Estudamos, através de modelagem matemática, aspectos estacionários, espaciais e temporais relacionados à propagação e controle de doenças infecciosas de transmissão direta por contato pessoa-a-pessoa. Elaboramos modelos matemáticos determinísticos fundamentados no princípio de ação de massas em Epidemiologia, levando em consideração a simetria no número de contatos entre suscetíveis e infectados, o que nos permitiu estimar a taxa per capita de contatos potencialmente infectantes e, por conseguinte, a força de infecção e os possíveis efeitos de diferentes programas de vacinação. O desenvolvimento do modelo de estado estacionário foi feito com base em dados sorológicos de rubéola (Azevedo Neto 1992) para uma população que ainda não havia sido imunizada por meio de vacinação. Analisamos, então, o efeito de três diferentes esquemas de vacinação para a rubéola, nos seguintes intervalos de idade: de 1 a 2 anos, de 7 a 8 anos e de 14 a 15 anos. A incerteza estatística na idade média de infecção foi estimada com o auxílio do método de Monte Carlo e tal metodologia foi aplicada a dados de varicela e hepatite A. Estudamos também o aspecto espacial, com a inclusão da variável distância na formulação de um modelo SIR e análise da influência do alcance de interação entre indivíduos. E, através do estudo da força de infecção em função da idade e do tempo, pudemos analisar, de modo qualitativo, diferentes cenários na evolução temporal de uma doença infecciosa. / We have studied, based on mathematical modelling, stationary, spatial and temporal features related to the propagation and control of directly transmitted infectious diseases through person-to-person contact. We have developed deterministic mathematical models founded on the mass-action principle of Epidemiology, taking into account the symmetry of contacts among susceptible and infectious individuals. Such symmetry enabled us to estimate the potentially infective per capita contact rate and, therefore, the force of infection and the possible effects of different vaccination programmes. The steady state modelling has been based on rubella serological data of a non-immunized population (Azevedo Neto 1992) and we have analysed three different vaccination schemes against rubella in the following age intervals: from 1 to 2 years of age, from 7 to 8 years of age, and from 14 to 15 years of age. The serological data variability has been considered in the estimation of the statistical uncertainty of the average age at infection by means of the Monte Carlo method and we have applied this methodology to varicella and hepatitis A data. The spatial feature in a SIR model has been studied with the analysis of the influence of the interaction range among individuals. We have also studied the force of infection as a function of age and time and we have analysed, in a qualitative way, different situations in the time evolution of an infectious disease.

Les Escherichia coli producteurs de Shiga-toxines (STEC) sont des agents pathogènes importants émergents en santé publique. Ces bactéries sont à l’origine des épidémies de colites hémorragiques et de syndrome hémolytique et urémique (SHU). La grande majorité des cas est liée à la consommation d’aliments contaminés par un type particulier de STEC appelés E. coli entérohémorragiques (EHEC) parmi lesquels on trouve les sérogroupes définis comme pathogènes par l’AFSSA : O26, O103, O111, O145 et O157.Les bovins ont depuis longtemps été identifiés comme un important réservoir de STEC. Bien que la transmission des STEC à l'homme soit fréquemment associée à la consommation de viande, les produits laitiers ont également été impliqués dans les cas humains. Le développement de méthodes rapides pour la détection des STEC les plus impliqués en pathologie humaine est donc essentiel pour assurer la sécurité des produits alimentaires. Cependant, la détection des STEC dans les aliments est problématique principalement en raison de la diversité des sérogroupes de STEC et de l'absence de caractéristiques biochimiques communes permettant de les distinguer des autres E. coli.L'objectif de cette thèse était d’optimiser le protocole de détection des STEC dans les aliments de manière à pouvoir proposer aux industriels des protocoles leur permettant une réelle maîtrise du « danger STEC » dans leur filière.Pour se faire, nous sommes intervenus à différentes étapes du protocole. Nous avons notamment sélectionné un milieu d’enrichissement permettant la détection des E. coli O26 dans les fromages au lait cru : EPT+ acriflavine + CT. Nous avons également évalué les performances d’une méthode de détection des E. coli O157 :H7 (VIDAS ECPT UP) dans la viande de boeuf. Cette nouvelle technique est basée sur l’utilisation de protéines recombinante de phage qui ciblent spécifiquement les E. coli O157. A travers cette étude, nous avons démontré la possibilité d’avoir des temps d’enrichissement minimes pour l’analyse d’échantillon de 25g (6h) et la faisabilité d’analyser des échantillons de 375g avec un ratio de dilution de ¼ et un enrichissement de 24h. Enfin nous nous sommes intéressés à l’étape de confirmation en mettant au point un test d’immuno-concentration automatisé (utilisant des protéines de phages spécifiques de nos bactéries cibles) permettant d’immuno-concentrer les 5 sérogroupes les plus connus de STEC (O26, O103, O111, O145 et O157) en une seule fois / Enterohemorrhagic Escherichia coli (EHEC) are an important subset of Shiga toxin–producing E. coli (STEC) associated with foodborne infections. These bacteria can cause hemorrhagic diarrhoeal disease and Haemolytic and Uremic Syndrome which are associated with some predominant serotypes defined by AFSSA institute: O26, O103, O111, O145 and O157.Cattle are the primary reservoir of STEC. Although STEC transmission to humans is frequently associated with consumption of meat, dairy products have also been implicated in human cases. Sensitive and rapid detection methods for STEC are essential for the food industry to ensure a safe food supply. However, the detection of STEC in foods is problematic because it’s an heterogeneous group which displays a broad range of both genotypic and phenotypic differences.The aim of this thesis was to optimize the research protocol of STEC strains in food in order to provide some protocols to the industries for improving risk management protocol.So, we involved in different steps of the protocol: the enrichment of E. coli O26 allowing their detection in raw milk cheeses after 24 h enrichment in EPT+ acriflavine + cefixime-tellurite. Then, we evaluated the VIDAS ECPT UP performances’ for the detection of E. coli O157: H7 in raw ground beef. Through this study, we showed the ability to reduce enrichment time for sample analysis of 25g (6h) and the feasibility of analyzing samples of 375g with a sample to broth ratio of ¼ after 24h enrichment. Thereafter we looked at the confirmation step. We developed and optimized automated VIDAS immuno-concentration of E. coli O157, O26, O103, O111 and O145 (VIDAS ESPT) with the use of recombinant phage proteins for capture

