Актуальность темы магистерской диссертации заключается в ее тесной связи с глобальной пандемией нового коронавируса, при этом особое внимание уделяется распространению эпидемии и борьбе с ней. Целью исследования является предоставление научной и научно обоснованной поддержки путем разработки моделей и симуляций политики профилактики эпидемий в сообществе. Основная цель диссертационной работы – оценить факторы, влияющие на эффективность стратегий профилактики и контроля, а также раскрыть ключевые факторы и механизмы передачи эпидемии. Посредством симуляционных экспериментов, анализа и сравнения результатов создается исчерпывающая информация, которая поможет лицам, принимающим решения, формулировать и осуществлять более эффективную политику профилактики эпидемий на уровне сообщества. Целью данного исследования является изучение влияния мобильности населения и планировки жилого массива на передачу заболеваний и эффективность стратегий профилактики эпидемий. Предметом исследования является разработка системы моделирования и симуляции политики предотвращения эпидемий на уровне сообщества с использованием модели SIR и сети «малого мира» в жилом сообществе с численностью населения 500 человек. Научная новизна данного исследования заключается в сочетании классической модели SIR с сетевой моделью маленького мира, а также в использовании агентной модели и программного обеспечения NetLogo для моделирования. Этот инновационный подход учитывает взаимодействие и связи между людьми в сообществе, позволяя более точно моделировать распространение болезней и оценивать эффекты различных стратегий профилактики эпидемий. Практическая значимость исследования заключается в обеспечении научной основы и руководства для лиц, принимающих решения. Путем проведения симуляционных экспериментов и анализа результатов исследование оптимизирует разработку и реализацию политики профилактики эпидемий на уровне сообщества, эффективно контролируя распространение заболеваний, защищая здоровье населения и решая проблемы, связанные с инфекционными заболеваниями. / The relevance of the master's thesis topic lies in its close connection to the global novel coronavirus pandemic, specifically focusing on the spread and control of the epidemic. The research aims to provide scientific and evidence-based support by developing community epidemic prevention policy models and simulations. The main goal of the thesis is to evaluate the factors influencing the effectiveness of prevention and control strategies and uncover the key factors and mechanisms of epidemic transmission. Through simulation experiments, analysis, and comparison of results, comprehensive information is generated to assist decision makers in formulating and implementing more effective community epidemic prevention policies. The objective of this study is to examine the influence of population mobility and the layout of a residential community on disease transmission and the effectiveness of epidemic prevention strategies. The subject of research focuses on developing a modeling and simulation framework for community epidemic prevention policies using the SIR model and small-world network in a residential community with a population size of 500 individuals. The scientific novelty of this study lies in the combination of the classic SIR model with the small-world network model, along with the introduction of the agent model and NetLogo software for simulation. This innovative approach considers the interactions and connections between individuals in a community, enabling a more accurate modeling of disease spread and evaluation of the effects of different epidemic prevention policies. The practical significance of the research lies in its provision of scientific basis and guidance to decision makers. By conducting simulation experiments and analyzing the results, the study optimizes the formulation and implementation of community epidemic prevention policies, effectively controlling the spread of diseases, protecting public health, and addressing the challenges posed by infectious diseases.

