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1
Sun, Lan. "Epidemic Content Distribution in Mobile Networks : A study of epidemic content distribution characteristic with social relationship evaluation." Thesis, KTH, Kommunikationssystem, CoS, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-118470.
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With the growing popularity of integrating mobile networks and social networks, people now enjoy a freer and more efficient means of communication. Smarter mobile devices facilitate modern human life. In the information age, various new types of information have begun to appear. How to disseminate content to people in a swift and fair way has long been a question. Choosing the right strategy for content distribution is especially crucial for mobile social networks. In this thesis project we use epidemic models for content distribution in mobile social networks. Stochastic mobility models and an SIR epidemic model are set up in the evaluation. We analyze the impact of various parameters of mobility models and epidemic model on content distribution’s success rate and delivery delay. Also, we exploit the social relationships to facilitate content distribution and show the impact of social relationships on content distribution. Simulations have shown that increasing speed and node number in the mobility models will have positive impact on content distribution success rate as well as decreasing the delay. The infect time limit and infect count limit of the epidemic model are also important for swiftly distributing content while considering energy consumption and fairness for nodes. In the social relationship simulation, nodes’ meeting times during a period of time are calculated and a threshold based on a certain level of meeting times is used for categorizing the friendship relationships between nodes. The results show that it will be easier for a successful distribution to be achieved as the social relationship between nodes gets stronger. Also, the delay shows a decreasing trend until reaching the ideal distribution delay time.Med den växande populariteten för att integrera mobila nätverk och sociala nätverk, människor njuta nu en friare och effektivare sätt att kommunicera. Smartare mobila enheter underlättar moderna människans liv. I den information som ålder, har olika nya typer av information börjat visas. Hur sprida innehåll till människor påett snabbt och rättvist sätt har länge varit en fråga. Att välja rätt strategi för distribution av innehåll är särskilt viktigt för mobila sociala nätverk. I den här avhandlingen projekt använder vi epidemiska modeller för distribution av innehåll i mobila sociala nätverk. Stokastiska rörlighet modeller och en SIR-epidemi modell sätts upp i utvärderingen. Vi analyserar effekterna av olika parametrar rörlighet modeller och epidemisk modell påinnehållsdistribution s framgång och leveransförsening. Dessutom utnyttjar vi de sociala relationerna för att underlätta distribution av innehåll och visa hur sociala relationer pådistribution av innehåll. Simuleringar har visat att ökad hastighet och nodnummer i rörlighet modellerna kommer att ha en positiv inverkan pådistribution av innehåll framgång samt att minska fördröjningen. Den infektera tid och infektera räkna gräns epidemin modellen är ocksåviktiga för att snabbt distribuera innehåll och samtidigt överväga energiförbrukning och rättvisa för noder. I den sociala relationen simulering är noder möte tid under en tidsperiod beräknas och en tröskel baserad påen viss nivåav mötestiden används för att kategorisera vänskap relationer mellan noder. Resultaten visade att det blir lättare för en lyckad spridning uppnås som den sociala relationen mellan noder blir starkare. Dessutom visar fördröjningen en nedåtgående trend tills den når fördröjningen av en ideal fördelning.
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Chilcote, Jonathan. "Epidemic and Opportunity: American Perceptions of the Spanish Influenza Epidemic." UKnowledge, 2016. http://uknowledge.uky.edu/history_etds/39.
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During the final months of the Great War, the loss of human life was not confined to the battlefields of Western Europe. The Spanish influenza virus was rapidly spreading around the globe¸ and would ultimately leave millions dead in its wake. Some American groups, both public and private, saw the pandemic as a blessing in disguise. They interpreted the pandemic as a sign that their work, whether religious, political, commercial, or health, was more vital to the world than ever before. Influenza reinforced their existing beliefs in the rightness and necessity of their causes, and used the pandemic as a call to increase their activities. American missionaries interpreted the pandemic and its spread as a sign of the backwardness of native peoples, and they argued that the United States and Americans had an increased duty after the War and pandemic to help foreign populations with education, sanitation, and religion. For American diplomats, the pandemic was a nuisance to their work of promoting and expanding American trade. Although it devastated societies, it was not destructive to international commerce. It did, though, provide an opportunity for Americans to teach foreign peoples about better health to protect them from future diseases, and to strengthen commercial ties with the rest of the world. The U.S. Government was greatly distracted with the war effort when the epidemic hit, and refused to take it seriously. They appropriated a small amount of money to the United States Public Health Service (PHS) to deal with the epidemic. This appropriation, although small, continued a trend of the federal government becoming more involved in health efforts at the expense of states, and was used as a justification for later federal health initiatives. The PHS actively used the influenza epidemic to push for their own expansion, arguing that their success in combatting influenza showed their merit, and used it to ensure that they would maintain their power and authority after the epidemic ceased. For all of these groups, the Spanish influenza epidemic provided an opportunity for their work, and reinforced their beliefs that their efforts were needed and vital to the nation and world.
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Hjerpe, Adam, and Linus Jägrell. "Epidemic Spreading of Messages." Thesis, KTH, Fysik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-129323.
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Rapidly growing popularity of mobile devices such as smartphones and digital tablets has changed the way people obtain information. Cellular and wireless local area networks provide almost ubiquitous connectivity. However, many scenarios threaten to leave us disconnected for extended periods of time. We study how peer-to-peer communication with mobile devices can be used without network infrastructure. With epidemic models for opportunistic content spreading we investigate the performance of such systems and compare them to simulated results. Real life mobility traces are used as a base to simulate how information is spread between the devices and two different types of spreading were studied in more detail. In particular, we investigate how fast a percentage of the total number of devices can receive the information. The results are displayed for the best performing device and indicate that these models does not necessarily have to agree with what actually happens. Nevertheless, we argue that the models provide a good mathematical framework for analyzing systems of this sort and conclude that these models can be extended to incorporate more general assumptions.
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Lloyd, Michael. "Nearest neighbour epidemic processes." Thesis, Heriot-Watt University, 1994. http://hdl.handle.net/10399/747.
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Павличева, Світлана Володимирівна, Светлана Владимировна Павлычева, Svitlana Volodymyrivna Pavlycheva, and O. Udoka. "Malaria epidemic in Nigeria." Thesis, Видавництво СумДУ, 2011. http://essuir.sumdu.edu.ua/handle/123456789/15950.
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The incidence of malaria is very high in Nigeria due to its tropical location. A number of factors appear to be contributing to the resurgence of malaria: rapid spread of resistance of malaria parasites to chloroquine and the other quinolines; frequent armed conflicts and civil unrest in many countries, forcing large populations to settle under difficult conditions, sometimes in areas of high malaria transmission
When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/15950
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Clancy, Damian. "Epidemic models in heterogeneous populations." Thesis, University of Nottingham, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.357928.
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McLean, Cory Y. (Cory Yuen Fu). "Epidemic modeling techniques for smallpox." Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/33148.
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Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.Includes bibliographical references (p. 119-121).
Infectious disease models predict the impact of outbreaks. Discrepancies between model predictions stem from both the disease parameters used and the underlying mathematics of the models. Smallpox has been modeled extensively in recent years to determine successful response guidelines for a future outbreak. Five models, which range in fidelity, were created for this thesis in an attempt to reveal the differences inherent in the mathematical techniques used in the models. The disease parameters were standardized across all models. Predictions for various outbreak scenarios are given, and the strengths and weaknesses of each modeling technique are discussed. The mixing strategy used greatly affects the predictions of the models. The results gathered indicate that mass vaccination should be considered as a primary response technique in the event of a future smallpox outbreak.
by Cory Y. McLean.