O comportamento de sistemas epidêmicos é frequentemente descrito de maneira determinística, através do emprego de equações diferenciais ordinárias. Este trabalho visa fornecer uma visão estocástica do problema, traçando um paralelo entre o encontro de indivíduos em uma população e o choque entre partículas de uma reação química. Através dessa abordagem é apresentado o algoritmo de Gillespie, que fornece uma forma simples de simular a evolução de um sistema epidêmico. Fundamentos de processos estocásticos são apresentados para fundamentar uma técnica para a estimação de parâmetros através de dados reais. Apresentamos ainda o modelo de Tau-leaping e o modelo difusivo elaborados através de equações diferenciais estocásticas que são aproximações do modelo proposto por Gillespie. A aplicação dos modelos apresentados é exemplificada através do estudo de dados reais da epidemia de dengue ocorrida no estado do Rio de Janeiro entre os anos de 2012 e 2013. / The behavior of epidemic systems is often described in a deterministic way, through the use of ordinary differential equations. This paper aims to provide a stochastic view of the problem, drawing a parallel between the encounter between individuals in a population and the clash between particles of a chemical reaction. Through this approach is presented the Gillespie algorithm, which provides a simple way to simulate the evolution of an epidemic system. Fundamentals of stochastic process theory are presented to support a technique for estimating parameters through real data. We present the model of Tau-leaping and the diffusive model elaborated by stochastic differential equations that are approximations of the model proposed by Gillespie. The application of the presented models is exemplified through the study of real data of the dengue epidemic occurred in the state of Rio de Janeiro between the years of 2012 and 2013.

This dissertation examines how certain epidemic outbreaks become "global threats", that is, diseases that become the focus of international regulations and organized responses while others do not. To answer this question, this dissertation draws upon archival data collected at the World Health Organization (WHO) archives in Geneva, the Western Cape Archives in Cape Town, the British Library, British National Archives, the Wellcome Library Archives in London, and twelve qualitative interviews with senior global health actors in order to analyze five cases when disease threats were prioritized internationally as well as how these constructions patterned responses to outbreaks. I begin by exploring the formation of the first international disease controls in the 19th century, the International Sanitary Conventions, created to prevent the spread of three diseases- plague, cholera and yellow fever. I probe how these earliest conventions patterned responses to diseases covered under them and limited responses to those beyond their scope. Examining how these conventions transformed, I explore why the same disease priorities were maintained by the WHO in their International Sanitary Regulations of the 1950's. Finally, I analyze the transformation of the International Health Regulations in 2005 and its effects on the assessment of disease threat. This dissertation shows that three factors structure the construction of disease threat: epidemic orientalism, economic concerns and field dynamics. Epidemic Orientalism, a discourse motivating the construction of disease threat that first emerged in the 17th, 18th and 19th centuries, positioned the colonized world as the space from which Europe and the Imperial powers needed to be protected. This orientalist gaze prioritizes the control of diseases emanating from colonial sites that threaten international trade and commerce and has been re-inscribed in all past and present regulations. These factors explain how and why plague, cholera and yellow fever came to be maintained as the primary diseases of international concern until the 21st century. As the WHO has recently been challenged in its authority to manage disease threats, these two factors are also mediated by the WHO's manipulation of symbolic power within a new field of infectious disease management which conditions responses to outbreaks today.

