Tesi sul tema "Epidemics"

Approved for public release; distribution is unlimited.<br>This thesis develops a mathematical model to explore epidemic spread through the Ground Combat Element (GCE) of the Marine Expeditionary Unit (MEU). The model will simulate an epidemic caused by a biological attack using an agent that has the ability to spread through person-to-person contact (small pox, hemorrhagic fever, etc.) A stochastic modeling process will be used along with widely accepted mathematical formulas for an SEIR (Susceptible-Exposed-Infectious-Removed) epidemic model. A heterogeneous population composed of numerous homogenous subgroups with varying interaction rates simulates the unique structure of military combat units. The model will be evaluated to determine which units facilitate the most rapid spread of the epidemic. The model will then test a number of different scenarios to determine the effects of varying quarantine techniques, vaccination strategies and protective postures on the spread of the disease.

Master of Science<br>Department of Electrical and Computer Engineering<br>Karen Garrett<br>Bala Natarajan<br>Caterina Scoglio<br>In this thesis, we propose a statistical model to predict disease dispersal in dynamic networks. We model the process of disease spreading using discrete time Markov chain. In this case, the vector of probability of infection is the state vector and every element of the state vector is a continuous variable between zero and one. In discrete time Markov chains, state probability vectors in each time step depends on state probability vector in the previous time step and one step transition probability matrix. The transition probability matrix can be time variant or time invariant. If this matrix’s elements are functions of elements of vector state probability in previous step, the corresponding Markov chain is non linear dynamical system. However, if those elements are independent of vector state probability, the corresponding Markov chain is a linear dynamical system. We especially focus on the dispersal of soybean rust. In our problem, we have a network of US counties and we aim at predicting that which counties are more likely to get infected by soybean rust during a year based on observations of soybean rust up to that time as well as corresponding observations to previous years. Other data such as soybean and kudzu densities in each county, daily wind data, and distance between counties helps us to build the model. The rapid growth in the number of Internet users in recent years has led malware generators to exploit this potential to attack computer users around the word. Internet users are frequent targets of malicious software every day. The ability of malware to exploit the infrastructures of networks for propagation determines how detrimental they can be to the network’s security. Malicious software can make large outbreaks if they are able to exploit the structure of the Internet and interactions between users to propagate. Epidemics typically start with some initial infected nodes. Infected nodes can cause their healthy neighbors to become infected with some probability. With time and in some cases with external intervention, infected nodes can be cured and go back to a healthy state. The study of epidemic dispersals on networks aims at explaining how epidemics evolve and spread in networks. One of the most interesting questions regarding an epidemic spread in a network is whether the epidemic dies out or results in a massive outbreak. Epidemic threshold is a parameter that addresses this question by considering both the network topology and epidemic strength.

Networks are a useful quantitative representation for complex systems of interacting entities arising in fields such as biological, physical and social sciences. A network representation provides a degree of simplification while capturing key connectivity patterns. This thesis focuses on two main themes: the study of community structure, an important mesoscopic feature of many networks, and its application to study spatiotemporal spread of infectious diseases. Community detection seeks to partition a network into dense sets of nodes that are connected sparsely to other dense sets. The notion of denseness is often relative to some "null model" that describes baseline connectivity that can be construed to occur randomly. In the first part of the thesis, we discuss the incorporation of spatial information into null models for community detection. We develop a spatial null model based on the radiation model of mobility. We test different spatial null models using static and temporal (multilayer) spatial benchmarks with planted partitions that represent interactions between human populations. Our results indicate that it is important to incorporate spatial information into null models for community detection, but it is best to incorporate only relevant information into null models, as extraneous information can lower performance. In the second part of the thesis, we present the results of community detection with different null models on disease-correlation networks generated form real and synthetic time series of disease occurrence. We use data sets for endemic diseases (established in a region, with occasional epidemic outbreaks) and emerging diseases (newly-discovered or introduced into a region for the first time). We study the spatial and temporal organization of partitions. Finally, we apply community detection with different null models to synthetic time series generated from an agent-based model (ABM) simulating the spread of endemic and emerging diseases between spatially-embedded cities with a planted, transport-based community structure. We compare the findings on real and synthetic data sets, and we searched for model parameter regimes in which we are able to detect planted partitions or other interesting communities. For emerging diseases, we find spatial communities that are associated with the first times the infection reached a node in both ABM and disease data. For endemic diseases, we are unable to find planted or spatial communities in the ABM data, but we detect spatial communities for two of the three disease data sets. For these diseases, we also detect temporal communities corresponding to some of the important time points in disease history. We hope that these results show that community structure of disease correlation networks appears to be more complicated than simple spatial patterns and is a fascinating topic to study.

Compartmental models constructed for stochastic epidemics are usually difficult to analyze mathematically or computationally. Researchers have mostly resorted to deterministic approximations or simulation to investigate these models. This dissertation describes three original computational methods for analyzing compartmental models of stochastic epidemics. The first method is the Markov Process Method which computes the probability law for the epidemic by solving the Chapman-Kolmogorov ordinary differential equations as an initial value problem using standard numerical analysis techniques. It is limited to models with small populations and few compartments and requires sophisticated numerical analysis tools and relatively extensive computer resources. The second method is the Probability Vector Method which can estimate the first few moments of a discrete time epidemic model over a limited time period (i.e. if Y(t) is the number of individuals in a given compartment then this method can estimate E[ Yr for small positive integers r. Size restrictions limit the maximum order of the moment that can be computed. For compartmental models with a constant, homogeneous population, this method requires modest computational resources to estimate the first two moments of Y(t). The third method is the Linear Extrapolation Method, which computes the moments of a compartmental model with a large population by extrapolating from the given moments of the same model with smaller populations. This method is limited to models that have some alternate way of calculating the moments for small populations. These moments should be computed exactly from probabilistic principles. When this is not practical, any method that can produce accurate estimates of these moments for small populations can be used. Two compartmental epidemic models are analyzed using these three methods. First, the simple susceptible/infective epidemic is used to illustrate each method and serves as a benchmark for accuracy and performance. These computations show that each algorithm is capable of producing acceptably accurate solutions (at least for the specific parameters that were used). Next, an HIV/AIDS model is analyzed and the numerical results are presented and compared with the deterministic and simulation solutions. Only the probability vector method could compete with simulation on the larger (i.e. more compartments) HIV/AIDS model.

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.<br>Includes bibliographical references (p. 37).<br>In this thesis, I looked at an extension of the Reed-Frost epidemic model which had two-sub-populations. By setting up a Markov chain to model the epidemic and finding the transition probabilities of that chain, MATLAB could be used to solve for the expected number of susceptibles and the expected duration. I simulated the model with more tan two sub-populations to find the average number of susceptibles and reviewed previously solved stochastic spatial models to understand how to solve the multiple-population Reed-Frost model on a network.<br>by Samantha Livingston.<br>M.Eng.