M.Eng.
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Ford, Ashley P. "Epidemic models and MCMC inference." Thesis, University of Warwick, 2014. http://wrap.warwick.ac.uk/66495/.
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Statistical inference and model choice for partially observed epidemics provide a variety of challenges both practical and theoretical. This thesis studies some related aspects of models for epidemics and their inference. The use of the matrix exponential to facilitate exact calculations in the General Stochastic Epidemic (GSE) is demonstrated, most usefully in providing the exact marginal likelihood when infection times are unobserved. The bipartite graph epidemic is defined and shown to be a flexible framework which encompasses many existing models. It also provides a way in which a deeper understanding of the relation between existing models could be obtained. The Indian buffet epidemic is introduced as a non-parametric approach to modelling unknown heterogeneous contact structures in epidemics. Inference for the Indian buffet epidemic is a challenging problem, some progress has been made. However the algorithms which have been studied do not yet scale to the size of problem where significant differences from the GSE are apparent. Evidence confirming and demonstrating the importance of understanding the tail behaviour of proposals in importance sampling is presented. The adverse impact of heavy tailed proposals on the Grouped Independence Metropolis-Hastings (GIMH) and Monte Carlo within Metropolis (MCWM) algorithms is demonstrated. A new algorithm, the Kernel Metropolis Hastings (KMH), is proposed as an approximate algorithm for low dimensional marginal inference in situations where the GIMH algorithm fails because of sticking. The KMH is demonstrated on a challenging 2-d problem.
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Pushmina, J. "The world economic crisis “epidemic”." Thesis, Ukrainian Academy of Banking of the National Bank of Ukraine, 2009. http://essuir.sumdu.edu.ua/handle/123456789/61316.
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Kostrygin, Anatolii. "Precise Analysis of Epidemic Algorithms." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLX042/document.
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La dissémination collaborative d'une information d'un agent à tous les autres agents d'un système distribué est un problème fondamental qui est particulièrement important lorsque l'on veut obtenir des algorithmes distribués qui sont à la fois robustes et fonctionnent dans un cadre anonyme, c'est-à-dire sans supposer que les agents possèdent des identifiants distincts connus. Ce problème, connu sous le nom de problème de propagation de rumeur , est à la base de nombreux algorithmes de communication sur des réseaux de capteurs sans-fil [Dimakis et al. (2010)] ou des réseaux mobiles ad-hoc. Il est aussi une brique de base centrale pour de nombreux algorithmes distribués avancés [Mosk-Aoyama et Shah (2008)].Les méthodes les plus connues pour surmonter les défis de robustesse et d'anonymat sont les algorithmes basés sur les ragots ( gossip-based algorithms ), c'est-à-dire sur la paradigme que les agents contact aléatoirement les autres agents pour envoyer ou récupérer l'information. Nousproposons une méthode générale d'analyse de la performance des algorithmes basés sur les ragots dans les graphes complets. Contrairement aux résultats précédents basés sur la structure précise des processus étudiés, notre analyse est basée sur la probabilité et la covariance des évènements correspondants au fait qu'un agent non-informé s'informe. Cette universalité nous permet de reproduire les résultats basiques concernant les protocoles classiques de push, pull et push-pull ainsi qu'analyser les certaines variantions telles que les échecs de communications ou les communications simultanés multiples réalisées par chaque agent. De plus, nous sommescapables d'analyser les certains modèles dynamiques quand le réseaux forme un graphe aléatoire échantillonné à nouveau à chaque étape [Clementi et al. (ESA 2013)]. Malgré sa généralité, notre méthode est simple et précise. Elle nous permet de déterminer l'espérance du temps de la diffusion à une constante additive près, ce qu'il est plus précis que la plupart des résultatsprécédents. Nous montrons aussi que la déviation du temps de la diffusion par rapport à son espérance est inférieure d'une constante r avec la probabilité au moins 1 − exp(Ω(r)).À la fin, nous discutons d'une hypothèse classique que les agents peuvent répondre à plusieurs appels entrants. Nous observons que la restriction à un seul appel entrant par agent provoque une décélération importante du temps de la diffusion pour un protocole de push-pull. En particulier, une phase finale du processus prend le temps logarithmique au lieu du temps double logarithmique. De plus, cela augmente le nombre de messages passés de Θ(n log log n) (valeur optimale selon [Karp et al. (FOCS 2000)]) au Θ(n log n) . Nous proposons une variation simple du protocole de push-pull qui rétablit une phase double logarithmique à nouveau et donc le nombre de messages passés redescend sur sa valeur optimalEpidemic algorithms are distributed algorithms in which the agents in thenetwork involve peers similarly to the spread of epidemics. In this work, we focus on randomized rumor spreading -- a class of epidemic algorithms based on the paradigm that nodes call random neighbors and exchange information with these contacts. Randomized rumor spreading has found numerous applications from the consistency maintenance of replicated databases to newsspreading in social networks. Numerous mathematical analyses of different rumor spreading algorithms can be found in the literature. Some of them provide extremely sharp estimates for the performance of such processes, but most of them are based on the inherent properties of concrete algorithms.We develop new simple and generic method to analyze randomized rumor spreading processes in fully connected networks. In contrast to all previous works, which heavily exploit the precise definition of the process under investigation, we only need to understand the probability and the covariance of the events that uninformed nodes become informed. This universality allows us to easily analyze the classic push, pull, and push-pull protocols both in their pure version and in several variations such as when messages fail with constant probability or when nodes call a random number of others each round. Some dynamic models can be analyzed as well, e.g., when the network is a random graph sampled independently each round [Clementi et al. (ESA 2013)]. Despite this generality, our method determines the expected rumor spreading time precisely apart from additive constants, which is more precise than almost all previous works. We also prove tail bounds showing that a deviation from the expectation by more than an additive number of r rounds occurs with probability at most exp(−Ω(r)).We further use our method to discuss the common assumption that nodes can answer any number of incoming calls. We observe that the restriction that only one call can be answered leads to a significant increase of the runtime of the push-pull protocol. In particular, the double logarithmic end phase of the process now takes logarithmic time. This also increases the message complexity from the asymptotically optimal Θ(n log log n) [Karp, Shenker, Schindelhauer, Vöcking (FOCS 2000)] to Θ(n log n). We propose a simple variation of the push-pull protocol that reverts back to the double logarithmic end phase and thus to the Θ(n log log n) message complexity
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Poletti, Piero. "Human Behavior in Epidemic Modelling." Doctoral thesis, Università degli studi di Trento, 2010. https://hdl.handle.net/11572/367834.
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Mathematical models represent a powerful tool for investigating the dynamics of human infection diseases, providing useful predictions about the spread of a disease and the effectiveness of possible control measures.
One of the central aspects to understand the dynamics of human infection is the heterogeneity in behavioral patters adopted by the host population. Beyond control measures imposed by public authorities, human behavioral changes can be triggered by uncoordinated responses driven by the diffusion of fear in the general population or by the risk perception.
In order to assess how and when behavioral changes can affect the spread of an epidemic, spontaneous social distancing - e.g. produced by avoiding crowded environments, using face masks or limiting travels - is investigated. Moreover, in order to assess whether vaccine preventable diseases can be eliminated through not compulsory vaccination programs, vaccination choices are investigated as well.
