Despite being developed in the late 1920s, compartmental epidemic modeling is still a rich and fruitful area of research. The original compartmental epidemic models were SIR (Susceptible, Infectious, Removed) models, which assume permanent immunity after recovery. SIR models, along with the more recent SEIR (Susceptible, Exposed, Infectious, Removed) models are still the gold standard in modeling pathogens that confer permanent immunity. This dissertation expands the SEIR structure to include a new class of spatial SEIR models. The exponential assumption of these models states that the latent and infectious times of the pathogen are exponentially distributed. Work that relaxes this assumption and still allows for mixing to occur at the population level is limited, thereby making strong assumptions about these times. We relax this assumption in a flexible way, by considering a hybrid approach that contains characteristics of both population level and individual level approaches. Next, we expand the Conditional Autoregressive (CAR) class of spatial models. This is to account for the Mumps data set we have procured, which contains mismatched lattice structures that cannot be handled by traditional CAR models. The use of CAR models is desirable here, as these models are known to produce spatial smoothing on lattices, and are a natural way to draw strength spatially in estimating spatial effects. Finally, we develop a pair of spatial SEIR models utilizing our CAR structure. The first utilizes the exponential assumption, which is very robust. The second develops a highly flexible spatial SEIR model by embedding the CAR structure into the SEIR structure. This allows for a realistic analysis of epidemic data occurring on a lattice. These models are applied to the Iowa Mumps epidemic of 2006. There are three questions of interest. First, what improvement do the methods proposed here provide over the current models in the literature? Second, did spring break, which occurred approximately 40 days into the epidemic, have an effect on the overall number of new infections? Thirdly, did the public's awareness of the epidemic change the rate at which mixing occurred over time? The spatial models in this dissertation are adequately constructed to answer these questions, and the results are provided.

The systems of equations created by Blower et al. (1995) and Jia et al. (2007) designed to model the dynamics of Tuberculosis are solved using the computer software SIMULINK. The results are first employed to examine the intrinsic transmission dynamics of the disease through two models developed by Blower et al. (1995). The "simple transmission model" was used primarily to give insight to the behavior of the susceptible, latent, and infectious groups of individuals. Then, we consider a more detailed transmission model which includes several additional factors. This model captures the dynamics of not only the susceptible, latent and infectious groups but also the non-infectious cases and the recovered cases. Using the SIMULINK results, it can be shown that the intrinsic dynamics of the disease contribute to the rise and decline of the disease seen in historical accounts. Next, the simulation results are used to study the equilibrium points of the disease which can be obtained by varying the parameters and therefore changing the value for the basic reproduction ratio (R0 ). Our model uses the system of equations developed by Jia et al. (2007). The SIMULINK results are used to visually confirm the hypothesis proposed by Jia et al. (2007) that the equilibrium behavior of the system when R0 > 1 is globally asymptotically stable.

The static linearity test is one of the fundamental production tests used to measure DC performance of analog to digital converters (ADCs). It comes with high test equipment cost. An ADC built-in-self-test (BIST) is an attractive solution. However the stringent linearity requirement for an on-chip signal generator has made it prohibitive. The stimulus error identification and removal (SEIR) method has greatly reduced the linearity requirement. However, it requires a highly stable voltage offset, which remains a daunting task. This work exploits the inherit capacitive sample-and-hold circuit used in various ADC architectures to inject offset with very good constancy. A 16-bit successive approximate register (SAR) ADC with the proposed BIST scheme is modeled and simulated in Matlab to prove its validity. The results show that the estimation error on the maximum INL is less than 0.07 LSB. This BIST solution is then naturally extended to the calibration of an ADC. It is shown missing codes of such ADC can be effectively estimated and calibrated out. / text

Este trabalho consiste numa abordagem inicial sobre o dengue e aspectos epidemiológicos ut ilizados no desenvolvimento de um modelo de transmissão para esta doença infecciosa. O objetivo é desenvolver e implementar o modelo epidemiológico SEIR de transmissão do dengue associado ao modelo para sistemas "multi-patch": com a finalidade de avaliar teoricamente o efeito da migração dos humanos no curso da epidemia em redes de populações acopladas. Apresentam-se o modelo SEIR de transmissão do dengue, com dinãmica vital, para uma população hipotética interagindo, e o modelo para sistemas "multi-patch" associado ao modelo SEIR, considerando a migração nas redes de populações acopladas, onde uma população é dividida em sítios. Com simulações numéricas pode-se avaliar a progressão da epidemia nesta rede, bem como verificar o efeito da migração dos humanos. / This work consists of an initial survey over dengue and its epidemic aspects used in the development of a transmission pattern of t his infectious disease. The goal is to develop an epidemiological dengue transmission model (SEIR model) associated with a multi-patch system in order to theoretically evaluate the human migration effect during the epidemic. The SEIR transmission model is presented with vital dynamics in an interacting hypothetic set of humans and mosquitoes, considering the movement in coupled map lattices, in which a population is split in patches. Using numerical simulations we could evaluate the epidemic growth in this lattice as well as the human movement.