Submitted by Irene Nascimento (irene.kessia@ufpe.br) on 2016-10-17T18:29:55Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) phd_efsb_FINAL_BIBLIOTECA.pdf: 7882904 bytes, checksum: df094c44eb4ce5be12596263047790ed (MD5)<br>Made available in DSpace on 2016-10-17T18:29:55Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) phd_efsb_FINAL_BIBLIOTECA.pdf: 7882904 bytes, checksum: df094c44eb4ce5be12596263047790ed (MD5) Previous issue date: 2016-08-29<br>FACEPE<br>Context: In Software Engineering, technology transfer has been treated as a problem that concernsonly two agents (innovation and adoption agents) working together to fill the knowledge gap between them. In this scenario, the transfer is carried out in a “peer-to-peer” fashion, not changing the reality of individuals and organizations around them. This approach works well when one is just seeking the adoption of a technology by a“specific client”. However, it can not solve a common problem that is the adoption of new technologies by a large mass of potential new users. In a wider context like this, it no longer makes sense to focus on “peer-to-peer” transfer. A new way of looking at the problem is necessary. It makes more sense to approach it as diffusion of innovations, where there is an information spreading in a community, similar to that observed in epidemics. Objective: This thesis proposes a paradigm shift to show the adoption of programming languages can be formally addressed as an epidemic. This focus shift allows the dynamics of programming language adoption to be mathematically modelled as such, and besides finding models that explain the community’s behaviour when adopting programming languages, it allows some predictions to be made, helping both individuals who wish to adopt a new language that might seem to be a new industry standard, and language designers to understand in real time the adoption of a particular language by a community. Method: After a proof of concept with data from Sourceforge (2000 to 2009), data from GitHub (2009 to January 2016), a well-known open source software repository, and Stack Overflow (2008 to March 2016), a popular Q&A system for software developers, were obtained and preprocessed. Using cumulative biological growth functions, often used in epidemiological contexts, we obtained adjusted models to the data. Once with the adjusted models, we evaluated their predictive capabilities through repeated applications of hypothesis testing and statistical calculations in different versions of the models obtained after adjusting the functions to samples of different time frames from the repositories. Results: We show that programming language adoption can be formally considered an epidemiological phenomenon by adjusting a well-known mathematical function used to describe such phenomena. We also show that, using the models found, it is possible to forecast programming languages adoption. We also show that it is possible to have similar insights by observing user data, as well as data from the community itself, not using software developers as susceptible individuals. Limitations: The forecast of the adoption outcome (asymptote) needs to be taken with care because it varies depending on the sample size, which also influences the quality of forecasts in general. Unfortunately, we not always have control over the sample size, because it depends on the population under analysis. The forecast of programming language adoption is only valid for the analysed population; generalizations should be made with caution. Conclusion: Addressing programming languages adoption as an epidemiological phenomenon allows us to perform analyses not possible otherwise. We can have an overview of a population in real time regarding the use of a programming language, which allows us, as innovation agents, to adjust our technology if it is not achieving the desired “penetration”; as adoption agents, we may decide, ahead of our competitors, to adopt a seemingly promising technology that may ultimately become a standard.<br>Contexto: Em Engenharia de Software, transferência de tecnologia tem sido tratada como um problema pontual, um processo que diz respeito a dois agentes (os agentes de inovação e adoção) trabalhando juntos para preencher uma lacuna no conhecimento entre estes dois. Neste cenário, a transferência é realizada “ponto a ponto”, envolvendo e tendo efeito apenas nos indivíduos que participam do processo. Esta abordagem funciona bem quando se está buscando apenas a adoção da tecnologia por um “cliente” específico. No entanto, ela não consegue resolver um problema bastante comum que é a adoção de novas tecnologias por uma grande massa de potenciais novos usuários. Neste contexto mais amplo, não faz mais sentido focar em transferência ponto a ponto, faz-se necessária uma nova maneira de olhar para o problema. É mais interessante abordá-lo como difusão de inovações, onde existe um espalhamento da informação em uma comunidade, de maneira semelhante ao que se observa em epidemias. Objetivo: Esta tese de doutorado mostra que a adoção de linguagens de programação pode ser tratada formalmente como uma epidemia. Esta mudança conceitual na maneira de olhar para o fenômeno permite que a dinâmica da adoção de linguagens de programação seja modelada matematicamente como tal, e além de encontrar modelos que expliquem o comportamento da comunidade quando da adoção de uma linguagem de programação, permite que algumas previsões sejam realizadas, ajudando tanto indivíduos que desejem adotar uma nova linguagem que parece se apresentar como um novo padrão industrial, quanto ajudando projetistas de linguagens a entender em tempo real a adoção de uma determinada linguagem pela comunidade. Método: Após uma prova de conceito com dados do Sourceforge (2000 a 2009), dados do GitHub (2009 a janeiro de 2016) um repositório de projetos software de código aberto, e Stack Overflow (2008 a março de 2016) um popular sistema de perguntas e respostas para desenvolvedores de software, from obtidos e pré processados. Utilizando uma função de crescimento biológico cumulativo, frequentemente usada em contextos epidemiológicos, obtivemos modelos ajustados aos dados. Uma vez com os modelos ajustados, realizamos avaliações de sua precisão. Avaliamos suas capacidades de previsão através de repetidas aplicações de testes de hipóteses e cálculos de estatísticas em diferentes versões dos modelos, obtidas após ajustes das funções a amostras de diferentes tamanhos dos dados obtidos. Resultados: Mostramos que a adoção de linguagens de programação pode ser considerada formalmente um fenômeno epidemiológico através do ajuste de uma função matemática reconhecidamente útil para descrever tais fenômenos. Mostramos também que é possível, utilizando os modelos encontrados, realizar previsões da adoção de linguagens de programação em uma determinada comunidade. Ainda, mostramos que é possível obter conclusões semelhantes observando dados de usuários e dados da comunidade apenas, não usando desenvolvedores de software como indivíduos suscetíveis. Limitações: A previsão do limite superior da adoção (assíntota) não é confiável, variando muito dependendo do tamanho da amostra, que também influencia na qualidade das previsões em geral. Infelizmente, nem sempre teremos controle sob o tamanho da amostra, pois ela depende da população em análise. A adoção da linguagem de programação só é válida para a população em análise; generalizações devem ser realizadas com cautela. Conclusão: Abordar o fenômeno de adoção de linguagens de programação como um fenômeno epidemiológico nos permite realizar análises que não são possíveis de outro modo. Podemos ter uma visão geral de uma população em tempo real no que diz respeito ao uso de uma linguagem de programação, o que nos permite, com agentes de inovação, ajustar a tecnologia caso ela não esteja alcançando o alcance desejado; como agentes de adoção, podemos decidir por adotar uma tecnologia aparentemente promissora que pode vir a se tornar um padrão.

