey worldwide linguistic indicators and trends through the analysis of a large-scale dataset of microblogging posts. We show that available data allow for the study of language geography at scales ranging from country-level aggregation to specific city neighborhoods. The high resolution and coverage of the data allows us to investigate different indicators such as the linguistic homogeneity of different countries, the touristic seasonal patterns within countries and the geographical distribution of different languages in multilingual regions. This work highlights the potential of geolocalized studies of open data sources to improve current analysis and develop indicators for major social phenomena in specific communities.

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

BackgroundMathematical 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.MethodsWe 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.ResultsReal-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.ConclusionsOur 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.

Towards a characterization of behavior-disease models.

The last decade saw the advent of increasingly realistic epidemic models that leverage on the availability of highly detailed census and human mobility data. Data-driven models aim at a granularity down to the level of households or single individuals. However, relatively little systematic work has been done to provide coupled behavior-disease models able to close the feedback loop between behavioral changes triggered in the population by an individuals perception of the disease spread and the actual disease spread itself. While models lacking this coupling can be extremely successful in mild epidemics, they obviously will be of limited use in situations where social disruption or behavioral alterations are induced in the population by knowledge of the disease. Here we propose a characterization of a set of prototypical mechanisms for self-initiated social distancing induced by local and non-local prevalence-based information available to individuals in the population. We characterize the effects of these mechanisms in the framework of a compartmental scheme that enlarges the basic SIR model by considering separate behavioral classes within the population. The transition of individuals in/out of behavioral classes is coupled with the spreading of the disease and provides a rich phase space with multiple epidemic peaks and tipping points. The class of models presented here can be used in the case of data-driven computational approaches to analyze scenarios of social adaptation and behavioral change.

The role of information diffusion in the evolution of social networks

Every day millions of users are connected through online social networks, generating a rich trove of data that allows us to study the mechanisms behind human interactions. Triadic closure has been treated as the major mechanism for creating social links: if Alice follows Bob and Bob follows Charlie, Alice will follow Charlie. Here we present an analysis of longitudinal micro-blogging data, revealing a more nuanced view of the strategies employed by users when expanding their social circles. While the network structure affects the spread of information among users, the network is in turn shaped by this communication activity. This suggests a link creation mechanism whereby Alice is more likely to follow Charlie after seeing many messages by Charlie. We characterize users with a set of parameters associated with different link creation strategies, estimated by a Maximum-Likelihood approach. Triadic closure does have a strong effect on link formation, but shortcuts based on traffic are another key factor in interpreting network evolution. However, individual strategies for following other users are highly heterogeneous. Link creation behaviors can be summarized by classifying users in different categories with distinct structural and behavioral characteristics. Users who are popular, active, and influential tend to create traffic-based shortcuts, making the information diffusion process more efficient in the network.

Random Walks and Search in Time-Varying Networks

The random walk process underlies the description of a large number of real-world phenomena. Here we provide the study of random walk processes in time-varying networks in the regime of time-scale mixing, i.e., when the network connectivity pattern and the random walk process dynamics are unfolding on the same time scale. We consider a model for time-varying networks created from the activity potential of the nodes and derive solutions of the asymptotic behavior of random walks and the mean first passage time in undirected and directed networks. Our findings show striking differences with respect to the well-known results obtained in quenched and annealed networks, emphasizing the effects of dynamical connectivity patterns in the definition of proper strategies for search, retrieval, and diffusion processes in time-varying networks.

Controlling Contagion Processes in Activity Driven Networks

The vast majority of strategies aimed at controlling contagion processes on networks consider the connectivity pattern of the system either quenched or annealed. However, in the real world, many networks are highly dynamical and evolve, in time, concurrently with the contagion process. Here, we derive an analytical framework for the study of control strategies specifically devised for a class of time-varying networks, namely activity-driven networks. We develop a block variable mean-field approach that allows the derivation of the equations describing the coevolution of the contagion process and the network dynamic. We derive the critical immunization threshold and assess the effectiveness of three different control strategies. Finally, we validate the theoretical picture by simulating numerically the spreading process and control strategies in both synthetic networks and a large-scale, real-world, mobile telephone call data set.

Quantifying the effect of temporal resolution on time-varying networks

Time-varying networks describe a wide array of systems whose constituents and interactions evolve over time. They are defined by an ordered stream of interactions between nodes, yet they are often represented in terms of a sequence of static networks, each aggregating all edges and nodes present in a time interval of size Δt. In this work we quantify the impact of an arbitrary Δt on the description of a dynamical process taking place upon a time-varying network. We focus on the elementary random walk, and put forth a simple mathematical framework that well describes the behavior observed on real datasets. The analytical description of the bias introduced by time integrating techniques represents a step forward in the correct characterization of dynamical processes on time-varying graphs.