Este trabalho consiste numa abordagem inicial sobre o dengue e aspectos epidemiológicos ut ilizados no desenvolvimento de um modelo de transmissão para esta doença infecciosa. O objetivo é desenvolver e implementar o modelo epidemiológico SEIR de transmissão do dengue associado ao modelo para sistemas "multi-patch": com a finalidade de avaliar teoricamente o efeito da migração dos humanos no curso da epidemia em redes de populações acopladas. Apresentam-se o modelo SEIR de transmissão do dengue, com dinãmica vital, para uma população hipotética interagindo, e o modelo para sistemas "multi-patch" associado ao modelo SEIR, considerando a migração nas redes de populações acopladas, onde uma população é dividida em sítios. Com simulações numéricas pode-se avaliar a progressão da epidemia nesta rede, bem como verificar o efeito da migração dos humanos. / This work consists of an initial survey over dengue and its epidemic aspects used in the development of a transmission pattern of t his infectious disease. The goal is to develop an epidemiological dengue transmission model (SEIR model) associated with a multi-patch system in order to theoretically evaluate the human migration effect during the epidemic. The SEIR transmission model is presented with vital dynamics in an interacting hypothetic set of humans and mosquitoes, considering the movement in coupled map lattices, in which a population is split in patches. Using numerical simulations we could evaluate the epidemic growth in this lattice as well as the human movement.

Este trabalho consiste numa abordagem inicial sobre o dengue e aspectos epidemiológicos ut ilizados no desenvolvimento de um modelo de transmissão para esta doença infecciosa. O objetivo é desenvolver e implementar o modelo epidemiológico SEIR de transmissão do dengue associado ao modelo para sistemas "multi-patch": com a finalidade de avaliar teoricamente o efeito da migração dos humanos no curso da epidemia em redes de populações acopladas. Apresentam-se o modelo SEIR de transmissão do dengue, com dinãmica vital, para uma população hipotética interagindo, e o modelo para sistemas "multi-patch" associado ao modelo SEIR, considerando a migração nas redes de populações acopladas, onde uma população é dividida em sítios. Com simulações numéricas pode-se avaliar a progressão da epidemia nesta rede, bem como verificar o efeito da migração dos humanos. / This work consists of an initial survey over dengue and its epidemic aspects used in the development of a transmission pattern of t his infectious disease. The goal is to develop an epidemiological dengue transmission model (SEIR model) associated with a multi-patch system in order to theoretically evaluate the human migration effect during the epidemic. The SEIR transmission model is presented with vital dynamics in an interacting hypothetic set of humans and mosquitoes, considering the movement in coupled map lattices, in which a population is split in patches. Using numerical simulations we could evaluate the epidemic growth in this lattice as well as the human movement.

Orientadores: Jorge Alberto Achcar, Luiz Koodi Hotta / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-17T21:22:44Z (GMT). No. of bitstreams: 1 Diniz_MarcioAugusto_M.pdf: 2168206 bytes, checksum: 900902dfc4c68974431fbf2286d5cca6 (MD5) Previous issue date: 2011 / Resumo: A modelagem matemática de epidemias apresenta grande relevância para a área de epidemiologia por possibilitar uma melhor compreensão do desenvolvimento da doença na população e permitir analisar o impacto de medidas de controle e erradicação. Neste contexto, os modelos compartimentais SEIR (Suscetíveis - Expostos - Infectantes - Removidos) que foram introduzidos por Kermarck e Mckendrick (1927 apud YANG, 2001, Capítulo 1) são extremamente utilizados. Esta dissertação discute o modelo SEIR encontrado em Lekone e Finkenstädt (2006) que considera a introdução das medidas de intervenção na taxa de contato entre suscetíveis e infectantes, e é aplicado aos dados parcialmente observados da epidemia de febre hemorrágica Ebola, ocorrida no Congo em 1995, através de métodos bayesianos. Em uma segunda etapa, o modelo é modificado a fim de considerar a introdução das medidas de intervenção também na taxa de remoção. A utilização da taxa de remoção não homogênea permite uma quantificação do impacto das medidas de intervenção mais próxima da realidade. Além disso, nos dois modelos considerados, uma análise da incerteza gerada pela observação parcial dos dados e uma análise de sensibilidade da escolha das distribuições a priori são realizadas a partir de simulações. E também, é apresentada uma discussão sobre erros de especificação da taxa de remoção Por fim, os dois modelos são aplicados aos dados da epidemia de febre hemorrágica Ebola e os resultados são discutidos / Abstract: Mathematical modeling of epidemics has great relevance to the area of epidemiology by enabling a better understanding of the development of the disease in the population and allow the analysis of the impact of eradication and control measures. In this context, SEIR (Susceptible-Exposed-Infectious-Removed) compartmental models that were introduced by Kermarck e Mckendrick (1927 apud YANG, 2001, Chapter 1) are extremely used. This essay discusses the SEIR model found in Lekone e Finkenstädt (2006) that considers the introduction of intervention measures in the contact rate between susceptible and infectious, and is applied to data partially observed the outbreak of Ebola hemorrhagic fever in Congo, held in 1995, by Bayesian methods. In a second step, the model is modified in order to consider the introduction of intervention measures in the removal rate. The use of time in-homogeneous removal rate allows quantification of the impact of intervention measures closer to reality. In addition, both models considered, an analysis of uncertainty generated by partial observation and a sensitivity analysis of the choice of a priori distributions are made from simulations. And also, a discussion about errors of removal rate specification. Finally, the two models are applied to the data of Ebola hemorrhagic fever epidemic and the results are discussed / Mestrado / Métodos Estatísticos / Mestre em Estatística