Made available in DSpace on 2015-03-03T11:52:29Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-07-30Bitstream added on 2015-03-03T12:06:38Z : No. of bitstreams: 1 000811185_20160630.pdf: 241917 bytes, checksum: 980a2b2d7ef326c13784a7051c0be59f (MD5) Bitstreams deleted on 2016-07-01T13:02:15Z: 000811185_20160630.pdf,. Added 1 bitstream(s) on 2016-07-01T13:03:14Z : No. of bitstreams: 1 000811185.pdf: 1318806 bytes, checksum: b28e0cb8cfb5c183cc9d4bb267805af1 (MD5)<br>This thesis aimed to identify patterns of Aedes (Stegomya) L. aegypti, vector of dengue disease in cities of São Paulo state between 2003-2011. The studied cities were Araçatuba, Bauru, Campinas, Marília, São José do Rio Preto, São Paulo, Santos, Sorocaba, Ribeirão Preto and Presidente Prudente in Brazil. The statistical technique of Cluster Analysis was used to classify these cities, where the variables related to dengue vector were chosen. The annual variables adopted were mean maximum temperature, mean minimum temperature, rainy days, average rainfall, population density, index of house infestation (IIP), resistance to temephos, rate of indigenous and imported dengue cases, as well as the altitude as fixed variable. The results showed that the patterns of dengue are dynamic throughout the studied period for the cities in focus. Cities were grouped into three more permanent groups, although there are changes in formation of these groups over studied time. The most consistent groups indicated a relation to the climatic classification of Köppen-Geiger, showing that the climate affects the dengue vector and its epidemiology. The city of Santos was classified as the only group in each year to present a distinct profile for bioecology and resistance to temephos in Ae. aegypti and dengue consecutively

Orientador: Fernando Frei<br>Banca: Pitágoras da Conceição Bispo<br>Banca: Luciamare Perinetti Alves Martins<br>Resumo:Essa dissertação teve por objetivo principal a identificação de padrões do Aedes (Stegomya) aegypti L., vetor da doença dengue, em municípios do estado de São Paulo entre os anos de 2003 a 2011. Os municípios estudados foram Araçatuba, Bauru, Campinas, Marília, São José do Rio Preto, São Paulo, Santos, Sorocaba, Ribeirão Preto e Presidente Prudente. Foi utilizada a técnica estatística de Análise de Agrupamentos para classificação dos municípios, onde foram escolhidas as variáveis relacionadas ao vetor da dengue. As variáveis anuais adotadas foram temperatura média máxima, temperatura média mínima, dias de chuva, precipitação média, densidade populacional, índice de infestação predial (IIP), resistência ao temephos, taxa de casos de dengue autóctones e importados, além da altitude como variável fixa. As variáveis estudadas não classificaram de forma consistente os municípios em todo o período analisado. Os municípios foram agrupados em três grupos mais permanentes, apesar de existir alteração na formação desses agrupamentos ao longo do tempo avaliado. Os grupos mais frequentes na análise temporal indicaram relação com a classificação climática de Köppen-Geiger, exibindo a relação intensa do clima com o vetor e a epidemiologia da dengue. O município de Santos foi classificado como grupo único em todos os anos por apresentar um perfil distinto para a bioecologia e resistência ao temephos do Ae. aegypti, e consecutivamente da dengue<br>Abstract: This thesis aimed to identify patterns of Aedes (Stegomya) L. aegypti, vector of dengue disease in cities of São Paulo state between 2003-2011. The studied cities were Araçatuba, Bauru, Campinas, Marília, São José do Rio Preto, São Paulo, Santos, Sorocaba, Ribeirão Preto and Presidente Prudente in Brazil. The statistical technique of Cluster Analysis was used to classify these cities, where the variables related to dengue vector were chosen. The annual variables adopted were mean maximum temperature, mean minimum temperature, rainy days, average rainfall, population density, index of house infestation (IIP), resistance to temephos, rate of indigenous and imported dengue cases, as well as the altitude as fixed variable. The results showed that the patterns of dengue are dynamic throughout the studied period for the cities in focus. Cities were grouped into three more permanent groups, although there are changes in formation of these groups over studied time. The most consistent groups indicated a relation to the climatic classification of Köppen-Geiger, showing that the climate affects the dengue vector and its epidemiology. The city of Santos was classified as the only group in each year to present a distinct profile for bioecology and resistance to temephos in Ae. aegypti and dengue consecutively<br>Mestre

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.<br>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 thesis investigates the representation of a stochastic epidemic process as a directed random graph; we use this representation to impute the missing information in final size data to make Bayesian statistical inference about the model parameters using MCMC techniques. The directed random graph representation is analysed, in particular its behaviour under the condition that the epidemic has a given final size. This is used to construct efficient updates for MCMC algorithms. The MCMC method is extended to include two-level mixing models and two-type models, with a general framework given for an arbitrary number of levels and types. Partially observed epidemics, that is, where the number of susceptibles is unknown or where only a subset of the population is observed, are analysed. The method is applied to several well known data sets and comparisons are made with previous results. Finally, the method is applied to data of an outbreak of Equine Influenza (H3N8) at Newmarket in 2003, with a comparison to another analysis of the same data. Practical issues of implementing the method are discussed and are overcome using parallel computing (GNU OpenMP) and arbitrary precision arithmetic (GNU MPFR).

The systems of interest in this study are the spread of epidemics and invasions from a small propagule introduced into an arena that was initially devoid of the given species or stage of illness. In reaction-diffusion models, populations are continuous. Populations at low densities have the same growth functions as populations at high densities. In nature, such low densities would signify extinction of a population or of a disease. This property can be removed from reaction-diffusion models by small changes in the formulation so that small populations become extinct. This can be achieved by the use of a threshold density or an Allee effect, so there is negative growth at low densities. Both these alterations were made to the Fisher model, a predator-prey model and a two stage and a three stage epidemic model. A semi-numerical method, termed the Shooting method, was developed to predict the shapes and velocities of these wave fronts. This was found to correctly predict the velocity, the peak density of the invading stage or species and the width of the wave front. It was found that in oscillatory cases of the multi species models, a high threshold can remove the wave train or wake which would normally follow the wave front, so the wave becomes a soliton. The next step is to investigate probable causes of persistence behind the initial wavefront. To do this, discrete time and space versions of the models were formulated so that experiments investigating persistence can be carried out in a two dimensional arena with less computational effort. The formulations were chosen so that at reasonable time and space steps the discrete models show no behaviour different to that of the reaction diffusion model, and so that the Shooting method could also be used to make predictions about these wavefronts. Three mechanisms of persistence are investigated; environmental heterogeneity, long range dispersal and self organised patterns.

