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    Modèles d’épidémies en dimension infinie et optimisation des stratégies de vaccination

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    This thesis is motivated by the mathematical modelling of heterogeneity in human contacts and the consequences on the dynamic and the control of contagious diseases.In the first part of the thesis, we introduce and study an infinite-dimensional deterministic SIS (Susceptible/Infected/Susceptible) model which takes into account the heterogeneity of contacts within a large population. Thanks to the monotonic properties of the flow of these equations, we prove a result on the long-time behavior of the proportion of infected people. The basic reproduction number R0, defined as the spectralradius of a kernel operator, determines whether there exists a stable endemic equilibrium (R0 > 1) or if all the solutions tends to the disease-free equilibrium (R0 1) ou si toutes les solutions convergent vers l’état d’équilibre sans individus infectés (R0 1, il suffit de vacciner une proportion 1-1/R0 de la population atteindre l'immunité de groupe et éradiquer la maladie selon le théorème du seuil. Dans les modèles hétérogènes, ce théorème reste vrai mais avec une meilleure répartition des doses, on peut espérer atteindre l'immunité de groupe à moindre coût. Ainsi, nous étudions le problème où l’on cherche à minimiser à la fois le coût de la vaccination et une fonction perte qui peut être soit lenombre de reproduction effectif, soit la proportion totale d’infectés dans l’état endémique. En prouvant la continuité de ces deux fonctions pertes par rapport à une certaine topologie bien choisie, nous obtenons l’existence de stratégies Pareto optimales. Nous montrons également que si le nombre de reproduction de base est strictement supérieur à 1, alors la stratégie qui consiste à vacciner selon le profil des susceptibles dansl’état endémique est critique au sens où elle conduit à un nombre de reproduction effectif égal à 1.Enfin, nous étudions les propriété du nombre de reproduction effectif et le problème de minimisation bi-objectif associé. Nous démontrons une généralisation de la conjecture de Hill-Longini sur la concavité et la convexité du nombre de reproduction effectif ainsi que d'autres résultats théoriques sur cette fonction perte. Ces derniers seront ensuite illustrés par de nombreux exemples. En particulier, les trois questions suivantes nous guideront notre analyse.- Est-il possible de toujours vacciner optimalement quand les doses de vaccins ne sont disponibles qu'au fur et à mesure ?- Quel est l’effet de l’assortativité (propension des individus à créer des liens avec des individus aux caractéristiques communes) sur le profils des vaccination optimale ?- Que se passe-t-il quand tous les individus de la population ont le même nombre de contacts