Estuda-se o espalhamento de doenças contagiosas utilizando modelos suscetível-infectado-recuperado (SIR) representados por equações diferenciais ordinárias (EDOs) e por autômatos celulares probabilistas (ACPs) conectados por redes aleatórias. Cada indivíduo (célula) do reticulado do ACP sofre a influência de outros, sendo que a probabilidade de ocorrer interação com os mais próximos é maior. Efetuam-se simulações para investigar como a propagação da doença é afetada pela topologia de acoplamento da população. Comparam-se os resultados numéricos obtidos com o modelo baseado em ACPs aleatoriamente conectados com os resultados obtidos com o modelo descrito por EDOs. Conclui-se que considerar a estrutura topológica da população pode dificultar a caracterização da doença, a partir da observação da evolução temporal do número de infectados. Conclui-se também que isolar alguns infectados causa o mesmo efeito do que isolar muitos suscetíveis. Além disso, analisa-se uma estratégia de vacinação com base em teoria dos jogos. Nesse jogo, o governo tenta minimizar os gastos para controlar a epidemia. Como resultado, o governo realiza campanhas quase-periódicas de vacinação. / The spreading of contagious diseases is studied by using susceptible-infected-recovered (SIR) models represented by ordinary differential equations (ODE) and by probabilistic cellular automata (PCA) connected by random networks. Each individual (cell) of the PCA lattice experiences the influence of others, where the probability of occurring interaction with the nearest ones is higher. Simulations for investigating how the disease propagation is affected by the coupling topology of the population are performed. The numerical results obtained with the model based on randomly connected PCA are compared to the results obtained with the model described by ODE. It is concluded that considering the topological structure of the population can pose difficulties for characterizing the disease, from the observation of the time evolution of the number of infected individuals. It is also concluded that isolating a few infected subjects can cause the same effect than isolating many susceptible individuals. Furthermore, a vaccination strategy based on game theory is analyzed. In this game, the government tries to minimize the expenses for controlling the epidemic. As consequence, the government implements quasi-periodic vaccination campaigns.

Submitted by Anna Patricia Pachas Manrique (annapamanrique@gmail.com) on 2017-02-23T20:20:56Z No. of bitstreams: 1 20_02 (1).pdf: 1460371 bytes, checksum: e98c8f4713680550a770e8efcc7ffa14 (MD5) / Approved for entry into archive by Janete de Oliveira Feitosa (janete.feitosa@fgv.br) on 2017-08-03T17:52:37Z (GMT) No. of bitstreams: 1 20_02 (1).pdf: 1460371 bytes, checksum: e98c8f4713680550a770e8efcc7ffa14 (MD5) / Made available in DSpace on 2017-08-18T14:34:31Z (GMT). No. of bitstreams: 1 20_02 (1).pdf: 1460371 bytes, checksum: e98c8f4713680550a770e8efcc7ffa14 (MD5) Previous issue date: 2016-08-29 / The speed and comprehensiveness global level with the pathogen has spread in recent years has drawn attention to the importance of the contact’s social network structure. In fact, the topology of the networks in which members of society interact has influenced the dynamics of epidemics. Studies have shown that pathogens when disiparem in scale-free networks have different effects when compared broadcast in random networks, such as the classic models. In these there were epidemic threshold, may somehow the health ministry have a control on the dissipation of diseases by applying certain measures such as vaccines. Already in models in which are considered the networks, specifically the free network scale, the threshold disappears. Thus, the epidemic threshold depends on the topology is required to include within this structure models Because of the importance of these networks, random networks and scalefree have been implemented along the epidemics of propagation models to check the epidemic threshold and the characteristic time, noting that the epidemic threshold disappears / A velocidade e a abrangência a nível mundial com que os agentes patogênicos tem se disseminado nos últimos anos tem chamado a atenção para a importância da estrutura da rede social de contato . De fato, a topologia das redes na qual os membros da sociedade interagem têm influenciado na dinâmica das epidemias.Estudos têm demostrado que os agentes patogênicos ao se dissiparem em redes livres de escala tem efeitos diferentes se comparado quando difundidos em redes aleatórias, como nos modelos clássicos. Nestes existiam limiar de epidemia ,podendo de alguma forma as entidades de saúde ter um controle sobre a dissipação das enfermidades , aplicando certas medidas como as vacinas por exemplo. Já nos modelos nos quais são consideradas as redes , especificamente a rede livre de escala,este limiar desaparece. Desta forma, o limiar de epidemia ao depender da topologia se faz necessário incluir esta estrutura dentro dos modelos epidemiológicos. Devido a importância destas redes , redes aleatórias e principalmente redes livres de escala foram implementadas junto a modelos de propagação de epidemias para verificar o limiar de epidemia e o tempo característico , verificando que o limiar de epidemia desaparece.