Estudamos o modelo epidemiológico denominado susceptível-exposto-infectado (SEI) na rede quadrada por meio de simulações numéricas. Nesse modelo, cada sítio da rede pode estar susceptível, exposto ou infectado. Um sítio susceptível nas vizinhanças de um infectado se torna infectado com uma certa probabilidade e exposto com probabilidade complementar. Sítios infectados ou expostos permanecem para sempre nessa condição. Mostramos que os aglomerados gerados a partir de um único infectado numa rede repleta de suscetíveis são os mesmos aglomerados presentes na percolação isotrópica. Calculamos os expoentes críticos dinâmicos com bastante precisão permitindo colocar o modelo SEI na classe de universalidade da percolação dinâmica. / We have studied the epidemiologic model called susceptible-exposed-infected (SEI) on a square lattice by numerical simulations. In this model, each site of the lattice may be susceptible, exposed or infected. A susceptible site in the neighborhood of an infected site becomes infected with a given probability, or exposed with a complementary probability. Infected and exposed sites remain forever in these states. We have shown that clusters generated by a single infected site in a lattice full of susceptible are the same clusters as in the isotropic percolation. The critical dynamic exponents were calculated with large precision allowing to put the SEI model into the dynamical percolation universality class.

Introdução - No litoral sul do Estado de São Paulo, no período de 1975 a 1978, ocorreu uma epidemia, a Encefalite pelo arbovírus Rocio. A região foi objeto de estudo de diversos investigadores. Altas taxas de morbidade e mortalidade devido ao processo epidêmico foram observadas e causaram impacto socioeconômico. A maioria dos indivíduos infectados, no início da epidemia, era do sexo masculino e estava em idade produtiva, sendo trabalhadores rurais da região. Diante das limitações hospitalares e inespecificidade do tratamento na época, houve desde uma lenta convalescença, seqüelas até a ocorrência de óbitos, afetando a economia da região, que repercutiu principalmente na queda no turismo. Mediante este fato, justifica-se a importância deste estudo histórico-documental da encefalite por arbovírus Rocio. Objetivo - Objetivou-se relatar acontecimentos sociais e naturais, medidas clínicas, impactos midiáticos e avanços científicos relacionados à doença, verificando, a trajetória do Rocio. Método - Foi feita uma revisão de literatura de trabalhos publicados desde o início da epidemia até os dias atuais. As fontes consultadas foram teses, dissertações, livros, periódicos, bancos de dados de jornais e revistas, bases de dados cooperativas, relatórios de instituições públicas, contato com especialistas e comunicações em eventos. Resultados - Foi possível analisar como a mídia impressa relatou os acontecimentos sociais relacionados à epidemia e como foi a reação popular às notícias veiculadas, além de discutir a possibilidade de o homem voltar a ser acometido pelo Rocio, diante das atuais mudanças climáticas, acelerada urbanização e pressão sobre a cobertura vegetal no litoral sul do Estado, o que altera a ecologia das populações dessa região. Conclusões - Houve o desencontro entre informações veiculadas pela mídia e dados científicos fornecidos por pesquisadores e autoridades sanitárias, o que dificultava a aceitação da epidemia pela população e viabilizava a distorção de informações e criação de barreiras aos métodos de combate ao possível vetor. Ainda não se sabe como o vírus Rocio tornou-se emergente no litoral sul do Estado em 1975 e o porquê do seu silenciamento, entretanto é conhecido que esse arbovírus ainda mantém atividade, possibilitando o retorno da epidemia no país. / Introduction - On the south coast of São Paulo State, Brazil, there was an encephalitis epidemic due to the arbovirus Rocio from 1975 to 1978. Thus, the region has been the object of study by researchers. High rates of morbidity and mortality caused an enormous social impact. The most infected individuals at the beginning of the epidemic was male and was in the productive age. Facing the limitations of the hospital and nonspecific treatment at the time, there was since a slow convalescence, sequels and even the occurrence of deaths, affecting the regional economy, which mainly reflected the drop in local tourism. In view of this fact, it is the importance of this historical and documentary study of encephalitis caused by arbovirus Rocio during the epidemic period. Aim - The aim of this study was to report social and natural events, clinical measurements, media impacts and scientific advances related to the disease, checking the trajectory of virus Rocio. Method It was made a literature review of studies published since the beginning of the epidemic until the present day. The sources which were consulted: theses, dissertations, books, periodicals, databases of newspapers and magazines, electronic databases, reports from public institutions, contact with specialists in communications and events. Results - In this study, it was possible to analize how the written press communicated the social reactions related to the epidemic and how the population reacted the news communicated, in addition was possible to discuss the possibility of the human being be affected by Rocio again due to the current climate change, accelerated urbanization and pressure on the vegetation on the coast south of the State, thus changing the ecology of the population of that region. Conclusions - There was a contradiction between the information carried by the media and scientific data provided by researchers and health authorities, which hindered the acceptance of the epidemic by the population and facilitated the distortion of information. This fact created barriers to methods of combating the possible vector. It is not known how the virus Rocio has become emerging on the south coast of the State in 1975 and why it became silent, however it is know that the arbovirus still has activity, what allows the return of the epidemic in the country.