The severity of the outbreak of an infectious disease is highly dependent upon the structure of the population through which it spreads. This thesis considers the stochastic SIR (susceptible → infective → removed) household epidemic model, in which individuals mix with other individuals in their household at a far higher rate than with any other member of the population. This model gives a more realistic view of dynamics for the transmission of many diseases than the traditional model, in which all individuals in a population mix homogeneously, but retains mathematical tractability, allowing us to draw inferences from disease data. This thesis considers inference from epidemics using data which has been acquired after an outbreak has finished and whilst it is still in its early, `emerging' phase. An asymptotically unbiased method for estimating within household infectious contact rate(s) from emerging epidemic data is developed as well as hypothesis testing based on final size epidemic data. Finally, we investigate the use of both emerging and final size epidemic data to estimate the vaccination coverage required to prevent a large scale epidemic from occurring. Throughout the thesis we also consider the exact form of the households epidemic model which should be used. Specifically, we consider models in which the level of infectious contact between two individuals in the same household varies according to the size of their household.

The subject of this thesis is the study of a system of multiple simultaneously spreading diseases, or strains of diseases, in a structured host population. The disease spread is modelled using the well-studied SEIR compartmental model; host population structure is imposed through the use of random graphs, in which each host individual is explicitly connected to a predetermined set of other individuals. Two different graph structures are used: Zipf power-law distributed graphs, in which individuals vary greatly in their number of contacts; and Poisson distributed graphs, in which there is very little variation in the number of contacts. Three separate explorations are undertaken. In the first, the extent to which two SEIR processes will overlap due to chance is examined in the case where they do not affect each other's ability to spread. The overlap is found to increase with increased heterogeneity in the number of contacts, all things equal. Introducing differences in infection probability or a delay between introducing the two strains produces more complex dynamics. I then extend the model to allow strains to modify each other's transmissibility. This is found to lead to modest changes in the size of the outbreak of affected strains, and larger effects on the size of the overlap. The extent of the effect is found to depend strongly on the order in which the strains are introduced to the population. Zipf graphs experience somewhat larger reductions in outbreak size and less reduction of overlap size, but overall the two graphs experience similar effects. This is due to the reduced effect of modification in key high-degree vertices in the Zipf graph being offset by higher local clustering. Finally, I introduce recombination and competition by replacement into the model from the first project. The number of recombinant strains that arise is found to be either very low or very high, with chance governing which occurs. Recombinant strains in Zipf distributed graphs have a significant chance of failing to spread, but not in Poisson distributed graphs. Replacement competition in the presence of a growing number of strains is found to both increase the chance of a strain failing to spread, and to reduce the overall size of outbreaks. This effect is equal in both graph types.

Thesis (Ph. D.)--University of Missouri-Columbia, 2004.<br>The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (June 29, 2006) Vita. Includes bibliographical references.

The SIR (Susceptible/Infectious/Recovered) whooping cough model involving nonlinear ordinary differential equations is studied and extended to incorporate (i) diffusion (ii) convection and (iii) diffusion-convection in one-space dimension. Firstand second-order finite-difference methods are developed to obtained the numerical solutions of the ordinary differential equations. Though implicit in nature, with the resulting improvements in stability, the methods are applied explicitly. The proposed methods are economical and reliable in comparison to classical numerical methods. When extended to the numerical solutions of the partial differential equations, the solutions are found by solving a system of linear algebraic equations at each time step, as opposed to solving a non-linear system, which often happens when solving non-linear partial differential equations.

Submitted by Geyciane Santos (geyciane_thamires@hotmail.com) on 2015-12-07T21:04:32Z No. of bitstreams: 1 Dissertação - Júlio Santos da Silva.pdf: 1884637 bytes, checksum: fed454bdbcab8a4b1135f660e0aa341d (MD5)<br>Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2016-01-19T18:43:57Z (GMT) No. of bitstreams: 1 Dissertação - Júlio Santos da Silva.pdf: 1884637 bytes, checksum: fed454bdbcab8a4b1135f660e0aa341d (MD5)<br>Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2016-01-19T19:00:14Z (GMT) No. of bitstreams: 1 Dissertação - Júlio Santos da Silva.pdf: 1884637 bytes, checksum: fed454bdbcab8a4b1135f660e0aa341d (MD5)<br>Made available in DSpace on 2016-01-19T19:00:14Z (GMT). No. of bitstreams: 1 Dissertação - Júlio Santos da Silva.pdf: 1884637 bytes, checksum: fed454bdbcab8a4b1135f660e0aa341d (MD5) Previous issue date: 2012-07-26<br>FAPEAM - Fundação de Amparo à Pesquisa do Estado do Amazonas<br>Manaus, in the late 19th century and early 20th century, experienced an exceptional populational growth due to the attraction of migrants to the exploitation and manufacture of rubber. With the increase in its population, the city of Manaus started to face the manifestation of various epidemics. When it won international renown, Manaus, implemented numerous actions put into practice by the Government to receive the migrants. The arrival of doctors and their reflections on the city also resulted in policies that led to public facilities, such as the construction of public health institutions and the discipline of public spaces. These actions were important to provide the city with laws and equipment to combat diseases and make it healthy to people and to national and foreign investments.<br>Manaus, no final do século XIX e início do século XX, experimentou um acréscimo populacional excepcional em decorrência da atração de migrantes para a exploração e fabricação da borracha. Com o aumento populacional, a cidade de Manaus começou a enfrentar a manifestação de diversas epidemias. Ao ganhar projeção internacional, Manaus implementou inúmeras ações postas em prática pelo poder público para receber os migrantes. A chegada dos médicos e suas reflexões sobre a cidade também propiciaram políticas que levaram ao aparelhamento público, tais como a construção de instituições de saúde e o disciplinamento dos espaços públicos. Estas ações foram importantes para dotar a cidade com leis e equipamentos no combate às doenças e torná-la saudável às pessoas e aos investimentos nacionais e estrangeiros.

Worms – programs that self-replicate automatically over computer networks – are a serious threat to hosts connected to the Internet. They infect hosts by exploiting software vulnerabilities, and they can use their victims for many malicious activities. Past outbreaks show that worms can spread too fast for humans to respond, hence worm containment must be automatic. We propose Vigilante: a new end-to-end architecture to contain worms automatically. In Vigilante, hosts detect worms by instrumenting vulnerable programs to analyze infection attempts. We introduce <i>dynamic data-flow analysis:</i> a broad-coverage host-based algorithm that can detect unknown worms, by tracking the flow of data from network messages, and disallowing unsafe uses of that data. We also show how to integrate other host-based detection mechanisms into the Vigilante architecture. Upon detection, hosts generate <i>self-certifying alerts </i>(SCAs), a new type of security alert that can be inexpensively verified by any vulnerable host. Using SCAs, hosts can cooperate to contain an outbreak, without having to trust each other. Vigilante broadcasts SCAs over an overlay network that propagates alerts rapidly and resiliently. Hosts receiving an SCA protect themselves by generating filters with <i>vulnerability condition slicing: </i>an algorithm that performs dynamic analysis of the vulnerable program to identify control-flow conditions that lead to successful attacks. These filters block the worm attack, including all mutations that follow the execution path identified by the SCA, while introducing a negligible performance overhead. Our results show that Vigilante can contain fast spreading worms that exploit unknown vulnerabilities without false positives. Vigilante does not require any changes to hardware, compilers, operating systems or the source code of vulnerable programs; therefore, it can be used to protect software as it exists today in binary form.