The proposed models are based on an evolutionary game theory framework. Considering dynamical games allows explicitly modeling the coupled dynamics of disease transmission and human behavioral changes. Specifically, the information diffusion is modeled through an imitation process in which the convenience of different behaviors depends on the perceived risk of infection and vaccine side effects. The proposed models allow the investigation of the effects of misperception of risks induced by partial, delayed or incorrect information (either concerning the state of the epidemic or vaccine side effects) as well.
The performed investigation highlights that a small reduction in the number of potentially infectious contacts in response to an epidemic and an initial misperception of the risk of infection can remarkably affect the spread of infection. On the other hand, the analysis of vaccination choices showed that concerns about proclaimed risks of vaccine side effects can result in widespread refusal of vaccination which in turn leads to drops in vaccine uptake and suboptimal vaccination coverage.
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Poletti, Piero. "Human Behavior in Epidemic Modelling." Doctoral thesis, University of Trento, 2010. http://eprints-phd.biblio.unitn.it/422/1/tesi.pdf.
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Mathematical models represent a powerful tool for investigating the dynamics of human infection diseases, providing useful predictions about the spread of a disease and the effectiveness of possible control measures.
One of the central aspects to understand the dynamics of human infection is the heterogeneity in behavioral patters adopted by the host population. Beyond control measures imposed by public authorities, human behavioral changes can be triggered by uncoordinated responses driven by the diffusion of fear in the general population or by the risk perception.
In order to assess how and when behavioral changes can affect the spread of an epidemic, spontaneous social distancing - e.g. produced by avoiding crowded environments, using face masks or limiting travels - is investigated. Moreover, in order to assess whether vaccine preventable diseases can be eliminated through not compulsory vaccination programs, vaccination choices are investigated as well.
The proposed models are based on an evolutionary game theory framework. Considering dynamical games allows explicitly modeling the coupled dynamics of disease transmission and human behavioral changes. Specifically, the information diffusion is modeled through an imitation process in which the convenience of different behaviors depends on the perceived risk of infection and vaccine side effects. The proposed models allow the investigation of the effects of misperception of risks induced by partial, delayed or incorrect information (either concerning the state of the epidemic or vaccine side effects) as well.
The performed investigation highlights that a small reduction in the number of potentially infectious contacts in response to an epidemic and an initial misperception of the risk of infection can remarkably affect the spread of infection. On the other hand, the analysis of vaccination choices showed that concerns about proclaimed risks of vaccine side effects can result in widespread refusal of vaccination which in turn leads to drops in vaccine uptake and suboptimal vaccination coverage.
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Lynteris, Christos. "Epidemic events : state-formation, class struggle and biopolitics in three epidemic crises of modern China." Thesis, University of St Andrews, 2010. http://hdl.handle.net/10023/2150.
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Based on extended research on Chinese medical and epidemiological archival material dating back to the beginning of the 20th century, and on six months of internship in epidemiology in Beijing’s Medical School and in Haidian District’s Centre of Disease Control and Prevention, this thesis explores the conjunction of three major epidemiological crises in modern Chinese history with processes of State formation: the 1911 Manchurian pneumonic plague, the 1952 germ-warfare, and the 2003 SARS outbreak. Analysing the three crises as Events in line with Alain Badiou’s epistemology it seeks to establish how different strategies of governmental fidelity to the imagined cause of each crisis have led to distinct modes of organisation and valorisation of the social: Republican China and its decline to fascism; the clash between professional revolutionaries and technocrats in Maoist China; and the emergence of the “Harmonious Society” of mass exploitation and repression today. This conjunction between State formation and epidemiological Events is explored with the use of Foucault’s genealogical method in a quest for a historical materialist approach that posits at its epicentre processes of class composition, decomposition and recomposition, and their contested enclosure by the governmental apparati of capture. The present thesis thus examines the three major epidemiological crises of modern China as forming grounds for biopolitical strategies that give rise to modes of subjectivation and circuits of debt/guilt within the context of the class struggle. And at the same time, it aims to create a new field of investigation for anthropology: the relation of State and Event, from a viewpoint that contests the accepted relation of event and structure expounded by Marshall Sahlins, proposing as the main object of this investigation the conjunction between necessity and will that can never be reduced either to the naturalism of historical determinism, nor to the culturalism of subjective contingency.
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Spencer, Simon. "Stochastic epidemic models for emerging diseases." Thesis, University of Nottingham, 2008. http://eprints.nottingham.ac.uk/11132/.
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In this thesis several problems concerning the stochastic modelling of emerging infections are considered. Mathematical modelling is often the only available method of predicting the extent of an emerging disease and assessing proposed control measures, as there may be little or no available data on previous outbreaks. Only stochastic models capture the inherent randomness in disease transmission observed in real-life outbreaks, which can strongly influence the outcome of an emerging epidemic because case numbers will initially be small compared with the population size. Chapter 2 considers a model for diseases in which some of the cases exhibit no symptoms and are therefore difficult to observe. Examples of such diseases include influenza, mumps and polio. This chapter investigates the problem of determining whether or not the epidemic has died out if a period containing no symptomatic individuals is observed. When modelling interventions, it is realistic to include a delay between observing the presence of infection and the implementation of control measures. Chapter 3 quantifies the effect that the length of such a delay has on an epidemic amongst a population divided into households. As well as a constant delay, an exponentially distributed delay is also considered. Chapter 4 develops a model for the spread of an emerging strain of influenza in humans. By considering the probability that an outbreak will be contained within a region in which an intervention strategy is active, it becomes possible to quantify and therefore compare the effectiveness of intervention strategies.
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Eze, Jude Ikechukwu. "Modelling HIV/AIDS epidemic in Nigeria." Thesis, University of Glasgow, 2009. http://theses.gla.ac.uk/642/.