L’objectif de cette thèse est la modélisation, l’analyse mathématique et la simulation numérique de quelques modèles de transmission du VIH-SIDA dans une population sexuellement active donnée en général et en particulier dans celle du Mali. Nous proposons de modèles basés sur les connaissances actuelles de la transmission du virus du VIH. A cet effet, nous présentons trois modèles : un modèle comportemental en épidémiologie, un modèle qui incorpore le rôle des campagnes de sensibilisation en santé publique et un modèle de co-circulation de deux formes recombinantes du VIH-1. Dans le premier modèle, des résultats d’existence et d’unicité de la solution d’un problème parabolique semi-linéaire décrivant l’évolution d’une population soumise à l’infection du VIH sont présentés. La population est divisée en individus dont le risque comportemental est faible et en individus dont les comportement sont très risqués et qui interagissent entre eux. Une variable continue représentant ce risque comportemental est introduit. Le comportement asymptotique en temps du problème est étudié. Certains résultats numériques concernant la répartition de la population selon la variable représentant le risque comportemental sont présentés dans le cas de l’infection du VIH-SIDA au Mali. Dans les deux derniers modèles, nous obtenons une analyse complète de la stabilité de ces modèles à l’aide des techniques de Lyapunov suivant la valeur du taux de reproduction de base . Nous proposons une méthode alternative au taux de reproduction de base qui permet de confiner l’évolution de la maladie dans des limites fixées. Nous illustrons ces modèles par des simulations numériques. Ces dernières sont faites à partir de nos modèles confrontés aux données du Mali concernant la propagation du VIH-SIDA. / The objective of this thesis is the modeling, mathematical analysis and numerical simulation of a few models of transmission of the HIV-AIDS in a sexually active population given in general and in particular in that of Mali. We propose models based on the epidemiology currently known from the transmission of the HIV virus. Thus, we present three models of the transmission of HIV: a individual behavior and epidemiological model, a model that incorporates the role of public health education program on HIV and a mathematical model for the co-circulating into two circulating recombinants forms of HIV-1. In the first model, Somé results of existence and uniqueness of solution of a semilinear,parabolic problem describing the evolution of a population subjected to a disease are presented. The population is divided into individuals whose behavioral risk is low and in individuals whose behavior are very risky and that interact between them. A continuous variable representing a behavioral risk is introduced. The asymptotic in time of the problem is studied, and the existence of a non zero stationary state is proved. Somé numerical results concerning the distribution of the population according to the variable representing a behavioral risk are presented within the disease of the HIV-AIDS in Mali. In the last two models, we obtain a thorough analysis of the stability of these models using the Lyapunov techniques according to the value of the basic reproduction ratio,R0. We propose an alternative method to the basic reproductive rate R0 which allows to confine the evolution of the disease in the fixed limits. Numerical simulations are done to illustrate the behaviour of the model, using data collected in the literature regarding the spread of HIV in Mali.