It is now widely acknowledged that spatial structure and hence the spatial position of host populations plays a vital role in the spread of infection. In this work I investigate an ensemble of techniques for understanding the stochastic dynamics of spatial and discrete epidemic processes, with especial consideration given to SIR disease dynamics for the Levins-type metapopulation. I present a toolbox of techniques for the modeller of spatial epidemics. The highlight results are a novel form of moment closure derived directly from a stochastic differential representation of the epidemic, a stochastic simulation algorithm that asymptotically in system size greatly out-performs existing simulation methods for the spatial epidemic and finally a method for tackling optimal vaccination scheduling problems for controlling the spread of an invasive pathogen.

The objective of this thesis is to study the e ect of under-reporting in epidemics. In particular, there are two broad questions we investigate: In the situation of under-reporting in epidemics, what would happen if the data were treated as if no under-reporting were occurring? Such assumption leads to an under-estimation of the contact rate, implying an under-estimation of the reproduction number. By allowing for the fact that under-reporting is occurring, how and how well can we estimate the reporting rate and other parameters of the model? We explore the above questions by considering the stochastic Markovian SIR epidemic in which various reporting processes are incorporated. We consider cases of constant reporting probability and move on to more realistic assumptions such as the reporting probability depending on time, the number of reported cases and the dependence on the source of infection for each infected individual. We develop various methodologies, based on temporal data, to account for underreporting in the Bayesian framework using MCMC to sample from the posterior distributions of the model parameters. An introduction to the spatial aspect is also considered with the SIR model with reporting process on Z.

Le cholera est une maladie diarrhéique aiguë due à la consommation d’eau ou d’aliments contaminés par des souches toxigéniques de Vibrio cholerae. Selon le “paradigme du choléra”, la maladie est provoquée par une exposition à un réservoir environnemental de V. cholerae avec des épidémies directement modulées par des facteurs environnementaux. Cependant, comme divers arguments plaident contre ce dogme, nous avons voulu élucider les mécanismes de la dynamique des épidémies de cholera dans trois foyers situés en Haïti, en République Démocratique du Congo (RDC) et en Afrique de l’Ouest. Nous avons associé une analyse temporo-spatiale des épidémies à une étude génétique des isolats de V. cholerae. En Haïti, nous avons cherché à savoir si les épidémies actuelles étaient dues à des souches toxigéniques de V. cholerae O1 durablement implantées dans l’environnement aquatique. En Afrique de l’Ouest, notre étude a révélé qu’Accra, la capitale du Ghana, était le principal foyer de choléra pour l’ensemble des pays d’Afrique de l’Ouest situés à l’Ouest du Nigeria. Le réseau d’eau d’Accra a probablement joué un rôle dans la propagation rapide de V. cholerae vers la majorité des quartiers de la ville. Les épidémies de choléra ont diffusé vers les autres pays sous la forme de vagues épidémiques et plusieurs épidémies ont été liées à la migration de populations à risque comme certains pêcheurs. En conclusion, notre réflexion globale sur les épidémies de choléra dans ces trois foyers distincts nous donne une vision cohérente des mécanismes d’émergence et de diffusion du choléra<br>Cholera is an acute diarrheal disease caused by consumption of water or food contaminated with toxigenic Vibrio cholerae. According to the "cholera paradigm", the disease is contracted by exposure to environmental reservoirs of V. cholerae, with outbreaks driven directly by climatic factors. However, as recent findings argue against this dogma, we aimed to elucidate the dynamics of cholera outbreaks in three global foci: Haiti, Democratic Republic of the Congo (DRC) and West Africa. We combined spatiotemporal analysis of epidemics with genetic assessment of V. cholerae isolates. In Haiti, we assessed whether outbreak re-emergence during the rainy season was due to toxigenic V. cholerae O1 strains that have settled into the aquatic environment. Instead, we found that the re-emergence of outbreaks was likely due to persisting outbreaks during the dry season that were insufficiently controlled, rather than an environmental reservoir of V. cholerae O1. In West Africa, our study revealed that Accra, Ghana was the hotspot of cholera in the entire region of West Africa, west of Nigeria. The Accra water network likely played a role in rapid diffusion of V. cholerae throughout the city. Cholera outbreaks spread from Accra into other countries in a wave-like fashion. Distinct outbreaks were linked via migration of at-risk populations, such as certain fishermen. In conclusion, our global reflection of cholera epidemics in these three distinct foci provides a coherent vision of the mechanisms of cholera emergence and diffusion

One major aim of statistics is to systematically study outcomes of interest in a population by observing the properties of a sample of that population. Some outcomes, such as the total number of people infected in an epidemic, can depend on properties of the whole population, such as the structure of contacts among the individuals, or contact network. A network is a collection of individuals as well as the pairwise connections between them. This dissertation explores how the effects of network structure on infectious outcomes yield challenges for statistical analysis, and suggests strategies to address them. In Section I, we consider an intervention to reduce the spread of an epidemic on a collection of individuals in partially-connected networks, and show how network structure and mixing across networks can reduce the probability of observing true intervention effects, or statistical power. In Section II, we show how accounting for estimated properties of an epidemic contact network can improve statistical power, and that this improvement depends on the properties of the whole network as well as the epidemic spreading through them. Finally, in Section III, we derive the conditions under which a particular kind of network - the Degree-Corrected Stochastic Blockmodel - is susceptible to extensive epidemic spread, enabling statistical analysts to estimate when and to what extent the challenges and corrections explored here require consideration. We will conclude with a discussion of how the estimates and derivations in the final two sections can be used as adjustment covariates when assessing the effect of treatment on epidemic spread.<br>Biostatistics

