The world continues to face outbreaks of disease due to natural causes as well as the threat of biological warfare. Mathematical modeling provides an avenue by which to predict and ultimately prevent widespread outbreaks. A wide variety of modeling tools have been used in the study of the spread of diseases, including Ordinary Differential Equations, Partial Differential Equations, and Difference Equations. In this study, an agent-based model is used to study the spread and control of epidemics and is based on Sirakoulis, et al. [1]. The computer program NetLogo [2] is used for simulation. The development and set-up procedures for this model are fully discussed. The model is used to study the effectiveness of vaccination and quarantine as methods of epidemic control. It is determined that the most effective means of controlling an epidemic is to quarantine individuals with symptoms. In addition, the effect of the adjacent contact coefficient in the model is examined and further development and uses of the model are discussed.

A pesquisa na area de redes complexas tem evoluido bastante, e e nesta linha que o presente trabalho visa aportar, dando enfase especial no processo epidemico sobre redes. Desse modo, foi feito uma analise geral das redes complexas em conjunto com suas propriedades. Apos isso, desenvolveu-se o processo de contagio da epidemia do tipo suscetivel-infectado sobre uma rede aleatoria uniforme e sobre uma rede aleatoria com ligacoes preferenciais. Ambas abordagens foram desenvolvidas usando equacoes mestras para finalmente fazer sua analise com metodos analiticos e computacionais. / Research in the area of complex networks has evolved greatly, and over this line that this present work aims to contribute, with particular emphasis on the epidemic process over networks. Along these lines, a general review about complex networks is made with their main properties. After that, a susceptible-infected contagion process is developed over a uniform random network and a preferential attachment network. Both approaches were developed using master equations to finally analyze them with analytical and computatio- nal methods.

This thesis offers a critical analysis of the rise of syndromic surveillance systems for the advanced detection of pandemic threats within contemporary global health security frameworks. The thesis traces the iterative evolution and ascendancy of three such novel syndromic surveillance systems for the strengthening of health security initiatives over the past two decades: 1) The Program for Monitoring Emerging Diseases (ProMED-mail); 2) The Global Public Health Intelligence Network (GPHIN); and 3) HealthMap. This thesis demonstrates how each newly introduced syndromic surveillance system has become increasingly oriented towards the integration of digital algorithms into core surveillance capacities to continually harness and forecast upon infinitely generating sets of digital, open-source data, potentially indicative of forthcoming pandemic threats. This thesis argues that the increased centrality of the algorithm within these next-generation syndromic surveillance systems produces a new and distinct form of infectious disease surveillance for the governing of emergent pathogenic contingencies. Conceptually, the thesis also shows how the rise of this algorithmic mode of infectious disease surveillance produces divergences in the governmental rationalities of global health security, leading to the rise of an algorithmic governmentality within contemporary contexts of Big Data and these surveillance systems. Empirically, this thesis demonstrates how this new form of algorithmic infectious disease surveillance has been rapidly integrated into diplomatic, legal, and political frameworks to strengthen the practice global health security – producing subtle, yet distinct shifts in the outbreak notification and reporting transparency of states, increasingly scrutinized by the algorithmic gaze of syndromic surveillance.

A pesquisa na area de redes complexas tem evoluido bastante, e e nesta linha que o presente trabalho visa aportar, dando enfase especial no processo epidemico sobre redes. Desse modo, foi feito uma analise geral das redes complexas em conjunto com suas propriedades. Apos isso, desenvolveu-se o processo de contagio da epidemia do tipo suscetivel-infectado sobre uma rede aleatoria uniforme e sobre uma rede aleatoria com ligacoes preferenciais. Ambas abordagens foram desenvolvidas usando equacoes mestras para finalmente fazer sua analise com metodos analiticos e computacionais. / Research in the area of complex networks has evolved greatly, and over this line that this present work aims to contribute, with particular emphasis on the epidemic process over networks. Along these lines, a general review about complex networks is made with their main properties. After that, a susceptible-infected contagion process is developed over a uniform random network and a preferential attachment network. Both approaches were developed using master equations to finally analyze them with analytical and computatio- nal methods.