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Nigeria is one of the countries most affected by the HIV/AIDS pandemic, third only to India and South Africa. With about 10% of the global HIV/AIDS cases estimated to be in the country, the public health and socio-economic implications are enormous. This thesis has two broad aims: the first is to develop statistical models which adequately describe the spatial distribution of the Nigerian HIV/AIDS epidemic and its associated ecological risk factors; the second, to develop models that could reconstruct the HIV incidence curve, obtain an estimate of the hidden HIV/AIDS population and a short term projection for AIDS incidence and a measure of precision of the estimates. To achieve these objectives, we first examined data from various sources and selected three sets of data based on national coverage and minimal reporting delay. The data sets are the outcome of the National HIV/AIDS Sentinel Surveillance Survey conducted in 1999, 2001, 2003 and 2005 by the Federal Ministry of Health; the outcome of the survey of 1057 health and laboratory facilities conducted by the Nigerian Institute of Medical Research in 2000; and case by case HIV screening data collected from an HIV/AIDS centre of excellence. A thorough review of methods used by WHO/UNAIDS to produce estimates of the Nigerian HIV/AIDS scenario was carried out. The Estimation and Projection Package (EPP) currently being used for modelling the epidemic partitions the population into at-risk, not-at-risk and infected sub-populations. It also requires some parameter input representing the force of infection and behaviour or high risk adjustment parameter. It may be difficult to precisely ascertain the size of these population groups and parameters in countries as large and diverse as Nigeria. Also, the accuracy of vital rates used in the EPP and Spectrum program is doubtful. Literature on ordinary back-calculation, nonparametric back-calculation, and modified back-calculation methods was reviewed in detail. Also, an indepth review of disease mapping techniques including multilevel models and geostatistical methods was conducted. The existence of spatial clusters was investigated using cluster analysis and some measure of spatial autocorrelation (Moran I and Geary c coefficients, semivariogram and kriging) applied to the National HIV/AIDS Surveillance data. Results revealed the existence of spatial clusters with significant positive spatial autocorrelation coefficients that tended to get stronger as the epidemic developed through time. GAM and local regression fit on the data revealed spatial trends on the north-south and east - west axis. Analysis of hierarchical, spatial and ecological factor effects on the geographical variation of HIV prevalence using variance component and spatial multilevel models was performed using restricted maximum likelihood implemented in R and empirical and full Bayesian methods in WinBUGS. Results confirmed significant spatial effects and some ecological factors were significant in explaining the variation. Also, variation due to various levels of aggregation was prominent. Estimates of cumulative HIV infection in Nigeria were obtained from both parametric and nonparametric back-calculation methods. Step and spline functions were assumed for the HIV infection curve in the parametric case. Parameter estimates obtained using 3-step and 4-step models were similar but the standard errors of these parameters were higher in the 4-step model. Estimates obtained using linear, quadratic, cubic and natural splines differed and also depended on the number and positions of the knots. Cumulative HIV infection estimates obtained using the step function models were comparable with those obtained using nonparametric back-calculation methods. Estimates from nonparametric back-calculation were obtained using the EMS algorithm. The modified nonparametric back-calculation method makes use of HIV data instead of the AIDS incidence data that are used in parametric and ordinary nonparametric back-calculation methods. In this approach, the hazard of undergoing HIV test is different for routine and symptom-related tests. The constant hazard of routine testing and the proportionality coefficient of symptom-related tests were estimated from the data and incorporated into the HIV induction distribution function. Estimates of HIV prevalence differ widely (about three times higher) from those obtained using parametric and ordinary nonparametric back-calculation methods. Nonparametric bootstrap procedure was used to obtain point-wise confidence interval and the uncertainty in estimating or predicting precisely the most recent incidence of AIDS or HIV infection was noticeable in the models but greater when AIDS data was used in the back-projection model. Analysis of case by case HIV screening data indicate that of 33349 patients who attended the HIV laboratory of a centre of excellence for the treatment of HIV/AIDS between October 2000 and August 2006, 7646 (23%) were HIV positive with females constituting about 61% of the positive cases. The bulk of infection was found in patients aged 15-49 years, about 86 percent of infected females and 78 percent of males were in this age group. Attendance at the laboratory and the proportion of HIV positive tests witnessed a remarkable increase when screening became free of charge. Logistic regression analysis indicated a 3-way interaction between time period, age and sex. Removing the effect of time by stratifying by time period left 2-way interactions between age and sex. A Correction factor for underreporting was ascertained by studying attendance at the laboratory facility over two time periods defined by the cost of HIV screening. Estimates of HIV prevalence obtained from corrected data using the modified nonparametric back-calculation are comparable with UN estimates obtained by a different method. The Nigerian HIV/AIDS pandemic is made up of multiple epidemics spatially located in different parts of the country with most of them having the potential of being sustained into the future given information on some risk factors. It is hoped that the findings of this research will be a ready tool in the hands of policy makers in the formulation of policy and design of programs to combat the epidemic in the country. Access to data on HIV/AIDS are highly restricted in the country and this hampers more in-depth modelling of the epidemic. Subject to data availability, we recommend that further work be done on the construction of stratification models based on sex, age and the geopolitical zones in order to estimate the infection intensity in each of the population groups. Uncertainties surrounding assumptions of infection intensity and incubation distribution can be minimized using Bayesian methods in back-projection.
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Giles, Philip R. "Bayesian inference for stochastic epidemic models." Thesis, University of Newcastle Upon Tyne, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.420008.
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Sherborne, Neil. "Non-Markovian epidemic dynamics on networks." Thesis, University of Sussex, 2018. http://sro.sussex.ac.uk/id/eprint/79084/.
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The use of networks to model the spread of epidemics through structured populations is widespread. However, epidemics on networks lead to intractable exact systems with the need to coarse grain and focus on some average quantities. Often, the underlying stochastic processes are Markovian and so are the resulting mean-field models constructed as systems of ordinary differential equations (ODEs). However, the lack of memory (or memorylessness) does not accurately describe real disease dynamics. For instance, many epidemiological studies have shown that the true distribution of the infectious period is rather centred around its mean, whereas the memoryless assumption imposes an exponential distribution on the infectious period. Assumptions such as these greatly affect the predicted course of an epidemic and can lead to inaccurate predictions about disease spread. Such limitations of existing approaches to modelling epidemics on networks motivated my efforts to develop non-Markovian models which would be better suited to capture essential realistic features of disease dynamics. In the first part of my thesis I developed a pairwise, multi-stage SIR (susceptible-infected-recovered) model. Each infectious node goes through some K 2 N infectious stages, which for K > 1 means that the infectious period is gamma-distributed. Analysis of the model provided analytic expressions for the epidemic threshold and the expected final epidemic size. Using available epidemiological data on the infectious periods of various diseases, I demonstrated the importance of considering the shape of the infectious period distribution. The second part of the thesis expanded the framework of non-Markovian dynamics to networks with heterogeneous degree distributions with non-negligible levels of clustering. These properties are ubiquitous in many real-world networks and make model development and analysis much more challenging. To this end, I have derived and analysed a compact pairwise model with the number of equations being independent of the range of node degrees, and investigated the effects of clustering on epidemic dynamics. My thesis culminated with the third part where I explored the relationships between several different modelling methodologies, and derived an original non-Markovian Edge-Based Compartmental Model (EBCM) which allows both transmission and recovery to be arbitrary independent stochastic processes. The major result is a rigorous mathematical proof that the message passing (MP) model and the EBCM are equivalent, and thus, the EBCM is statistically exact on the ensemble of configuration model networks. From this consideration I derived a generalised pairwise-like model which I then used to build a model hierarchy, and to show that, given corresponding parameters and initial conditions, these models are identical to MP model or EBCM. In the final part of my thesis I considered the important problem of coupling epidemic dynamics with changes in network structure in response to the perceived risk of the epidemic. This was framed as a susceptible-infected-susceptible (SIS) model on an adaptive network, where susceptible nodes can disconnect from infected neighbours and, after some fixed time delay, connect to a random susceptible node that they are not yet connected to. This model assumes that nodes have perfect information on the state of all other nodes. Robust oscillations were found in a significant region of the parameter space, including an enclosed region known as an 'endemic bubble'. The major contribution of this work was to show that oscillations can occur in a wide region of the parameter space, this is in stark contrast with most previous research where oscillations were limited to a very narrow region of the parameter space. Any mathematical model is a simplification of reality where assumptions must be made. The models presented here show the importance of interrogating these assumptions to ensure that they are as realistic as possible while still being amenable to analysis.
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Ndeffo, Mbah Martial Loth. "Optimizing epidemic control under economic constraints." Thesis, University of Cambridge, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.609007.
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SOUZA, Danillo Barros de. "Analytic solutions to stochastic epidemic models." Universidade Federal de Pernambuco, 2017. https://repositorio.ufpe.br/handle/123456789/25518.