Associamos independentemente a cada vértice v de un grafo infinito G um raio de infecção aleatório R_v e definimos um modelo de percolação sujeito às seguintes regras: (1) no tempo zero só a raiz é declarada infectada, (2) um vértice é declarado infectado em um instante t, t>0, se está a uma distância no maximo R_v de algum vértice v previamente infectado, e (3) vértices infectados permanecem infectados para sempre. Dizemos que há sobrevivência em uma realização particular do modelo se o número final de vértices infectados é infinito. Neste trabalho damos condições suficientes sobre o grafo G para a transição de fase deste modelo, estabelecendo limitantes não triviais para o parâmetro crítico quando os raios R_v têm distribuição geometrica de parâmetro 1-p. Além disto, restringindo nosso estudo para o caso das árvores esfericamente simétricas, obtemos um melhor limitante superior para este parâmetro. Finalmente, concluímos que o parâmetro crítico para o modelo nas árvores homogêneas de grau d+1 se comporta assintoticamente como 1/(2d). / We assign independently to each vertex v of an infinite graph G, a random radius of infection R_v and define a percolation model subject to the following rules: (1) at time zero, only the root is declared infected, (2) a vertex is declared infected at time t, t>0, if it is at distance at most R_v of some vertex v previously infected, and (3) infected vertices stay infected forever. We say that there is survival in a particular realization of the model if the final number of infected vertices is infinite. In this work, we give sufficient conditions on the graph G for the phase transition of this model, by stating non-trivial bounds for the critical parameter when the radii have geometrical distribution with parameter 1-p. In addition, restricting our study to the case of the spherically symmetric trees, we obtain an improved upper bound for this critical parameter. Finally, we conclude that the critical parameter for the model on homogeneous trees of degree (d+1) behaves asymptotically as 1/(2d).

Estudamos um sistema de partículas a tempo discreto cuja dinâmica é a seguinte. Considere que no instante inicial sobre cada inteiro não negativo há uma partícula, inicialmente inativa. A partícula da origem é ativada e instantaneamente ativa um conjunto aleatório contíguo de partículas que estão a sua direita. Como regra, no instante seguinte ao que foi ativada, cada partícula ativa realiza esta mesma dinâmica de modo independente de todo o resto. Dizemos que o processo sobrevive se em qualquer momento sempre há ao menos uma partícula ativa. Chamamos este processo de Firework, associando a dinâmica de ativação de uma partícula inativa a uma infecção ou explosão. Nosso interesse é estabelecer se o processo tem probabilidade positiva de sobrevivência e apresentar limites para esta probabilidade. Isto deve ser feito em função da distribuição da variável aleatória que define o raio de ação de uma partícula. Associando o processo de ativação a uma infecção, podemos pensar este modelo como um modelo epidêmico. Consideramos também algumas variações dessa dinâmica. Dentre elas, variantes com partículas distribuídas sobre a semirreta dos reais positivos (nesta vertente, existem condições para as distâncias entre partículas consecutivas) e também com as partículas distribuídas sobre vértices de árvores. Estudamos também para esses casos a transição de fase e probabilidade de sobrevivência. Nesta variante os resultados obtidos são funções da sequência de distribuições dos alcances das explosões e da estrutura dos lugares onde se localizam as partículas. Consideramos também variações do modelo onde cada partícula ao ser ativada, permanece ativa durante um tempo aleatório e nesse período emite explosões que ocorrem em instantes aleatórios. / We studied a discrete time particle system whose dynamic is as follows. Consider that at time zero, on each non-negative integer, there is a particle, initially inactive. A particle which is placed at origin is activated and instantly activates a contiguous random set of particles that is on its right. As a rule, the next moment to what it has been activated, each active particle carries the same behavior independently of the rest. We say that the process survives if the amount of particles activated along the process is infinite. We call this the Firework process, associating the activation dynamic of a particle to an infection or explosion process. Our interest is to establish whether the process has positive probability of survival and to present limits to this probability. This is done according to the distribution random variable that defines the radius of infection of each active particle, Associating the activation process to an infection, we think this model as a model epidemic. We also consider some variations of this dynamic. Among them, variants with particles distributed over the half line (there are conditions for the distances between consecutive particles) and also with particles distributed over the vertices of a tree. We studied phase transitions and the correspondent survival probability. In this variant the results depend on the sequence of probability distributions for the range of the explosions and on the particles displacement. We also consider a variation where each particle after activated, remains active during a random time period emitting explosions that occur in random moments.

Objectives: Explain ideas to achieve meaningful, synergistic partnerships in combating the opioid crisis by leveraging unique areas of healthcare expertise (i.e., medical, payer, pharmacy) in collaboration with other key healthcare and policy experts. Describe innovative, results-driven solutions in development or in the marketplace to address opioid prescribing practices from the unique perspective of providers, pharmacists, health plans, patients and caregivers. Learn about the system breakdowns from patient and family member perspectives. Share possibilities for better integrating the voice and role of individuals living with addiction and caregivers into important solutions combating the opioid crisis. Identify the greatest, most near-term opportunities for improvements or system-wide changes, generally and for PQA.