Tese (doutorado)—Universidade de Brasília, Instituto de Ciências Biológicas, Departamento de Fitopatologia, Programa de Pós-Graduação em Fitopatologia, 2015.<br>Submitted by Patrícia Nunes da Silva (patricia@bce.unb.br) on 2016-02-05T13:05:53Z No. of bitstreams: 1 2015_AlaersonMaiaGeraldine_Parcial.pdf: 11895274 bytes, checksum: 0a59c54f104d2e95f8af0824dd15d853 (MD5)<br>Approved for entry into archive by Guimaraes Jacqueline(jacqueline.guimaraes@bce.unb.br) on 2016-02-05T13:52:50Z (GMT) No. of bitstreams: 1 2015_AlaersonMaiaGeraldine_Parcial.pdf: 11895274 bytes, checksum: 0a59c54f104d2e95f8af0824dd15d853 (MD5)<br>Made available in DSpace on 2016-02-05T13:52:50Z (GMT). No. of bitstreams: 1 2015_AlaersonMaiaGeraldine_Parcial.pdf: 11895274 bytes, checksum: 0a59c54f104d2e95f8af0824dd15d853 (MD5)<br>Apesar do grande número de estudos sobre doenças causadas por Sclerotiniasclerotiorum, os processos componentes do ciclo das doenças nos diferentes hospedeiros são quase sempre estudados independentemente. O ciclo das doenças causadas por Sclerotiniaé bastante complexo, e pode ser dividido em quatro fases, correspondendo a estruturas típicas do ciclo de vida do patógeno. Essas fases correspondem à formação e função biológica de quatro tipos de propágulos: (1) escleródios, (2) apotécios e ascósporos, (3) pétalas infectadas, e (4) hifas infecciosas. Um etográfico serve para sintetizar o conhecimento relevante sobre a epidemiologia de uma doença. No primeiro capítulo, versões sucessivas de um etográfico são usadas para discutir a fenomenologia do mofo-branco do feijoeiro, enfatizando as relações entre propágulos de S. sclerotiorum, os sucessivos estágios da doença e os estágios de desenvolvimento do hospedeiro. O etográfico descreve a fenomenologia do mofo-branco do feijoeiro através do exame dos vários estágios do ciclo da doença em maior detalhamento do que geralmente é apresentado, e leva em consideração a concatenação de eventos pertinente ao ciclo. O método é útil em identificar os estágios-chave do ciclo e em explicitar as relações entre os estágios da doença, os quatro tipos de propágulos e os fatores que afetam seus respectivos processos de infecção. A abordagem também é útil como primeiro passo para modelagem quantitativa do mofo-branco do feijoeiro. No capítulo 2, foram analisados os estágios sucessivos (fases das epidemias), bem como seus processos de regulação e fatores envolvidos. Foram estudadas epidemias em lavouras de feijão, em condições ambientais naturais prevalecentes no período de inverno no Brasil Central. Os conjuntos de epidemias experimentais objetivaram promover uma série de epidemias de mofo branco. Cinquenta e sete epidemias, representando uma grande variação em níveis de severidade e formas de progresso da doença foram monitorados com atenção específica para os quatro tipos de propágulos considerados. As epidemias foram analisadas por diferentes técnicas estatísticas e três grupos (A, B e C) de epidemias foram identificados. O Grupo A inclui epidemias de lento estabelecimento, desenvolvidas em uma baixa taxa de infecção e levaram a incidências e severidades finais muito baixas. As epidemias no Grupo C tiveram um início precoce, progrediram muito rapidamente com uma taxa de infecção inicialmente elevada, seguida de estabilização. As epidemias no Grupo B apresentaram um comportamento intermediário, inicialmente com baixa taxa de progresso da doença, seguido por um forte aumento da taxa de infecção da folhagem em fases posteriores. Supõe-se que a infeção planta-a-planta (infecção secundária) ocorre raramente em epidemias do grupo A devido menor frequência de contatos efetivos, resultando em um pequeno número de lesões na folhagem e baixa incidência de plantas doentes (média de 12% de incidência). Por outro lado, presume-se que, em epidemias do Grupo C, infecções planta-a-planta ocorrem com frequência, devido maior frequência de contatos efetivos, que conduz a um número muito maior de lesões e maior incidência de plantas doentes (média de 81% de plantas doentes). Portanto, mesmo considerando a relevância do inóculo primário na forma de escleródios e a subsequente formação de apotécios, o papel das infecções subsequentes por outros propágulos em epidemias de mofo-branco deve ser levado em conta. No capítulo 3 é descrita a estrutura de um modelo de epidemias de mofo-branco em feijão que enfatiza os sucessivos tipos de propágulos do patógeno e sua interação com plantas hospedeiras. Um etográfico descrevendo o ciclo de infecção em feijão mofo-branco foi desenvolvido utilizando símbolos e conceitos desenvolvidos para análise de sistemas. Em seguida um modelo simplificado foi construído utilizando o programa STELLA® 10,6 (Isee system, EUA). Em seguida, oito parâmetros do modelo foram ajustados para variar em quatro níveis. Análises de sensibilidade e métodos estatísticos foram então conduzidos a fim de identificar lacunas, quais parâmetros mais contribuem para variabilidade dos resultados e quais parâmetros são altamente correlacionados com as saídas do modelo. A análise de sensibilidade do sub-modelo de germinação de escleródios mostrou que mudanças na taxa relativa de escleródios germinados (RRGSC) causou variação na área abaixo da curva de progresso da doença (AUDPC), que foram menores do que os causados pela variação no número de inicial de escleródios (SC). A análise de sensibilidade do sub-modelo de infecção de flor mostrou que alterações nos valores da taxa relativa de senescência floral (RRFS) causou menor variação na AUDPC do que mudanças na taxa relativa de infecção floral (RRFI). No terceiro sub-modelo de simulação de infecção da folhagem de feijão, a taxa relativa de infecção primária na folhagem (RRP) teve o mais forte efeito sobre os valores AUDPC. Diferentes análises (análise de variância e análise de componentes principais) indicam que SC, RRGS, RRFI, RRP e RRS foram os parâmetros mais importantes do modelo de simulação de epidemias de mofo-branco. Três grupos de epidemias foram estabelecidas utilizando os resultados do modelo (valores de AUDPC) como um critério para a formação de grupos. Como resultados, os três grupos de epidemias foram confirmados pela análise de discriminante envolvendo uma combinação de parâmetros do modelo de simulação mofo branco. Claramente, o patossistemaPhaseolusvulgaris - Sclerotiniasclerotiorum é muito mais complexo do que o modelo teórico geral para doenças "de juros simples", mesmo que a quantidade de inóculo inicial (na forma de propágulo 1, escleródios) permaneça como um dos mais importantes parâmetros, como mostrado por análise de sensibilidade.<br>Despite the large number of studies on Sclerotiniadiseases on several hosts, the processes composing disease cycles are almost always studied separately.The cycle of Sclerotiniadiseases is complex, and can be divided in four broad phases, corresponding to typical structures of the pathogen life cycle. These phases correspond to the formation and the biological functions of four different types of propagules: (1) sclerotia, (2) apothecia and ascospores, (3) infected petals, and (4) infectious hyphae. An ethograph graphically synthesizes knowledge relevant to epidemiology of a disease. In the first chapter, successive versions of an ethograph are used to discuss the phenomenology of the bean white mould cycle and to highlight relationships among S. sclerotiorum propagules, successive stages of the disease and bean developmental stages. The ethograph describe the phenomenology of bean white mould through the examination of the several stages of the disease cycle in more detail than it is usually attempted and taking into account the concatenation of events. The method is useful to identify key stages and to explicit the relationships among disease stages of the disease cycle, the four types of propagules, and the factors that affect their respective processes of infection. It constitutes an initial step to for the development of a quantitative, simulation model. In Chapter 2 we analysed these successive stage (phases), as well as their regulating processes and factors. Sets of experimental epidemics were created in bean fields under natural environmental conditions prevailing in the winter season in Central Brazil. The sets of experimental epidemics aimed to promote a range of white mould epidemics. Fifty-seven epidemics, representing a wide variation in severity levels and in disease progress shapes, were monitored, with specific attention paid to the four considered propagule types. Epidemics were analysed by different statistical techniques and three groups (A, B, or C) of epidemics were distinguished. Group A includes epidemics which were slow to establish, developed at a low rate, and led to very low terminal incidence and severity. Epidemics in Group C had an earlier onset, progressed very rapidly with an initially high rate of increase, followed by stabilization. Epidemics in Group B displayed an intermediate behaviour, with an initially low rate of disease increase, followed by a strong increase of the rate of foliage infection at later stages. It is assumed that plant-to-plant spread (secondary infection) occurs rarely in Group A epidemics because of the lower frequency of effective contacts, resulting into a small number of lesions on the foliage and low incidence of diseased plants (average 0.12% of incidence). By contrast, it is assumed that, in epidemics of Group C, plant-to-plant spread occurs frequently, because of the higher frequency of effective contacts, leading to a much higher number of lesions and higher incidence of diseased plants (average 0.81% of incidence). Therefore, even if the primary inoculum in the form of sclerotia and the subsequent formation of apothecia are, in part, relevant, the role of subsequent infections by other propagules on white mould epidemics must be taken into account. In chapter 3 we described the structure of a model for bean white mould epidemics that emphasizes on the successive types of pathogen propagules and their interaction with host plants. An ethograph describing the infection cycle in bean white mould was developed using symbols and concepts developed for system analysis and a simplified model was built using the STELLA® 10.6 programme (Isee systems, USA). Next, eight model parameters were set to vary in four levels for model evaluation. Sensitivity analyses and statistical methods were then conducted in order to identify gaps, which inputs contribute most to output variability and which parameters are most highly correlated with the outputs. Sensitivity analysis of the sclerotia germination sub-model showed that changes in the relative rate of germinated sclerotia (RRGSC) caused variation in the area under disease progress curve (AUDPC) that were smaller than those caused by variation in the parameter initial number of sclerotia (SC). Sensitivity analysis of the flower infection sub-model showed that changes in values of the relative rate of flower senescence (RRFS) caused narrower AUDPC variation than changes in the relative rate of flower infection, RRFI. In the third sub-model simulating infection of bean foliage, the relative rate of primary infection on foliage, RRP, had the strongest effect on AUDPC values. Different analyses (analyses of variance and principal component analysis) indicate that SC, RRGS, RRFI, RRP and RRS were the most important parameters of the white mould epidemic simulation model. Three epidemics groups were established using the outputs of the model (AUDPC values) as a criterion for group formation. As a result three epidemic groups were defined by discriminant analysis involving a combination of parameters of the white mould simulation model. Clearly, the bean (Phaseolus vulgaris) - Sclerotiniasclerotiorumpathosystem is much more complex than the theoretical general “simple interest” diseases model, even if the amount of initial inoculum (in the form of propagule 1, sclerotia) remains as one of the most important parameters, as shown by sensitivity analysis.