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Even the simplest outbreaks might not be easily predictable. Fortunately, deterministic and stochastic models, systems differential equations and computational simulations have proved to be useful to a better understanding of the mechanics that leads to an epidemic outbreak. Whilst such systems are regularly studied from a modelling viewpoint using stochastic simulation algorithms, numerous potential analytical tools can be inherited from statistical and quantum physics, replacing randomness due to quantum fluctuations with low copy number stochasticity. Here, the Fock space representation, used in quantum mechanics, is combined with the symbolic algebra of creation and annihilation operators to consider explicit solutions for the master equations describing epidemics represented via the SIR model (Susceptible-Infected-Recovered), originally developed via Kermack and McKendrick’s theory. This is illustrated with an exact solution for a short size of population, including a consideration of very short time scales for the next infection, which emphasises when stiffness is present even for small copy numbers. Furthermore, we present a general matrix representation for the SIR model with an arbitrary number of individuals following diagonalization. This leads to the solution of this complex stochastic problem, including an explicit way to express the mean time of epidemic and basic reproduction number depending on the size of population and parameters of infection and recovery. Specifically, the project objective to apply use of the same tools in the approach of system governed by law of mass action, as previously developed for the Michaelis-Menten enzyme kinetics model [Santos et. al. Phys Rev. E 92, 062714 (2015)]. For this, a flexible symbolic Maple code is provided, demonstrating the prospective advantages of this framework compared to Gillespie stochastic simulation algorithms.
Mesmo os surtos mais simples podem não ser facilmente previsíveis. Felizmente, modelos determinísticos e estocásticos, equações diferenciais de sistemas e simulações computa- cionais provaram ser úteis para uma melhor compreensão da mecânica que leva a um surto epidêmico. Enquanto tais sistemas são regularmente estudados a partir de um ponto de vista de modelagem usando algoritmos de simulação estocástica, inúmeras ferramentas analíticas potenciais podem ser herdadas da física estatística e quântica, substituindo aleatoriedade devido a flutuações quânticas com baixa estocástica de número de cópias. Aqui, a representação do espaço de Fock, usada na mecânica quântica, é combinada com a álgebra simbólica dos operadores de criação e aniquilação para considerar soluções explícitas para as equações mestra que descrevem epidemias representadas via modelo SIR (Suscetível-Infectado-Recuperado), originalmente desenvolvido pela teoria de Kermack e McKendrick. Isto é ilustrado com uma solução exata para um tamanho pequeno de população, considerando escalas de tempo muito curtas para a próxima infecção, que enfatiza quando a rigidez está presente mesmo para números de cópias pequenos. Além disso, apresentamos uma representação matricial geral para o modelo SIR com um número arbitrário de indivíduos após diagonalização. Isto nos leva à solução deste problema es- tocástico complexo, além de ter uma maneira explícita de expressar o tempo médio de epidemia e o número básico de reprodução, ambos dependendo do tamanho da população e parâmetros de infecção e recuperação. Especificamente, o objetivo é utilizar as mesmas ferramentas na abordagem de um sistema regido por lei de ação das massas, como anterior- mente desenvolvido para o modelo de cinética enzimática de Michaelis-Menten [Santos et. Al PRE 2015]. Para isso, é fornecido um código Maple simbólico flexível, demonstrando as vantagens potenciais desta estrutura comparados aos algoritmos de simulação estocástica de Gillespie.
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Li, Zihao. "Power Study on Testing Epidemic Alternatives." FIU Digital Commons, 2013. http://digitalcommons.fiu.edu/etd/820.
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Detecting change points in epidemic models has been studied by many scholars. Yao (1993) summarized five existing test statistics in the literature. Out of those test statistics, it was observed that the likelihood ratio statistic showed its standout power. However, all of the existing test statistics are based on an assumption that population variance is known, which is an unrealistic assumption in practice. To avoid assuming known population variance, a new test statistic for detecting epidemic models is studied in this thesis. The new test statistic is a parameter-free test statistic which is more powerful compared to the existing test statistics. Different sample sizes and lengths of epidemic durations are used for the power comparison purpose. Monte Carlo simulation is used to find the critical values of the new test statistic and to perform the power comparison. Based on the Monte Carlo simulation result, it can be concluded that the sample size and the length of the duration have some effect on the power of the tests. It can also be observed that the new test statistic studied in this thesis has higher power than the existing test statistics do in all of cases.
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Burch, Mark G. "Statistical Methods for Network Epidemic Models." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1471613656.
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Zong, Susan Rong. "A model for the AIDS epidemic /." The Ohio State University, 1992. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487841548269467.
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Brettle, Raymond Patrick. "Human immunodeficiency virus : the Edinburgh epidemic." Thesis, University of Edinburgh, 1995. http://hdl.handle.net/1842/20883.
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For a variety of socio-economic reasons an epidemic of injection drug use (IDU) involving heroin occurred during the early 1980's in Edinburgh: one third were female, most were young, unemployed and living on large council estates. At the peak of this IDU epidemic, HIV arrived and rapidly spread through this community. By July 1989 over 1000 individuals or 0.1% of the population of Lothian (750,000) had been recognised to have been infected with HIV, the majority via IDU. This is of the same order as the worst affected region in England (North West Thames). The majority of these individuals however live in the City of Edinburgh with a population of only around 300,000 (1981 census). Consequently a realistic prevalence for this population is actually 0.3% or 3 times the worst affected English region. Thus this new area of medicine has considerable relevance for future medicine in Edinburgh and Scotland. The thesis describes the disease, the epidemiology of Injection Drug Use and IDU related HIV and the early epidemic in Edinburgh. It also describes the clinical services that were developed at the City Hospital in Edinburgh and the problems that this new service encountered. The provision of health care for this difficult patient population facilitated a variety of research projects. The thesis describes some of the results of these projects particularly those concerned with natural history, clinical presentation and use of antiretroviral therapy in IDU related HIV. Lastly the factors found to affect the transmission of HIV to the heterosexual partners of the patients are presented together with their relevance for other populations.
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Black, Andrew James. "The stochastic dynamics of epidemic models." Thesis, University of Manchester, 2010. https://www.research.manchester.ac.uk/portal/en/theses/the-stochastic-dynamics-of-epidemic-models(196cf4a1-2db2-4696-bc64-64fb28cb0b7d).html.
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This thesis is concerned with quantifying the dynamical role of stochasticity in models of recurrent epidemics. Although the simulation of stochastic models can accurately capture the qualitative epidemic patterns of childhood diseases, there is still considerable discussion concerning the basic mechanisms generating these patterns. The novel aspect of this thesis is the use of analytic methods to quantify the results from simulations. All the models are formulated as continuous time Markov processes, the temporal evolutions of which is described by a master equation. This is expanded in the inverse system size, which decomposes the full stochastic dynamics into a macroscopic part, described by deterministic equations, plus a stochastic fluctuating part. The first part examines the inclusion of non-exponential latent and infectious periods into the the standard susceptible-infectious-recovered model. The method of stages is used to formulate the problem as a Markov process and thus derive a power spectrum for the stochastic oscillations. This model is used to understand the dynamics of whooping cough, which we show to be the mixture of an annual limit cycle plus resonant stochastic oscillations. This limit cycle is generated by the time-dependent external forcing, but we show that the spectrum is close to that predicted by the unforced model. It is demonstrated that adding distributed infectious periods only changes the frequency and amplitude of the stochastic oscillations---the basic mechanisms remain the same. In the final part of this thesis, the effect of seasonal forcing is studied with an analysis of the full time-dependent master equation. The comprehensive nature of this approach allows us to give a coherent picture of the dynamics which unifies past work, but which also provides a systematic method for predicting the periods of oscillations seen in measles epidemics. In the pre-vaccination regime the dynamics are dominated by a period doubling bifurcation, which leads to large biennial oscillations in the deterministic dynamics. Vaccination is shown to move the system away from the biennial limit cycle and into a region where there is an annual limit cycle and stochastic oscillations, similar to whooping cough. Finite size effects are investigated and found to be of considerable importance for measles dynamics, especially in the biennial regime.
