Differential mobility and local variation in infection attack rate.

Infectious disease transmission is an inherently spatial process in which a host's home location and their social mixing patterns are important, with the mixing of infectious individuals often different to that of susceptible individuals. Although incidence data for humans have traditionally been aggregated into low-resolution data sets, modern representative surveillance systems such as electronic hospital records generate high volume case data with precise home locations. Here, we use a gridded spatial transmission model of arbitrary resolution to investigate the theoretical relationship between population density, differential population movement and local variability in incidence. We show analytically that a uniform local attack rate is typically only possible for individual pixels in the grid if susceptible and infectious individuals move in the same way. Using a population in Guangdong, China, for which a robust quantitative description of movement is available (a travel kernel), and a natural history consistent with pandemic influenza; we show that local cumulative incidence is positively correlated with population density when susceptible individuals are more connected in space than infectious individuals. Conversely, under the less intuitively likely scenario, when infectious individuals are more connected, local cumulative incidence is negatively correlated with population density. The strength and direction of correlation changes sign for other kernel parameter values. We show that simulation models in which it is assumed implicitly that only infectious individuals move are assuming a slightly unusual specific correlation between population density and attack rate. However, we also show that this potential structural bias can be corrected by using the appropriate non-isotropic kernel that maps infectious-only code onto the isotropic dual-mobility kernel. These results describe a precise relationship between the spatio-social mixing of infectious and susceptible individuals and local variability in attack rates. More generally, these results suggest a genuine risk that mechanistic models of high-resolution attack rate data may reach spurious conclusions if the precise implications of spatial force-of-infection assumptions are not first fully characterized, prior to models being fit to data

On the Measurement of Privacy as an Attacker's Estimation Error

A wide variety of privacy metrics have been proposed in the literature to evaluate the level of protection offered by privacy enhancing-technologies. Most of these metrics are specific to concrete systems and adversarial models, and are difficult to generalize or translate to other contexts. Furthermore, a better understanding of the relationships between the different privacy metrics is needed to enable more grounded and systematic approach to measuring privacy, as well as to assist systems designers in selecting the most appropriate metric for a given application. In this work we propose a theoretical framework for privacy-preserving systems, endowed with a general definition of privacy in terms of the estimation error incurred by an attacker who aims to disclose the private information that the system is designed to conceal. We show that our framework permits interpreting and comparing a number of well-known metrics under a common perspective. The arguments behind these interpretations are based on fundamental results related to the theories of information, probability and Bayes decision.Comment: This paper has 18 pages and 17 figure

Determinants of the Spatiotemporal Dynamics of the 2009 H1N1 Pandemic in Europe: Implications for Real-Time Modelling

Influenza pandemics in the last century were characterized by successive waves and differences in impact and timing between different regions, for reasons not clearly understood. The 2009 H1N1 pandemic showed rapid global spread, but with substantial heterogeneity in timing within each hemisphere. Even within Europe substantial variation was observed, with the UK being unique in experiencing a major first wave of transmission in early summer and all other countries having a single major epidemic in the autumn/winter, with a West to East pattern of spread. Here we show that a microsimulation model, parameterised using data about H1N1pdm collected by the beginning of June 2009, explains the occurrence of two waves in UK and a single wave in the rest of Europe as a consequence of timing of H1N1pdm spread, fluxes of travels from US and Mexico, and timing of school vacations. The model provides a description of pandemic spread through Europe, depending on intra-European mobility patterns and socio-demographic structure of the European populations, which is in broad agreement with observed timing of the pandemic in different countries. Attack rates are predicted to depend on the socio-demographic structure, with age dependent attack rates broadly agreeing with available serological data. Results suggest that the observed heterogeneity can be partly explained by the between country differences in Europe: marked differences in school calendars, mobility patterns and sociodemographic structures. Moreover, higher susceptibility of children to infection played a key role in determining the epidemiology of the 2009 pandemic. Our work shows that it would have been possible to obtain a broad-brush prediction of timing of the European pandemic well before the autumn of 2009, much more difficult to achieve with simpler models or pre-pandemic parameterisation. This supports the use of models accounting for the structure of complex modern societies for giving insight to policy makers