    Epidemics models in infinite-dimension and optimal vaccination strategies

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    Cette thèse est motivée par la modélisation mathématique de l'hétérogénéité des contats dans les populations humaines et son impact sur la dynamique et le contrôle d'une maladie transmissible.La première partie de la thèse porte sur l'étude d'un modèle SIS (Susceptible/Infected/Susceptible) déterministe en dimension infinie qui prend en compte l’hétérogénéité des contacts dans une population de grande taille. Grâce aux propriétés monotones que vérifient les solutions de ces équations différentielles, nous prouvons un résultat qui, comme pour les modèles en dimension finie, donne le comportement en temps long de la proportion d'infectés. En effet, le nombre de reproduction de base R0, défini comme le rayon spectral d'un opérateur à noyau, détermine s'il existe un équilibre endémique stable (R0 > 1) ou si toutes les solutions convergent vers l’état d’équilibre sans individus infectés (R0 1, il suffit de vacciner une proportion 1-1/R0 de la population atteindre l'immunité de groupe et éradiquer la maladie selon le théorème du seuil. Dans les modèles hétérogènes, ce théorème reste vrai mais avec une meilleure répartition des doses, on peut espérer atteindre l'immunité de groupe à moindre coût. Ainsi, nous étudions le problème où l’on cherche à minimiser à la fois le coût de la vaccination et une fonction perte qui peut être soit lenombre de reproduction effectif, soit la proportion totale d’infectés dans l’état endémique. En prouvant la continuité de ces deux fonctions pertes par rapport à une certaine topologie bien choisie, nous obtenons l’existence de stratégies Pareto optimales. Nous montrons également que si le nombre de reproduction de base est strictement supérieur à 1, alors la stratégie qui consiste à vacciner selon le profil des susceptibles dansl’état endémique est critique au sens où elle conduit à un nombre de reproduction effectif égal à 1.Enfin, nous étudions les propriété du nombre de reproduction effectif et le problème de minimisation bi-objectif associé. Nous démontrons une généralisation de la conjecture de Hill-Longini sur la concavité et la convexité du nombre de reproduction effectif ainsi que d'autres résultats théoriques sur cette fonction perte. Ces derniers seront ensuite illustrés par de nombreux exemples. En particulier, les trois questions suivantes nous guideront notre analyse.- Est-il possible de toujours vacciner optimalement quand les doses de vaccins ne sont disponibles qu'au fur et à mesure ?- Quel est l’effet de l’assortativité (propension des individus à créer des liens avec des individus aux caractéristiques communes) sur le profils des vaccination optimale ?- Que se passe-t-il quand tous les individus de la population ont le même nombre de contacts ?This thesis is motivated by the mathematical modelling of heterogeneity in human contacts and the consequences on the dynamic and the control of contagious diseases.In the first part of the thesis, we introduce and study an infinite-dimensional deterministic SIS (Susceptible/Infected/Susceptible) model which takes into account the heterogeneity of contacts within a large population. Thanks to the monotonic properties of the flow of these equations, we prove a result on the long-time behavior of the proportion of infected people. The basic reproduction number R0, defined as the spectralradius of a kernel operator, determines whether there exists a stable endemic equilibrium (R0 > 1) or if all the solutions tends to the disease-free equilibrium (R0 <= 1).As an application, we formalize and study the problem of optimal allocation strategies for a vaccine that completely immunize from the disease those who received it. When we suppose that the contacts in the population are homogeneous, the threshold theorem states that the incidence of the infection will decrease if the proportion of vaccinated persons in the population is at least equal to 1-1/R0. In inhomogeneous models, this theorem remains true but with a better allocation of vaccine doses, we can hope for reaching herd immunity at lower cost. Hence, we study the problem where one tries to minimize simultaneously the cost of the vaccination, and a loss that may be either the effective reproduction number, or the overall proportion of infected individuals in the endemic state. By proving the continuity of these two loss functions, we obtain the existence of Pareto optimal strategies. We also show that vaccinating according to the profile of the endemic state is a critical allocation, in the sense that, if the initial reproduction number is larger than 1, then this vaccination strategy yields an effective reproduction number equal to 1.The last part of the thesis is a detailed study of the effective reproduction number and the bi-objective minimization problem associated. We prove a generalization of the Hill-Longini conjecture on the concavity and convexity of the effective reproduction number along with other theoretical results on this loss function. We then illustrate with multiple examples those properties. In particular, we investigate the three following questions.- Is it possible to always vaccinate optimally when the vaccine doses are given one at a time?- What is the effect of assortativity (the tendency to have more contacts with similar individuals) on the shape of optimal vaccination strategies?- What happens when every individuals have the same number of neighbors

    Going Beyond Counting First Authors in Author Co-citation Analysis

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    The present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed

    Méthode d'adaptation de discrétisation et de modèle basée sur l'adjoint pour les systèmes hyperboliques avec relaxation

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    International audienceIn this work, we use an adjoint-weighted residuals method for the derivation of an a posteriori model and discretization error estimators in the approximation of solutions to hyperbolic systems with stiff relaxation source terms and multiscale relaxation rates. These systems are parts of a hierarchy of models where the solution reaches different equilibrium states associated to different relaxation mechanisms. The discretization is based on a discontinuous Galerkin method which allows to account for the local regularity of the solution during the discretization adaptation. The error estimators are then used to design an adaptive model and discretization procedure which selects locally the model, the mesh, and the order of the approximation and balances both error components. Coupling conditions at interfaces between different models are imposed through local Riemann problems to ensure the transfer of information. The reliability of the present hpm-adaptation procedure is assessed on different test cases involving a Jin--Xin relaxation system with multiscale relaxation rates, and results are compared with standard hp-adaptation

    Variations on the Author

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    “Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship

    Appropriate Similarity Measures for Author Cocitation Analysis

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    We provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis

    Dispelling the Myths Behind First-author Citation Counts

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    We conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more sophisticated methods

    Author Index

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    koamabayili/VECTRON-author-checklist: VECTRON author checklist

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    We have done our best to complete the author checklist relating to the use of animals in the hut study. Note that the objective for the hut study was to evaluate the IRS treatment applications for residual efficacy against Anopheles mosquitoes, including the local An. coluzzii mosquito population. Cows were only used to attract mosquitoes into the huts and no tests were carried out directly on the cows. The author checklist is intended for use with studies where experiments are carried out on animals, which is why we have had such difficulty in completing this for the hut study, as many of the questions do not relate to how the cows were used
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