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Nirkhiwale, Supriya. "Optimal mobility patterns in epidemic networks." Thesis, Manhattan, Kan. : Kansas State University, 2009. http://hdl.handle.net/2097/1494.
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Soto, Martín Sara. "Morbillivirus infection in Mediterranean striped dolphins (Stenella coeruleoalba) during the 2007 epidemic and the post-epidemic years." Doctoral thesis, Universitat Autònoma de Barcelona, 2014. http://hdl.handle.net/10803/284390.
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En el verano de 2007 un elevado número de delfines listados (Stenella coeruleoalba) apareció varado en la costa Mediterránea en España. Los estudios histopatológicos, inmunohistoquímicos y de RT-PCR realizados a partir de muestras de estos delfines confirmaron la reaparición de una epidemia de morbillivirus, que se extendió posteriormente por el Mediterráneo Francés. En dichas muestras se detectó un Morbillivirus del delfín (DMV, considerado una cepa de la especie Morbillivirus de cetáceos CeMV) muy próximo al virus detectado en la epidemia anterior, ocurrida en 1990. Esta tesis reune tres artículos publicados en revistas científicas y un capítulo de un libro, en los que se describen los hallazgos patológicos en delfines listados varados durante la epidemia en 2007 en Cataluña, y los hallazgos patológicos y de RT-PCR en los delfines listados varados en Cataluña, Comunidad Valenciana y Andalucía en los años posteriores. Los delfines afectados por la epidemia de 2007 mostraron lesiones similares a las descritas en la epidemia de 1990, siendo neumonía bronquiolo-intersticial, depleción linfoide y meningoencefalitis no supurativa los hallazgos microscópicos principales. También en 2007 algunos delfines presentaban lesiones asociadas a agentes infecciosos oportunistas entre los que se encontraba, además de Toxoplasma gondii y hongos compatibles con Aspergillus spp., alfaherpesvirus. Este virus ha sido detectado en varios delfines afectados durante la epidemia, causando en un caso enfermedad concomitante a la infección por morbillivirus. Los delfines listados muertos durante la epidemia de 2007 mostraron menor longitud que los muertos en la epidemia de 1990, lo que podría sugerir que los delfines de mayor edad que estuvieron en contacto con el virus en 1990 estarían protegidos frente a una reinfección. Los estudios inmunohistoquímicos realizados con tejidos de cetáceos varados en Cataluña en los años transcurridos entre ambas epidemias respaldarían la hipótesis de ausencia de circulación del CeMV en el Mediterráneo en el periodo interepidémico. En los años posteriores a 2007 numerosos delfines listados han sido hallados esporádicamente en la costa Mediterránea española afectados por la forma crónica de la infección de morbillivirus. Esta presentación crónica de la enfermedad, descrita tras la epidemia de 1990, se caracteriza por la deteccción de lesiones y virus únicamente en el encéfalo de los delfines, a diferencia de la presencia de lesiones y virus en múltiples órganos que muestran los delfines afectados durante las epidemias. La forma crónica de morbillivirus en delfines muestra similitudes con otras infecciones crónicas debidas a morbillivirus, como la panencefalitis esclerosante subaguda causada por el virus del sarampión en humanos, y la encefalitis del perro viejo causada por el virus del moquillo canino. Sin embargo, dado que actualmente son más las incógnitas que las respuestas, se requeriría continuar investigando sobre el morbillivirus del delfín para poder aclarar aspectos como la patogenia y los mecanismos de persistencia del virus en los delfines afectados por la forma crónica.In the summer 2007 high number of striped dolphins (Stenella coeruleoalba) stranded on the Spanish Mediterranean coast. Histopathological, immunohistochemical and RT-PCR analysis performed with dolphin material from these strandings confirmed the re-emergence of a morbillivirus epizootic, which afterwards spread to French Mediterranean waters. The Dolphin morbillivirus (DMV, a Cetacean Morbillivirus (CeMV) viral strain) detected showed close relationship to the DMV strain isolated in the previous epizootic, occurred in 1990. This thesis aimed to compile three articles published in peer-reviewed journals and one book chapter describing the pathological findings observed in the striped dolphins affected by the 2007 epizootic in Catalonia, and the pathological and RT-PCR findings observed in Catalonia, Valencia Region and Andalusia in the following years. The lesions observed in the dolphins affected by the 2007 epizootic were similar to those described in the 1990 epizootic, with bronchiolo-interstitial pneumonia, lymphoid depletion and non-suppurative meningoencephalitis as main microscopic findings. In addition several dolphins affected in 2007 also showed, as occurred in 1990, secondary opportunistic infections. But beside to Toxoplasma gondii and Aspergillus spp. like fungus, alphaherpesvirus systemic concomitant infection and disease were also observed in the 2007 outbreak. Striped dolphins affected in 2007 were shorter in length than those affected in 1990, suggesting that older dolphins may have been protected from the infection due to a previous exposure to the virus in the first epizootic. The immunohistochemical studies performed with cetacean tissues from strandings occurred on the Catalonian coast between the 1990 and the 2007 morbillivirus epizootics would support the hypothesis that CeMV has not circulated in the Mediterranean Sea in the interepidemic period. In the years following the 2007 epizootic numerous striped dolphins have been randomly found along the Spanish Mediterranean coast showing the chronic form of morbillivirus infection already described after the 1990 epizootic. The chronic form is characterized by the detection of lesions and virus only in the brain of the affected dolphins, instead of the classic systemic distribution of lesions and virus observed during the epizootics. This presentation of the disease in dolphins shows similarities with other chronic diseases caused by morbilliviruses, as subacute sclerosing panencephalitis due to Measles virus in humans, and old dog encephalitis due to Canine distemper virus in dogs. However, further investigations would be required in order to clarify the pathogenesis and the viral persistence mechanisms in the dolphin morbillivirus chronic form.
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Ahillen, Caroline. "Agent-based modeling of the spread of the 1918-1919 Spanish Flu in three Canadian fur trading communities." Diss., Columbia, Mo. : University of Missouri-Columbia, 2006. http://hdl.handle.net/10355/4582.
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Thesis (M.A.)--University of Missouri-Columbia, 2006.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 (February 5, 2007) Includes bibliographical references.
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Sensi, Mattia. "A Geometric Singular Perturbation approach to epidemic compartmental models." Doctoral thesis, Università degli studi di Trento, 2021. http://hdl.handle.net/11572/286191.
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We study fast-slow versions of the SIR, SIRS and SIRWS epidemiological models, and of the SIRS epidemiological model on homogeneous graphs, obtained through the application of the moment closure method. The multiple time scale behavior is introduced to account for large differences between some of the rates of the epidemiological pathways. Our main purpose is to show that the fast-slow models, even though in nonstandard form, can be studied by means of Geometric Singular Perturbation Theory (GSPT). In particular, without using Lyapunov's method, we are able to not only analyze the stability of the endemic equilibria of the SIR and SIRS models, but also to show that in the remaining models limit cycles arise. We show that the proposed approach is particularly useful in more complicated (higher dimensional) models such as the SIRWS model and the SIRS on homogeneous graphs, for which we provide a detailed description of their dynamics by combining analytic and numerical techniques. In particular, for the latter we show that the model can give rise to periodic solutions, differently from the corresponding model based on homogeneous mixing.
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Sensi, Mattia. "A Geometric Singular Perturbation approach to epidemic compartmental models." Doctoral thesis, Università degli studi di Trento, 2021. http://hdl.handle.net/11572/286191.