Modelling the interplay between human behaviour and the spread of infectious diseases: From toy models to quantitative approaches

Prevenir la propagació de malalties infeccioses és un dels reptes més grans de la humanitat. Moltes malalties es transmeten per contacte, per la qual cosa la xarxa d'interaccions humanes actua com a substrat per a la propagació. Per aquest motiu, els models epidèmics sempre inclouen, ja sigui implícita o explícitament, una descripció de com els éssers humans interactuen entre ells. Malgrat això, actualment no es disposa d’una teoria general de la interacció entre el comportament humà i la propagació d'agents. L’objectiu d’aquesta tesi és contribuir a la descripció matemàtica del comportament humà en el context de les malalties infeccioses, treballant tant amb models quantitatius com qualitatius. En el primer capítol es desenvolupen dos models qualitatius per entendre com l’adopció de mesures profilàctiques de manera dinàmica basada en el risc pot causar cicles epidèmics. En el segon capítol, considerem aspectes estàtics específics del comportament humà -homofília i patrons de contacte heterogenis- i n'analitzem les implicacions en el control d'epidèmies. En contrast amb el què es creia anteriorment, demostrem que l'homofília en l'adopció d’eines profilàctiques no sempre resulta perjudicial. A més a més, qüestionem el paradigma actual de les estratègies d'immunització basades en el risc. L'últim capítol d'aquesta tesi se centra en enfocs quantitatius per modelitzar la propagació del SARS-CoV-2, en particular la primera onada i la propagació de la variant Delta. A més dels avenços metodològics, mostrem com l’adaptació voluntària del comportament va determinar el curs de l’epidèmia més enllà de les intervencions no farmacèutiques. En conjunt, aquesta tesi revela una nova fenomenologia, afegeix proves empíriques addicionals i proporciona noves eines per analitzar com evolucionen el comportament humà i les epidèmies. La combinació d'enfocaments quantitatius i qualitatius també proporciona una via per analitzar i interpretar l’enorme quantitat de dades recopilades durant la pandèmia de SARS-CoV-2.Prevenir la propagación de enfermedades infecciosas es uno de los mayores retos de la humanidad. Muchas enfermedades se transmiten por contacto, por lo que la red de interacciones humanas actúa como sustrato para su propagación. Por esta razón, los modelos epidémicos siempre incluyen una descripción de cómo interactúan los seres humanos entre ellos. Sin embargo, actualmente no existe una teoría general de la interacción entre el comportamiento humano y la propagación de agentes. El objetivo de esta tesis es contribuir a la descripción matemática del comportamiento humano en el contexto de las enfermedades infecciosas, trabajando tanto con modelos cuantitativos como cualitativos. El primer capítulo desarrolla dos modelos cualitativos para esbozar cómo la profilaxis dinámica basada en el riesgo puede sostener ciclos epidémicos. En el segundo capítulo, consideramos aspectos estáticos específicos del comportamiento humano -homofilia y patrones de contacto heterogéneos- y analizamos sus implicaciones en el control de epidemias. En contraste con resultados anteriores, demostramos que la homofilia en la adopción de herramientas profilácticas no siempre es perjudicial. Además, cuestionamos el paradigma actual de las estrategias de inmunización basadas en el riesgo. El último capítulo de esta tesis se centra en enfoques cuantitativos para modelizar la propagación del SARS-CoV-2, en particular, la primera oleada y la propagación de la variante Delta. Además de los avances metodológicos, mostramos cómo la adaptación voluntaria del comportamiento fue capaz de determinar el curso de la epidemia más allá de las intervenciones no farmacéuticas. En conjunto, esta tesis desvela una nueva fenomenología, añade pruebas empíricas adicionales y proporciona nuevas herramientas para analizar cómo evolucionan el comportamiento humano y las epidemias. La combinación de enfoques cuantitativos y cualitativos proporciona una vía muy útil para analizar e interpretar la gran cantidad de datos recopilados durante la pandemia de SARS-CoV-2. Preventing the spread of infectious diseases is one of the greatest challenges of humanity's past, present, and foreseeable future. Many infectious diseases are transmitted upon contact, and hence the complex web of human interactions acts as a substrate for their propagation. For this reason, epidemic models always comprise, either explicitly or implicitly, a description of how humans interact. However, the quest for a general theory of the interplay between human behaviour and the spread of pathogens is far from complete. The aim of this thesis is to contribute to the mathematical description of human behaviour in the context of infectious diseases, working with both quantitative and qualitative models. The first chapter develops two qualitative toy models to outline how dynamical risk-based prophylaxis can sustain epidemic cycles. In the second chapter, we consider specific static aspects of human behaviour -- homophily and heterogeneous contact patterns -- and analyse their implications on epidemic control. In contrast to previous belief, we show that homophily in the adoption of many prophylactic tools is not always detrimental. Furthermore, we question the current paradigm of risk-based immunisation strategies and show that targeting hubs is only optimal for protection with high efficacy. The last chapter of this thesis focuses on quantitative approaches to model the spread of SARS-CoV-2, in particular, the first wave and the spread of the Delta variant. Besides the methodological advances, we add evidence of how voluntary behavioural adaptation shaped the course of the epidemic beyond non-pharmaceutical interventions. Overall, this thesis unveils new phenomenology, adds additional empirical evidence, and provides new tools to analyse how human behaviour and epidemics coevolve. The flexible blend of quantitative and qualitative approaches may also provide a pathway to analyse and interpret the vast amount of data currently collected during the SARS-CoV-2 pandemic