Infectious diseases, including influenza, measles, and sexually transmitted diseases, spread from person to person. Different attempts have been made to modify or extend traditional epidemic models to relax homogeneity assumptions, so as to handle more complex and realistic situations. We propose a network-based approach to the modeling and prediction of infectious disease outbreaks. Our focus is on heterogeneous populations where there is variation in individual susceptibility, infectivity, and person-to-person contact patterns. To address the complexity of disease propagation over a contact network, we develop a Bayesian survival model that maps the network onto a latent space and uses latent positions to predict disease transmission. We present an R package (`epinet') implementation of our methods and an application to a high school contact network. The package uses C code to implement an MCMC algorithm to efficiently estimate parameters and predict disease outcomes. Our application involves contact data collected by mobile sensors distributed to individuals, and provides estimates of disease transmission in line with the network structure. In it, we address issues that are of direct interest to public health professionals, such as prediction of future outbreaks of diseases. Questions such as whether quarantine will help mitigate an outbreak can also be explored using our proposed model.

This thesis is concerned with the mathematical modelling for human immunodeficiency virus (HIV) and hepatitis C virus (HCV) epidemics in Australia. There are two parts to this thesis. Part I is aimed at modelling the transmission of HIV and HCV via needle sharing among injecting drug users (IDUs). The dynamical model of an epidemic through needle sharing among IDUs is derived. This model reveals the correlation between needle sharing and the epidemic prevalence among IDUs. The simulations of HIV and HCV prevalence and incidence among IDUs in Australia are made with this model. The comparison of simulated results with literature estimates shows that the modelled results are consistent with the literature estimates. The effects of needle sharing and cleaning on HIV and HCV prevalence and incidence among IDUs in Australia are evaluated. Part II is devoted to modelling the spread of HIV in the general community in Australia. A mathematical model is formulated to assess the epidemiological consequences of injecting drug use and sexual transmission in Australia. The effects of highly active antiretroviral therapies (HAART) on the HIV epidemic are included. The modelled results are in broad agreement with the literature estimates and observed data. The long-term effects of HAART are also discussed.

Thesis (M.A.)--Georgia State University, 2007. / Stephen H. Rapp, committee chair; Donald M. Reid, committee member. Electronic text (210 p. : ill. (some col.), maps, facsim.) : digital, PDF file. Description based on contents viewed Dec. 20, 2007; title from file title page. Includes bibliographical references (p. 192-210).