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We study fast-slow versions of the SIR, SIRS and SIRWS epidemiological models, and of the SIRS epidemiological model on homogeneous graphs, obtained through the application of the moment closure method. The multiple time scale behavior is introduced to account for large differences between some of the rates of the epidemiological pathways. Our main purpose is to show that the fast-slow models, even though in nonstandard form, can be studied by means of Geometric Singular Perturbation Theory (GSPT). In particular, without using Lyapunov's method, we are able to not only analyze the stability of the endemic equilibria of the SIR and SIRS models, but also to show that in the remaining models limit cycles arise. We show that the proposed approach is particularly useful in more complicated (higher dimensional) models such as the SIRWS model and the SIRS on homogeneous graphs, for which we provide a detailed description of their dynamics by combining analytic and numerical techniques. In particular, for the latter we show that the model can give rise to periodic solutions, differently from the corresponding model based on homogeneous mixing.
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Allander, Lisa. "Fitness and virulence of epidemic and non-epidemic clones of extensively drug-resistant (XDR) carbapenemase-producing Klebsiella pneumoniae." Thesis, Uppsala universitet, Institutionen för medicinsk biokemi och mikrobiologi, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-356714.
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Andersson, Håkan. "Limit theorems for some stochastic epidemic models." Stockholm : Stockholm University, 1994. http://catalog.hathitrust.org/api/volumes/oclc/40258819.html.
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Alharthi, Muteb. "Bayesian model assessment for stochastic epidemic models." Thesis, University of Nottingham, 2016. http://eprints.nottingham.ac.uk/33182/.
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Acrucial practical advantage of infectious diseases modelling as a public health tool lies in its application to evaluate various disease-control policies. However, such evaluation is of limited use, unless a sufficiently accurate epidemic model is applied. If the model provides an adequate fit, it is possible to interpret parameter estimates, compare disease epidemics and implement control procedures. Methods to assess and compare stochastic epidemic models in a Bayesian framework are not well-established, particularly in epidemic settings with missing data. In this thesis, we develop novel methods for both model adequacy and model choice for stochastic epidemic models. We work with continuous time epidemic models and assume that only case detection times of infected individuals are available, corresponding to removal times. Throughout, we illustrate our methods using both simulated outbreak data and real disease data. Data augmented Markov Chain Monte Carlo (MCMC) algorithms are employed to make inference for unobserved infection times and model parameters. Under a Bayesian framework, we first conduct a systematic investigation of three different but natural methods of model adequacy for SIR (Susceptible-Infective-Removed) epidemic models. We proceed to develop a new two-stage method for assessing the adequacy of epidemic models. In this two stage method, two predictive distributions are examined, namely the predictive distribution of the final size of the epidemic and the predictive distribution of the removal times. The idea is based onlooking explicitly at the discrepancy between the observed and predicted removal times using the posterior predictive model checking approach in which the notion of Bayesian residuals and the and the posterior predictive p−value are utilized. This approach differs, most importantly, from classical likelihood-based approaches by taking into account uncertainty in both model stochasticity and model parameters. The two-stage method explores how SIR models with different infection mechanisms, infectious periods and population structures can be assessed and distinguished given only a set of removal times. In the last part of this thesis, we consider Bayesian model choice methods for epidemic models. We derive explicit forms for Bayes factors in two different epidemic settings, given complete epidemic data. Additionally, in the setting where the available data are partially observed, we extend the existing power posterior method for estimating Bayes factors to models incorporating missing data and successfully apply our missing-data extension of the power posterior method to various epidemic settings. We further consider the performance of the deviance information criterion (DIC) method to select between epidemic models.
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Akre, Olof. "Etiological insights into the testicular cancer epidemic /." Stockholm, 1999. http://diss.kib.ki.se/1999/91-628-3689-7/.
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Gray, Bruce James. ""The killing fields" : the global landmine epidemic /." Title page, table of contents and abstract only, 1996. http://web4.library.adelaide.edu.au/theses/09ENV/09envg778.pdf.
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Wheeler, Karen A. "Modelling the spread of the AIDS epidemic." Thesis, Cardiff University, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.308594.
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Stacey, Adrian James. "Fungal growth : a mechanism for epidemic development." Thesis, University of Cambridge, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.621921.
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Fujie, Ryo, and Takashi Odagaki. "Effects of superspreaders in spread of epidemic." Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-193370.
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Goering, Max. "The modulus and epidemic processes on graphs." Thesis, Kansas State University, 2015. http://hdl.handle.net/2097/20364.
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Master of ScienceDepartment of Mathematics
Pietro Poggi-Corradini
This thesis contains three chapters split into two parts. In the first chapter, the discrete p-modulus of families of walks is introduced and discussed from various perspectives. Initially, we prove many properties by mimicking the theory from the continuous case and use Arne Beurling's criterion for extremality to build insight and intuition regarding the modulus. After building an intuitive understanding of the p-modulus, we proceed to switch perspectives to that of convex analysis. From here, uniqueness and existence of extremal densities is shown and a better understanding of Beurling's criterion is developed before describing an algorithm that approximates the value of the p-modulus arbitrarily well. In the second chapter, an exclusively edge-based approach to the discrete transboundary modulus is described. Then an interesting application is discussed with some preliminary numerical results. The final chapter describes four different takes of the Susceptible-Infected (SI) epidemic model on graphs and shows them to be equivalent. After developing a deep understanding of the SI model, the epidemic hitting time is compared to a variety of different graph centralities to indicate successful alternative methods in identifying important agents in epidemic spreading. Numerical results from simulations on many real-world graphs are presented. They indicate the effective resistance, which coincides with the 2-modulus for connecting families, is the most closely correlated indicator of importance to that of the epidemic hitting time. In large part, this is suspected to be due to the global nature of both the effective resistance and the epidemic hitting time. Thanks to the equivalence between the epidemic hitting time and the expected distance on an randomly exponentially weighted graph, we uncover a deeper connection- the effective resistance is also a lower bound for the epidemic hitting time, showing an even deeper connection.
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Fujie, Ryo, and Takashi Odagaki. "Effects of superspreaders in spread of epidemic." Diffusion fundamentals 6 (2007) 20, S. 1-2, 2007. https://ul.qucosa.de/id/qucosa%3A14194.
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Piletskiy, P. E., and D. I. Chumachenko. "Moving average method in epidemic process forecasting." Thesis, Sumy State University, 2017. http://essuir.sumdu.edu.ua/handle/123456789/55765.
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In this study, the application of the
moving average method to the forecasting of the
epidemic process is considered. As an example, the
method is used to predict the incidence of ixodes tick
borreliosis. To automate the calculation of the
forecast, a software package was developed. The
accuracy of the results was verified on real statistical
data on morbidity in the Kharkiv region.
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Castele, Daniel S. "Designing Within Historic Guidelines: an American Epidemic." University of Cincinnati / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1554211323496614.
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Xu, Xiaoguang. "Bayesian nonparametric inference for stochastic epidemic models." Thesis, University of Nottingham, 2015. http://eprints.nottingham.ac.uk/29170/.