Finite-difference numerical methods are developed for the solution of some systems in the biomedical sciences; namely, a predator-prey model and the SEIR (Susceptible/Exposed/ Infectious/Recovered) measles model. First-order methods are developed to solve the predator-prey model and one second-order method is developed to solve the SEIR measles model. The predator-prey model is extended to one-space dimension to incorporate diffusion. The SEIR measles model is extended to one-space dimension to incorporate (i) diffusion, (ii) convection and (iii) diffusion-convection. The SEIR measles model is extended further to model diffusion in two-space dimensions. The reaction terms in these systems of partial differntial equations contain nonlinear expressions. Nevetheless, it is seen that the numerical solutions are obtained by solving a linear algebraic system at each time step, as opposed to solving a nonlinear algebraic systems, which is often required when integrating non-linear partial differential equations. The development of each numerical method is made in the light of experience gained in solving the system of ordinary differential equations for each system. The numerical methods proposed for the solution of the initial-value problem for the predator-prey and measles models are characterized to be implicit. However, in each case it is seen that the numerical solutions are obtained explicitly. In a series of numerical experiments, in which the ordinary differential equations are solved first of all, it is seen that the proposed methods have superior stability properties to those of the well-known, first-order, Euler method to which they are compared. Incorporating the proposed methods into the numerical solution of partial differential equations is seen to lead to economical and reliable methods for solving the systems.

Les maladies infectieuses représentent aujourd’hui un problème majeur de santé publique. Devant l’augmentation des résistances bactériennes, l’émergence de nouveaux pathogènes et la propagation rapide de l’épidémie, le suivi et la surveillance de la transmission de la maladie devient particulièrement importants. Face à une telle menace, la société doit se préparer à l'avance pour réagir rapidement et efficacement si une telle épidémie est déclarée. Cela nécessite une mise en place des dispositifs de suivi et de prévention. Dans ce contexte, nous nous intéressons, dans le présent travail, à l’élaboration d’un Système d’Information Décisionnel Spatio-temporel pour le suivi et la surveillance du phénomène de propagation de l’épidémie de la grippe saisonnière au sein de la population de la ville d’Oran (Algérie). L’objectif de ce système est double : il consiste, d’une part, à comprendre comment l’épidémie se propage par l’utilisation du réseau social Small World (SW) et du modèle à compartiments d’épidémie SEIR (Susceptible-Exposed-Infected-Removed), et d’autre part, à stocker dans un entrepôt les données multiples tout en les analysant par un outil d’analyse en ligne de donnée Spatiale dit SOLAP (Spatial On-Line Analytical Processing). / Today, infectious diseases represent a major public health problem. With the increase of bacterial resistance, the emergence of new pathogens and the rapid spread of epidemic, monitoring and surveillance of disease transmission becomes important. In the face of such a threat, the society must prepare in advance to respond quickly and effectively if an outbreak is declared. This requires setting up monitoring mechanisms and prevention.In this context, we are particularly interested by development a Spatiotemporal decision support system for monitoring and preventing the phenomenon of seasonal influenza epidemic spread in the population of Oran (city at Algeria).The objective of this system is twofold: on one hand, to understand how epidemic is spreading through the social network by using SEIR (Susceptible-Exposed-Infected-Removed) compartmental model within Small World network, and on the other hand, to store multiple data in data warehouse and analyzing it by a specific online analysis tool Spatial OLAP (Spatial on-line Analytical Processing).

A modified SEIR compartmental model is constructed for COVID-19 in a metapopulational setting with fine-scaled population data. The model is stochastically simulated with GLEAMviz that provides realistic short and long distance mobility based on real-world data. A retrospective evaluation in both the temporal and spatial dimensions is conducted with over one year of collected data from the COVID-19 pandemic in Sweden. We find that to reproduce the multimodal behavior a seasonal scaling factor of 0.4 is necessary, which is introduced to the model by scaling R0 with corresponding sinusoidal. For the spatial dimension we divide Sweden into a southern, middle and northern region and the model is able to capture the dynamics in all regions. Additionally, we introduce compartmental models in a constructive manner and motivate metapopulational models, including how commuting is integrated by a force of infection. The next generation method for calculating the basic reproductive number for arbitrary compartmental models is also presented.