Consequences of Short Term Mobility Across Heterogeneous Risk Environments: The 2014 West African Ebola Outbreak

abstract: In this dissertation the potential impact of some social, cultural and economic factors on Ebola Virus Disease (EVD) dynamics and control are studied. In Chapter two, the inability to detect and isolate a large fraction of EVD-infected individuals before symptoms onset is addressed. A mathematical model, calibrated with data from the 2014 West African outbreak, is used to show the dynamics of EVD control under various quarantine and isolation effectiveness regimes. It is shown that in order to make a difference it must reach a high proportion of the infected population. The effect of EVD-dead bodies has been incorporated in the quarantine effectiveness. In Chapter four, the potential impact of differential risk is assessed. A two-patch model without explicitly incorporate quarantine is used to assess the impact of mobility on communities at risk of EVD. It is shown that the overall EVD burden may lessen when mobility in this artificial high-low risk society is allowed. The cost that individuals in the low-risk patch must pay, as measured by secondary cases is highlighted. In Chapter five a model explicitly incorporating patch-specific quarantine levels is used to show that quarantine a large enough proportion of the population under effective isolation leads to a measurable reduction of secondary cases in the presence of mobility. It is shown that sharing limited resources can improve the effectiveness of EVD effective control in the two-patch high-low risk system. Identifying the conditions under which the low-risk community would be willing to accept the increases in EVD risk, needed to reduce the total number of secondary cases in a community composed of two patches with highly differentiated risks has not been addressed. In summary, this dissertation looks at EVD dynamics within an idealized highly polarized world where resources are primarily in the hands of a low-risk community – a community of lower density, higher levels of education and reasonable health services – that shares a “border” with a high-risk community that lacks minimal resources to survive an EVD outbreak.Dissertation/ThesisDoctoral Dissertation Applied Mathematics 201

Critical behavior in interdependent spatial spreading processes with distinct characteristic time scales

