The principal motivations for studying epidemics and their dynamics are understanding the biological characteristics of the epidemic agents and reducing the economical and social costs originating from epidemic outbreaks. The most commonly used epidemic models have important assumptions such as the law of mass action, and the latent and infectious periods being exponentially distributed with xed parameters. Under this kind of suppositions the models are analyzed with well known algorithms as the Euler and Euler-Maruyama, and methodology and results from the theory of Markovian processes. However, these assumptions are selected largely for their analytic convenience and in many cases are far from describing the agent's transmissibility attributes in the population and its biological characteristics in a host. The epidemic models studied here relax two important epidemic assumptions. The first to be relaxed is the one that susceptible individuals are equally likely to acquire the disease. A structure for the kind of individual contacts that can result in the infection transmission is incorporated in the population. This contact structure can be non-homogeneous and it is modeled as a random graph whose edges describe the contacts between individuals. The second assumption that is generalized, is the distribution of the latent and infectious period in the host individuals. This research work allows the latent and infectious period to have a distribution other than the exponential and hence the epidemic process is more general than a Markovian process. As in most stochastic models, the infectious contact is modeled as a random variable with Poisson distribution. However, to introduce the individual variations, the transmission rate is assumed to be a non negative random variable. This work extends the epidemic models suggested by Newman (2002) in two directions. The first, studies the hierarchical networks that have a more complex network structure, involving the interaction of populations. The second direction examines the evolution in times for outbreaks in networks. In this work, results for discrete and continuous time are obtained. The results for the continuous time model considers the infectious process to be a bivariate Markovian process. However, the results for the final outbreaks size and the developed simulation program include the general case were the latent and infectious period can have a distribution other than exponential. This research work also analyze the effect of four control measures in the contact structure, and using the simulation program and Monte Carlo-likelihood methodology, it estimates the parameters for measles and influenza. The results here obtained can be directly applied to study the dynamics of other kind of “agents” such as information and ideas. For example, the dynamics can involve the spread of computer viruses, rumors, eating habits and personal positions regarding a fact or idea.

The principal motivations for studying epidemics and their dynamics are understanding the biological characteristics of the epidemic agents and reducing the economical and social costs originating from epidemic outbreaks. The most commonly used epidemic models have important assumptions such as the law of mass action, and the latent and infectious periods being exponentially distributed with xed parameters. Under this kind of suppositions the models are analyzed with well known algorithms as the Euler and Euler-Maruyama, and methodology and results from the theory of Markovian processes. However, these assumptions are selected largely for their analytic convenience and in many cases are far from describing the agent's transmissibility attributes in the population and its biological characteristics in a host. The epidemic models studied here relax two important epidemic assumptions. The first to be relaxed is the one that susceptible individuals are equally likely to acquire the disease. A structure for the kind of individual contacts that can result in the infection transmission is incorporated in the population. This contact structure can be non-homogeneous and it is modeled as a random graph whose edges describe the contacts between individuals. The second assumption that is generalized, is the distribution of the latent and infectious period in the host individuals. This research work allows the latent and infectious period to have a distribution other than the exponential and hence the epidemic process is more general than a Markovian process. As in most stochastic models, the infectious contact is modeled as a random variable with Poisson distribution. However, to introduce the individual variations, the transmission rate is assumed to be a non negative random variable. This work extends the epidemic models suggested by Newman (2002) in two directions. The first, studies the hierarchical networks that have a more complex network structure, involving the interaction of populations. The second direction examines the evolution in times for outbreaks in networks. In this work, results for discrete and continuous time are obtained. The results for the continuous time model considers the infectious process to be a bivariate Markovian process. However, the results for the final outbreaks size and the developed simulation program include the general case were the latent and infectious period can have a distribution other than exponential. This research work also analyze the effect of four control measures in the contact structure, and using the simulation program and Monte Carlo-likelihood methodology, it estimates the parameters for measles and influenza. The results here obtained can be directly applied to study the dynamics of other kind of “agents” such as information and ideas. For example, the dynamics can involve the spread of computer viruses, rumors, eating habits and personal positions regarding a fact or idea.

Thesis (Ph. D.)--University of Chicago, Department of Statistics, August 2003. / Includes bibliographical references. Also available on the Internet.

Caption title: An inaugural dissertation on yellow fever. / Dedicated to Dr. Wright Post, professor of anatomy and surgery in Columbia College, and also to Dr. Isaac Ledyard, health officer, Dr. James Tillary, resident physician, and Dr. Edward Miller, health commissioner.

Caption title: An inaugural dissertation on yellow fever. / Dedicated to Dr. Wright Post, professor of anatomy and surgery in Columbia College, and also to Dr. Isaac Ledyard, health officer, Dr. James Tillary, resident physician, and Dr. Edward Miller, health commissioner. Microform version available in the Readex Early American Imprints series.

Thesis (M.S.)--Humboldt State University, 2006. / Includes bibliographical references (leaves 62-67). Also available via Humboldt Digital Scholar.

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Complex networks is a vibrant research field and has received much attention over the last decade. Central to this area is the question of how networks around us are constructed. The essential notion of network research is that these systems are assembled in a decentralised way, thus no central agent is planning the network beforehand. Despite this lack of central coordination, many networks present intriguing universalities, such as broad degree distributions, in the form of power-laws. The subject of study in this thesis is a class of networks that are constructed by a node intrinsic variable, called fitness. The way these networks grow could be called a rich-get-richer mechanism. The fitter a node is, the more likely it is to acquire new connections inside the network. Several aspects that are directly connected to these networks are explored in this thesis. In the first part, the properties of growing networks that are driven by fitness are investigated and it is shown that the introduction of growth leads to a topological structure that is different from its static counterpart. In the subsequent chapter, percolation on fitness driven networks is studied. The results give insights into possible mechanisms that can stabilise systems. Furthermore, the theory can be used to identify vulnerable structures around us. In the following chapter, the world trade network is discussed. This numerical investigation highlights possible improvements to the methodology to make statistical analysis more robust. That chapter is followed by an analysis of time-varying networks. Time-varying networks represent an interesting construct that allows a formulation of stochastic processes on the same time-scale as the evolution of the network itself. This possibility is highly relevant to the investigation of epidemics, for instance. In the last chapter, a study of a system of clusters and their self-organised formation is presented.

Thesis. 1979. M.S.--Massachusetts Institute of Technology. Alfred P. Sloan School of Management. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND DEWEY. / Includes bibliographical references. / M.S.