Ziel dieser Arbeit ist es, die Rolle von Pfaden für die Ausbreitung von Infektionskrankheiten auf komplexen Netzwerken zu untersuchen. Wir zeigen die Relevanz von Pfaden im Kontext der Epidemiologie in statischen und zeitabhängigen Netzwerken. Ein zentrales Ergebnis ist hierbei die Erreichbarkeitsentwicklung, die eine Analyse der Pfadstruktur zeitabhängiger Netzwerke erlaubt. In dieser Dissertation wird der Einfluss zweier bestimmter Merkmale statischer Netzwerke auf die Eigenschaften ihrer Pfadstruktur untersucht. Als Fallbeispiel analysieren wir hierfür ein Viehhandelsnetzwerk in Deutschland. Dieses Netzwerk besitzt eine Riesenkomponente und eine modulare Struktur. Die wichtigsten Ergebnisse sind hierbei, dass Netzwerke, die nahe an der Perkolationsschwelle liegen, mit großer Wahrscheinlichkeit zwei disjunkte Risikoklassen für Knoten aufweisen und, dass eine modulare Struktur eine signifikante Verzögerung von Krankheitsausbrüchen zur Folge hat. Hervorzuheben sind außerdem die Methoden, die hier zur Analyse zeitabhängiger Netzwerke vorgestellt werden. Das sind Systeme, in denen das Auftreten von Kanten mit der Zeit variiert. In dieser Arbeit stellen wir eine neue Methode vor, mit der die kausale Erreichbarkeit eines zeitabhängigen Netzwerks berechnet werden kann. Darüber hinaus stellen wir Erreichbarkeitsentwicklung als eine neue Methode zur Berechnung kürzester Pfaddauern in zeitabhängigen Netzwerken vor. Diese Herangehensweise ermöglicht es, charakteristische Zeitskalen für das Durchqueren von zeitabhängigen Netzwerken aufzuzeigen. Die Kenntnis solcher Zeitskalen ist von fundamentaler Wichtigkeit für die Abschätzung von Zeiten, die für die Verbreitung von Epidemien benötigt werden. Die Erreichbarkeit eines zeitabhängigen Netzwerks kann mit ihrem aggregierten Gegenstück verglichen werden. Damit definieren wir die Kausalitätstreue, die die Güte einer statischen Approximation eines zeitabhängigen Netzwerks quantifiziert.<br>The objective of this thesis is to examine the role of paths for the spread of infectious diseases on complex networks. We demonstrate the importance of paths in the context of epidemiology for the case of static and temporal networks. As a central result, we introduce the unfolding accessibility method, that allows for the analysis of the path structure of temporal networks. In this thesis, we analyze the impact of two particular attributes of static networks on the properties of their path structure. As a case study, we analyze the properties of a livestock trade network in Germany. This network exhibits a giant component and a modular structure. The main findings here are that networks close to the percolation threshold are likely to show two disjoint risk classes for the nodes and, a modular structure causes a significant delay for disease outbreaks. Furthermore, special emphasis should be placed on the methods introduced in this thesis for the analysis of temporal networks, i.e. systems where the occurrence of edges varies over time. In this work we introduce a novel method to obtain the causal accessibility graph of a temporal network. Moreover, we introduce unfolding accessibility as a novel formalism for the evaluation of shortest path durations in temporal networks. This approach is able to reveal characteristic timescales for the traversal of temporal networks. Knowledge of these timescales is of fundamental importance for the estimation of times needed for the spread of infectious diseases. The accessibility graph of a temporal network can be compared to its aggregated counterpart. Hence we define the causal fidelity, which quantifies the goodness of the static approximation of a temporal network from the causal point of view.