AbstractThe spread of an infectious disease is well approximated by metapopulation networks connected by human mobility flow and upon which an epidemiological model is defined. In order to account for travel restrictions or cancellation we introduce a model with a parameter that explicitly indicates the ratio between the time scales of the intervening processes. We study the critical properties of the epidemic process and its dependence on such a parameter. We find that the critical threshold separating the absorbing state from the active state depends on the scale parameter and exhibits a critical behavior itself: a metacritical point – a critical value in the curve of critical points – reflected in the behavior of the attack rate measured for a wide range of empirical metapopulation systems. Our results have potential policy implications, since they establish a non-trivial critical behavior between temporal scales of reaction (epidemic spread) and diffusion (human mobility) processes

Epidemic processes in complex networks

In recent years the research community has accumulated overwhelming evidence for the emergence of complex and heterogeneous connectivity patterns in a wide range of biological and sociotechnical systems. The complex properties of real-world networks have a profound impact on the behavior of equilibrium and nonequilibrium phenomena occurring in various systems, and the study of epidemic spreading is central to our understanding of the unfolding of dynamical processes in complex networks. The theoretical analysis of epidemic spreading in heterogeneous networks requires the development of novel analytical frameworks, and it has produced results of conceptual and practical relevance. A coherent and comprehensive review of the vast research activity concerning epidemic processes is presented, detailing the successful theoretical approaches as well as making their limits and assumptions clear. Physicists, mathematicians, epidemiologists, computer, and social scientists share a common interest in studying epidemic spreading and rely on similar models for the description of the diffusion of pathogens, knowledge, and innovation. For this reason, while focusing on the main results and the paradigmatic models in infectious disease modeling, the major results concerning generalized social contagion processes are also presented. Finally, the research activity at the forefront in the study of epidemic spreading in coevolving, coupled, and time-varying networks is reported.Comment: 62 pages, 15 figures, final versio

The Effects of Spatio-Temporal Heterogeneities on the Emergence and Spread of Dengue Virus

The dengue virus (DENV) remains a considerable global public health concern. The interactions between the virus, its mosquito vectors and the human host are complex and only partially understood. Dependencies of vector ecology on environmental attributes, such as temperature and rainfall, together with host population density, introduce strong spatiotemporal heterogeneities, resulting in irregular epidemic outbreaks and asynchronous oscillations in serotype prevalence. Human movements across different spatial scales have also been implicated as important drivers of dengue epidemiology across space and time, and further create the conditions for the geographic expansion of dengue into new habitats. Previously proposed transmission models often relied on strong, unrealistic assumptions regarding key epidemiological and ecological interactions to elucidate the effects of these spatio-temporal heterogeneities on the emergence, spread and persistence of dengue. Furthermore, the computational limitations of individual based models have hindered the development of more detailed descriptions of the influence of vector ecology, environment and human mobility on dengue epidemiology. In order to address these shortcomings, the main aim of this thesis was to rigorously quantify the effects of ecological drivers on dengue epidemiology within a robust and computational efficient framework. The individual based model presented included an explicit spatial structure, vector and human movement, spatio-temporal heterogeneity in population densities, and climate effects. The flexibility of the framework allowed robust assessment of the implications of classical modelling assumptions on the basic reproduction number, R₀, demonstrating that traditional approaches grossly inflate R₀ estimates. The model's more realistic meta-population formulation was then exploited to elucidate the effects of ecological heterogeneities on dengue incidence which showed that sufficient levels of community connectivity are required for the spread and persistence of dengue virus. By fitting the individual based model to empirical data, the influence of climate and on dengue was quantified, revealing the strong benefits that cross-sectional serological data could bring to more precisely inferring ecological drivers of arboviral epidemiology. Overall, the findings presented here demonstrate the wide epidemiological landscape which ecological drivers induce, forewarning against the strong implications of generalising interpretations from one particular setting across wider spatial contexts. These findings will prove invaluable for the assessment of vector-borne control strategies, such as mosquito elimination or vaccination deployment programs