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

Tracking disease outbreaks from sparse data with Bayesian inference

The COVID-19 pandemic provides new motivation for a classic problem in epidemiology: estimating the empirical rate of transmission during an outbreak (formally, the time-varying reproduction number) from case counts. While standard methods exist, they work best at coarse-grained national or state scales with abundant data, and struggle to accommodate the partial observability and sparse data common at finer scales (e.g., individual schools or towns). For example, case counts may be sparse when only a small fraction of infections are caught by a testing program. Or, whether an infected individual tests positive may depend on the kind of test and the point in time when they are tested. We propose a Bayesian framework which accommodates partial observability in a principled manner. Our model places a Gaussian process prior over the unknown reproduction number at each time step and models observations sampled from the distribution of a specific testing program. For example, our framework can accommodate a variety of kinds of tests (viral RNA, antibody, antigen, etc.) and sampling schemes (e.g., longitudinal or cross-sectional screening). Inference in this framework is complicated by the presence of tens or hundreds of thousands of discrete latent variables. To address this challenge, we propose an efficient stochastic variational inference method which relies on a novel gradient estimator for the variational objective. Experimental results for an example motivated by COVID-19 show that our method produces an accurate and well-calibrated posterior, while standard methods for estimating the reproduction number can fail badly

Agent-Based Markov Modeling for Improved COVID-19 Mitigation Policies

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Agent-Based Markov Modeling for Improved COVID-19 Mitigation Policies

The year 2020 saw the covid-19 virus lead to one of the worst global pandemics in history. As a result, governments around the world have been faced with the challenge of protecting public health while keeping the economy running to the greatest extent possible. Epidemiological models provide insight into the spread of these types of diseases and predict the e_ects of possible intervention policies. However, to date, even the most data-driven intervention policies rely on heuristics. In this paper, we study how reinforcement learning (RL) and Bayesian inference can be used to optimize mitigation policies that minimize economic impact without overwhelming hospital capacity. Our main contributions are (1) a novel agent-based pandemic simulator which, unlike traditional models, is able to model _ne-grained interactions among people at speci_c locations in a community; (2) an RL- based methodology for optimizing _ne-grained mitigation policies within this simulator; and (3) a Hidden Markov Model for predicting infected individuals based on partial observations regarding test results, presence of symptoms, and past physical contacts

Statistical physics and epidemic inference: methods and applications

L'abstract è presente nell'allegato / the abstract is in the attachmen

Computational Methods for Assessment and Prediction of Viral Evolutionary and Epidemiological Dynamics

The ability to comprehend the dynamics of viruses’ transmission and their evolution, even to a limited extent, can significantly enhance our capacity to predict and control the spread of infectious diseases. An example of such significance is COVID-19 caused by the severe acute respiratory syndrome Coronavirus 2 (SARS-CoV-2). In this dissertation, I am proposing computational models that present more precise and comprehensive approaches in viral outbreak investigations and epidemiology, providing invaluable insights into the transmission dynamics, and potential inter- ventions of infectious diseases by facilitating the timely detection of viral variants. The first model is a mathematical framework based on population dynamics for the calculation of a numerical measure of the fitness of SARS-CoV-2 subtypes. The second model I propose here is a transmissibility estimation method based on a Bayesian approach to calculate the most likely fitness landscape for SARS-CoV-2 using a generalized logistic sub-epidemic model. Using the proposed model I estimate the epistatic interaction networks of spike protein in SARS-CoV-2. Based on the community structure of these epistatic networks, I propose a computational framework that predicts emerging haplotypes of SARS-CoV-2 with altered transmissibility. The last method proposed in this dissertation is a maximum likelihood framework that integrates phylogenetic and random graph models to accurately infer transmission networks without requiring case-specific data

COVID-19: Estimation of the transmission dynamics in Spain using a stochastic simulator and black-box optimization techniques

Background and objectives: Epidemiological models of epidemic spread are an essential tool for optimizing decision-making. The current literature is very extensive and covers a wide variety of deterministic and stochastic models. However, with the increase in computing resources, new, more general, and flexible procedures based on simulation models can assess the effectiveness of measures and quantify the current state of the epidemic. This paper illustrates the potential of this approach to build a new dynamic probabilistic model to estimate the prevalence of SARS-CoV-2 infections in different compartments. Methods: We propose a new probabilistic model in which, for the first time in the epidemic literature, parameter learning is carried out using gradient-free stochastic black-box optimization techniques simulating multiple trajectories of the infection dynamics in a general way, solving an inverse problem that is defined employing the daily information from mortality records. Results: After the application of the new proposal in Spain in the first and successive waves, the result of the model confirms the accuracy to estimate the seroprevalence and allows us to know the real dynamics of the pandemic a posteriori to assess the impact of epidemiological measures by the Spanish government and to plan more efficiently the subsequent decisions with the prior knowledge obtained. Conclusions:The model results allow us to estimate the daily patterns of COVID-19 infections in Spain retrospectively and examine the population’s exposure to the virus dynamically in contrast to seroprevalence surveys. Furthermore, given the flexibility of our simulation framework, we can model situations —even using non-parametric distributions between the different compartments in the model— that other models in the existing literature cannot. Our general optimization strategy remains valid in these cases, and we can easily create other non-standard simulation epidemic models that incorporate more complex and dynamic structuresThis work has received financial support from the Spanish Ministry of Science, Innovation, and Universities under Grant RTI2018-099646-B-I00, the Consellería de Educación, Universidade e Formación Profesional and the European Regional Development Fund under Grant ED431G-2019/04S

Approximate inference on graphical models: message-passing, loop-corrected methods and applications

L'abstract è presente nell'allegato / the abstract is in the attachmen