La dengue circule en Polynésie française sur un mode épidémique depuis plus de 35 ans. Néanmoins, en dépit de la taille relativement faible de la population de Polynésie française, la circulation de la dengue peut persister à de faibles niveaux pendant de nombreuses années. L’objectif de ce travail de thèse est de déterminer si l'épidémiologie de la dengue dans le système insulaire de la Polynésie française répond aux critères d’un contexte de métapopulation. Après avoir constitué une base de données regroupant les cas de dengue répertoriés sur les 35 dernières années, nous avons réalisé des analyses épidémiologiques descriptives et statistiques. Celles-ci ont révélé des disparités spatio-temporelles distinctes pour l’incidence de la dengue des archipels et des îles, mais la structure de l'épidémie globale à l’échelle de la Polynésie française pour un même sérotype ne semble pas être affectée. Les analyses de la métapopulation ont révélé l'incidence asynchrone de la dengue dans un grand nombre d’îles. Celle-ci s’observe plus particulièrement par la différence de dynamique de l’incidence entre les îles plus peuplées et celles ayant une population plus faible. La taille critique de la communauté nécessaire à la persistance de la dengue n’est même pas atteinte par la plus grande île de Polynésie Française, Tahiti. Ce résultat suggère que la dengue peut uniquement persister grâce à sa propagation d’île en île. L'incorporation de la connectivité des îles à travers des modèles de migration humaine dans un modèle mathématique a produit une dynamique de la dengue davantage en adéquation avec les données observées, que les tentatives de modélisation traitant la population dans son ensemble. Le modèle de la métapopulation a été capable de simuler la même dynamique que les cas de dengue observés pour l'épidémie et la transmission endémique qui a suivi pour la période de 2001 à 2008. Des analyses complémentaires sur la différenciation de l'incidence de la maladie et de l'infection seront probablement instructives pour affiner le modèle de métapopulation de l'épidémiologie de la dengue en Polynésie française<br>Dengue has been epidemic in French Polynesia for the past 35 years. Despite the relatively small population size in French Polynesia, dengue does not disappear and can persist at low levels for many years. In light of the large number of islands comprising French Polynesia, this thesis addresses the extent to which a metapopulation context may be the most appropriate to describe the epidemiology and persistence of dengue in this case. After compiling a database of dengue cases over the last 35 years, we used a number of descriptive and statistical epidemiological analyses that revealed distinct spatio-temporal disparity in dengue incidence for archipelago and islands. But the global structure of the epidemics of the same serotype were not affected. Metapopulation analyses revealed asynchronous dengue incidence among many of the islands and most notably larger islands lagged behind the smaller islands. The critical community size, which determines dengue persistence, was found to exceed even the largest island of Tahiti, suggesting that dengue can only exist by island-hopping. Incorporation of island connectedness through patterns of human migration into a mathematical model enabled a much better fit to the observed data than treating the population as a whole. The metapopulation model was able to capture to some extent the epidemic and low level transmission dynamics observed for the period of 2001-2008. Further analyses on differentiating incidence of disease and infection will likely prove informative for the metapopulation model of dengue epidemiology in French Polynesia

In my thesis I study the problem of predicting the evolution of the epidemic spreading on networks when incomplete information, in form of a partial observation, is available. I focus on the irreversible process described by the discrete time version of the Susceptible-Infected-Recovered (SIR) model on networks. Because of its intrinsic stochasticity, forecasting the SIR process is very difficult, even if the structure of individuals contact pattern is known. In today's interconnected and interdependent society, infectious diseases pose the threat of a worldwide epidemic spreading, hence governments and public health systems maintain surveillance programs to report and control the emergence of new disease event ranging from the seasonal influenza to the more severe HIV or Ebola. When new infection cases are discovered in the population it is necessary to provide real-time forecasting of the epidemic evolution. However the incompleteness of accessible data and the intrinsic stochasticity of the contagion pose a major challenge. The idea behind the work of my thesis is that the correct inference of the contagion process before the detection of the disease permits to use all the available information and, consequently, to obtain reliable predictions. I use the Belief Propagation approach for the prediction of SIR epidemics when a partial observation is available. In this case the reconstruction of the past dynamics can be efficiently performed by this method and exploited to analyze the evolution of the disease. Although the Belief Propagation provides exact results on trees, it turns out that is still a good approximation on general graphs. In this cases Belief Propagation may present convergence related issues, especially on dense networks. Moreover, since this approach is based on a very general principle, it can be adapted to study a wide range of issues, some of which I analyze in the thesis.

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.<br>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 investigates how health officials sought to preserve or recover good health during plague epidemics in Mantua, from 1463-1577. Scholarship on health boards in Italy has focused primarily on larger cities such as Milan, Florence and Venice, while many smaller cities and states which formed part of the wider network of interdependent health offices have yet to receive significant attention. This study attempts to address this imbalance by focussing on Mantua, a hitherto neglected area in the heart of northern Italy. Historians have shown by the sixteenth century health offices had wide-ranging responsibilities, yet their most important function remained tackling plague outbreaks through measures including trade and travel bans, quarantine periods and lazaretti. An analysis of the Mantuan health office’s actions and reactions reveal that it does not fit neatly with the health board model historians have established elsewhere in northern and central Italy. I will argue that while the hallmarks of the ‘Italian system’ of public health procedures are evident, closer examination of their organisation and composition reveals that they were shaped by the incidence and severity of outbreaks. Above all, however, they were dependent upon and defined by the evolving state apparatus and by participation of the wider community, both lay and ecclesiastic. Contrary to the view that permanent Italian health offices enforced plague regulations uniformly, there was a degree of flexibility in application within the structures created to fight plague. Further, it will be argued that by examining in detail symbolic acts, such as processions, in conjunction with practical methods we see with greater clarity how civic and ecclesiastical authorities worked together in the attempt to restore the city to good health. By exploring the dialogues between civic authorities, the people they governed and interactions between specific health agencies across the peninsula, this thesis contributes to the understanding of the Gonzagan state-building process and concepts of public health in Renaissance Italy.

This thesis is devoted to the study of different stochastic processes which have a common feature: they are Markov-modulated, which means that their evolution rules depend on the state occupied by an underlying Markov process. In the first part of this thesis, we analyse the stationary distribution and various first passage problems for Markov-modulated Brownian motions (MMBMs) as well as for two extensions: MMBMs with jumps and MMBMs modified by a temporary change of regime upon visits to level zero. The second part of this thesis is devoted to the use of Markov-modulated processes in mathematical finance, more precisely for the calculation of different option prices. We use a Fourier transform approach to price different European options (vanilla, exchange and quanto options) in the case where the value of the considered risky assets evolves like the exponential of a Markov-modulated Lévy process. The third part of this thesis is devoted to the study of some stochastic epidemic processes, namely the SIR processes. In our models, a Markov process is used to modulate the behaviour of the individuals who bring the disease. We use different martingale approaches as well as matrix analytic methods to obtain various information about the state of the population when the epidemic is over.<br>Doctorat en Sciences<br>info:eu-repo/semantics/nonPublished