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Modelling of infectious diseases is a topic of great importance. Despite the enormous attention given to the development of methods for efficient parameter estimation, there has been relatively little activity in the area of nonparametric inference for epidemics. In this thesis, we develop new methodology which enables nonparametric estimation of the parameters which govern transmission within a Bayesian framework. Many standard modelling and data analysis methods use underlying assumptions (e.g. concerning the rate at which new cases of disease will occur) which are rarely challenged or tested in practice. We relax these assumptions and analyse data from disease outbreaks in a Bayesian nonparametric framework. We first apply our Bayesian nonparametric methods to small-scale epidemics. In a standard SIR model, the overall force of infection is assumed to have a parametric form. We relax this assumption and treat it as a function which only depends on time. Then we place a Gaussian process prior on it and infer it using data-augmented Markov Chain Monte Carlo (MCMC) algorithms. Our methods are illustrated by applications to simulated data as well as Smallpox data. We also investigate the infection rate in the SIR model using our methods. More precisely, we assume the infection rate is time-varying and place a Gaussian process prior on it. Results are obtained using data augmentation methods and standard MCMC algorithms. We illustrate our methods using simulated data and respiratory disease data. We find our methods work fairly well for the stochastic SIR model. We also investigate large-scaled epidemics in a Bayesian nonparametric framework. For large epidemics in large populations, we usually observe surveillance data which typically provide number of new infection cases occurring during observation periods. We infer the infection rate for each observation period by placing Gaussian process priors on them. Our methods are illustrated by the real data, i.e. a time series of incidence of measles in London (1948-1957). Please note, the pagination in the online version differs slightly from the official, printed version because of the insertion of a list of corrections. The incorporation of the corrections into the text of the online version means that the page breaks appear at different points on p. 39-47, and p. 47-147 of the electronic version correspond to p. 48-148 of the printed version.
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Lindholm, Mathias. "Stochastic Epidemic Models : Different Aspects of Heterogeneity." Doctoral thesis, Stockholm : Department of Mathematics, Stockholm university, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-8335.
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Umar, Abdulkarim Mallam. "Stochastic SIR household epidemic model with misclassification." Thesis, University of Kent, 2016. https://kar.kent.ac.uk/62476/.
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Mata, May Anne Estrera. "Avian influenza epidemic recurrence and approximate stochastic models." Thesis, University of British Columbia, 2017. http://hdl.handle.net/2429/61410.
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This thesis is mainly concerned with avian flu epidemic recurrence, its current paradigm, and further mathematical research. Generally, this thesis aims to characterise the recurrent pattern of epidemics simulated by stochastic avian flu models using mathematical techniques. Of particular interest here are the stochastic fluctuations observed in recurrent epidemics. This thesis has two main parts.
The first part presents a thorough analysis of a simple stochastic avian flu model to provide insight into the role of different transmission routes in its recurrent dynamics. Recent modelling work on avian influenza in wild bird population takes into account demographic stochasticity and highlights the importance of environmental transmission in determining the outbreak periodicity, but only for a weak between-host transmission rates. A new analytic approach is used here to determine the relative contribution of environmental and direct transmission routes to the features of recurrent epidemics. Using an approximation method to describe noise-sustained oscillations, the recurrent epidemics simulated by the stochastic model is identified to be governed by the product of rotation and a slow-varying standard mean-reverting stochastic process, in a limiting sense. By analytically computing the intrinsic frequency and theoretical power spectral density, it can be shown that the outbreak periodicity can be explained by both types of transmission, and even by either one in the absence of the other.
The final part of this thesis presents a novel approach to understanding the role of parametric (e.g. seasonal) forcing and stochasticity in the stochastic fluctuations around a cyclic solution. An approximate description about these stochastic fluctuations is developed, which paves the way for a new mathematical tool to be used for analysing oscillations generated from the interactions of non-linear terms and stochasticity. The theory developed here is used to explore a stochastic avian flu model with seasonally forced environmental transmission which may be applicable to other stochastic system with seasonal forcing.
This thesis highlights the importance of approximation theory to analyse complex stochastic systems such as avian flu epidemic recurrence.Graduate Studies, College of (Okanagan)
Graduate
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MacGillivray, Neil. "Food, poverty and epidemic disease, Edinburgh, 1840-1850." Thesis, University of Edinburgh, 2004. http://hdl.handle.net/1842/1898.
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The thesis first examines the link between nutrition and disease, focusing on the poor of Edinburgh during the 184Os, a time of economic depression and food shortage. The development of nutritional science and the level of dietary knowledge amongst the medical profession are considered in the light of current nutritional guidelines. An assessment is made of the relationship between the 1947 scurvy epidemic and nutritional deficiency amongst the poor whose diet is then analysed. Institutional diets from contemporary tables of nutrition are subjected to computer analysis and their significance in terms of nutritional status discussed. There follows a description of the living conditions of the poor in the Old Town, emphasising the degree of overcrowding from inward migration and loss of housing stock following the demolition of streets and wynds in the course of city improvements and industrial developments. The history of the city’s water supply is explored and the absence of sewage provision is described in conjunction with an account of the foul bum controversy stressing the fact that the lack of water in the Old Town was critical in creating the fetid and hazardous environment where only the most primitive and inadequate methods of sanitation existed. Finally epidemic disease is studied, concentrating on the fever epidemics of 184 1- 44, 1847-49 and the cholera outbreak of 1848-49 but reviewing also the lesser epidemics of measles, whooping cough and scarlet fever. The history of the identification of typhus fever, relapsing fever and typhoid fever and their causation is described and the contagion-miasma debate is examined, assessing the contribution of Edinburgh physicians to the question. The lack of statistical information on Edinburgh’s morbidity and mortality is one of the factors discussed in a critical appraisal of the reaction of the medical profession and the city administration to these epidemics and to the social conditions in the midst of which they worked but few lived. In studying the cholera outbreak a database of 740 cholera victims has been prepared from the cholera returns maintained by the Royal College of Physicians of Edinburgh and the information contained therein evaluated.
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Cheung, Hoi-yan, and 張凱欣. "Effectiveness of school closure during an epidemic flu." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B45171324.
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Green, Nathan. "Optimal intervention of epidemic models with parameter uncertainty." Thesis, University of Liverpool, 2005. http://www.manchester.ac.uk/escholar/uk-ac-man-scw:76732.
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O'Neill, Philip Denis. "Contributions to the theory of stochastic epidemic models." Thesis, University of Nottingham, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.357103.
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Griffiths, Martin. "Backward bifurcation and associated phenomena in epidemic models." Thesis, University of Strathclyde, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.442131.
Full textAbstract:
The equilibrium phenomenon of backward bifurcation has in recent years been shown to occur in several deterministic differential equation models for the spread of infectious diseases. For simple epidemic models the disease is usually able to persist in the population when the basic reproduction ratio is greater than one, but dies out otherwise. However, for more complicated models in which backward bifurcation is exhibited the disease can, for certain parameter values, persist even when the basic reproduction ratio is less than one. Extended versions of deterministic models in which backward bifurcation is already known to be present are studied. By performing detailed equilibrium analyses we consider the possibility for the existence of multiple subcritical and supercritical endemic equilibria in these models, and the implications that this might have with regard to the dynamics of the system. In addition to extending the number of classes of the models, we examine the situation for which one or more of the parameters are functions of the population size. Corresponding stochastic models are also developed, and we look at the potential influence that the presence of backward bifurcation might exert on the probability of extinction for the disease. Our investigations are carried out using analytical and numerical methods, and also via computer simulations. We have been able to demonstrate the existence of, and then classify, a variety of differently shaped bifurcation diagrams for our extended models which, in conjunction with the results of our investigations into the stability of the endemic equilibria, would suggest the potential for extremely complex dynamic behaviour when the basic reproduction ratio is close to one. Some of the features of epidemic models in which backward bifurcation is known to be present have been identified. We have also found interesting links between the presence of backward bifurcation in the deterministic models and the probability of extinction in the stochastic versions.