Estuda-se o espalhamento de doenças contagiosas utilizando modelos suscetível-infectado-recuperado (SIR) representados por equações diferenciais ordinárias (EDOs) e por autômatos celulares probabilistas (ACPs) conectados por redes aleatórias. Cada indivíduo (célula) do reticulado do ACP sofre a influência de outros, sendo que a probabilidade de ocorrer interação com os mais próximos é maior. Efetuam-se simulações para investigar como a propagação da doença é afetada pela topologia de acoplamento da população. Comparam-se os resultados numéricos obtidos com o modelo baseado em ACPs aleatoriamente conectados com os resultados obtidos com o modelo descrito por EDOs. Conclui-se que considerar a estrutura topológica da população pode dificultar a caracterização da doença, a partir da observação da evolução temporal do número de infectados. Conclui-se também que isolar alguns infectados causa o mesmo efeito do que isolar muitos suscetíveis. Além disso, analisa-se uma estratégia de vacinação com base em teoria dos jogos. Nesse jogo, o governo tenta minimizar os gastos para controlar a epidemia. Como resultado, o governo realiza campanhas quase-periódicas de vacinação. / The spreading of contagious diseases is studied by using susceptible-infected-recovered (SIR) models represented by ordinary differential equations (ODE) and by probabilistic cellular automata (PCA) connected by random networks. Each individual (cell) of the PCA lattice experiences the influence of others, where the probability of occurring interaction with the nearest ones is higher. Simulations for investigating how the disease propagation is affected by the coupling topology of the population are performed. The numerical results obtained with the model based on randomly connected PCA are compared to the results obtained with the model described by ODE. It is concluded that considering the topological structure of the population can pose difficulties for characterizing the disease, from the observation of the time evolution of the number of infected individuals. It is also concluded that isolating a few infected subjects can cause the same effect than isolating many susceptible individuals. Furthermore, a vaccination strategy based on game theory is analyzed. In this game, the government tries to minimize the expenses for controlling the epidemic. As consequence, the government implements quasi-periodic vaccination campaigns.

No description available.

Cette thèse propose une étude mathématique des stratégies de vaccination.La partie I présente le cadre mathématique, notamment le modèle à compartiments Susceptible - Infected – Recovered.La partie II aborde les techniques mathématiques de type contrôle optimal employées afin de trouver une stratégie optimale de vaccination au niveau de la société. Ceci se fait en minimisant le coût de la société. Nous montrons que la fonction valeur associée peut avoir une régularité plus faible que celle attendue dans la littérature. Enfin, nous appliquons les résultats à la vaccination contre la coqueluche.La partie III présente un modèle où le coût est défini au niveau de l'individu. Nous reformulons le problème comme un équilibre de Nash et comparons le coût obtenu avec celui de la stratégie sociétale. Une application à la grippe A(H1N1) indique la présence de perceptions différentes liées à la vaccination.La partie IV propose une implémentation numérique directe des stratégies présentées. / This thesis propose a mathematical analysis of the vaccination strategies.The first part introduces the mathematical framework, in particular the Susceptible – Infected – Recovered compartmental model.The second part introduces the optimal control tools used to find an optimal vaccination strategy from the societal point of view, which is a minimizer of the societal cost. We show that the associated value function can have a less regularity than what was assumed in the literature. These results are then applied to the vaccination against the whooping cough.The third part defines a model where the cost is defined at the level of the individual. We rephrase this problem as a Nash equilibrium and compare this results with the societal strategy. An application to the Influenza A(H1N1) 2009-10 indicates the presence of inhomogeneous perceptions concerning the vaccination risks.The fourth and last part proposes a direct numerical implementation of the different strategies.