Gegenstand der Dissertation ist die Untersuchung von wiederkehrenden Ausbrüchen (wie z.B. Epidemien) in der Natur. Dies gelang anhand von Modellen, die die Dynamik von Phytoplankton und die Ausbreitung von Krankheiten zwischen Städten beschreiben. Diese beide Systeme bilden hervorragende Beispiele für solche Phänomene. Die Frage, ob die in der Zeit wiederkehrenden Ausbrüche ein Ausdruck chaotischer Dynamik sein können, ist aktuell in der Ökologie und fasziniert Wissenschaftler dieser Disziplin. Wir konnten zeigen, dass sich das Plankton-Modell im Falle von periodischem Antreiben über die Nährstoffe in einem chaotischen Regime befindet. Diese Dynamik wurde als die komplexe Wechselwirkung zweier Oszillatoren verstanden. Ebenfalls wurde die Ausbreitung von Epidemien in Netzwerken wechselwirkender Städte mit unterschiedlichen Grössen untersucht. Dafür wurde zunächst die Kopplung zwischen zwei Städten als Verhältnis der Stadtgrössen eingeführt. Es konnte gezeigt werden, dass das System sich in einem globalen zweijährigen Zyklus, der auch in den realen Daten beobachtet wird, befinden kann. Der Effekt von Heterogenität in der Grösseverteilung ist durch gewichtete Kopplung von generischen Modellen (Zelt- und Logistische Abbildung) in Netzwerken im Detail untersucht worden. Eine neue Art von Kopplungsfunktion mit nichtlinearer Sättigung wurde eingeführt, um die Stabilität des Systems zu gewährleisten. Diese Kopplung beinhaltet einen Parameter, der es erlaubt, die Netzwerktopologie von globaler Kopplung in gerichtete Netzwerke gleichmässig umzuwandeln. Die Dynamik des Systems wurde anhand von Bifurkationsdiagrammen untersucht. Zum Verständnis dieser Dynamik wurde eine effektive Theorie, die die beobachteten Bifurkationen sehr gut nachahmt, entwickelt. / One of the most striking features of ecological systems is their ability to undergo sudden outbreaks in the population numbers of one or a small number of species. The similarity of outbreak characteristics, which is exhibited in totally different and unrelated (ecological) systems naturally leads to the question whether there are universal mechanisms underlying outbreak dynamics in Ecology. It will be shown into two case studies (dynamics of phytoplankton blooms under variable nutrients supply and spread of epidemics in networks of cities) that one explanation for the regular recurrence of outbreaks stems from the interaction of the natural systems with periodical variations of their environment. Natural aquatic systems like lakes offer very good examples for the annual recurrence of outbreaks in Ecology. The idea whether chaos is responsible for the irregular heights of outbreaks is central in the domain of ecological modeling. This question is investigated in the context of phytoplankton blooms. The dynamics of epidemics in networks of cities is a problem which offers many ecological and theoretical aspects. The coupling between the cities is introduced through their sizes and gives rise to a weighted network which topology is generated from the distribution of the city sizes. We examine the dynamics in this network and classified the different possible regimes. It could be shown that a single epidemiological model can be reduced to a one-dimensional map. We analyze in this context the dynamics in networks of weighted maps. The coupling is a saturation function which possess a parameter which can be interpreted as an effective temperature for the network. This parameter allows to vary continously the network topology from global coupling to hierarchical network. We perform bifurcation analysis of the global dynamics and succeed to construct an effective theory explaining very well the behavior of the system.

This dissertation focuses on a comparative study of small-world characteristics in geographical, epidemic, and virtual spaces. Small-world network is the major component of the “new science of networks” that emerged recently in research related to complex networks. It has shown a great potential to model the complex networks encountered in geographical studies. This dissertation, in an attempt to understand the emergence of small-world phenomenon in spatial networks, has investigated the smallworld properties in aforementioned three spaces. Specifically, this dissertation has studied roadway transportation networks at national, metropolitan, and intra-city scales via network autocorrelation methods to investigate the distance effect on the emergence of small-world properties. This dissertation also investigated the effect of small-world network properties on the epidemic diffusion and different control strategies through agent-based simulation on social networks. The ASLevel Internet in the contiguous U.S. has been studied in its relation between local and global connections, and its correspondence with small-world characteristics. Through theoretical simulations and empirical studies on spatial networks, this dissertation has contributed to network science with a new method – network autocorrelation, and better understanding from the perspective of the relation between local and global connections and the distance effect in networks. A small-world phenomenon results from the interplay between the dynamics occurring on networks and the structure of networks; when the influencing distance of the dynamics reaches to the threshold of the network, the network will logically emerge as a small-world network. With the aid of numerical simulation a small-world network has a large number of local connections and a small number of global links. It is also found that the epidemics will take shorter time period to reach largest size on a small-world network and only particular control strategy, such as targeted control strategy, will be effective on smallworld networks. This dissertation bridges the gap between new science of networks and the network study in geography. It potentially contributes to GIScience with new modeling strategy for representing, analyzing, and modeling complexity in hazards prevention, landscape ecology, and sustainability science from a network-centric perspective.

Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / Typescript. Vita. Includes bibliographical references (leaves 220-247). Also available on the Internet.