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<p dir="ltr">Network models are essential for representing a myriad of real-world problems. Two of the most important categories of networks are centralized and distributed networks. In this thesis, we investigate the efficient resource allocation for one centralized communication network and two distributed epidemic networks.</p><p dir="ltr">In Chapter 2, we study three proposed centralized coded caching schemes with uncoded pre-fetching for scenarios where end users are grouped into classes with different file demand sets. We provide a lower bound for the transmission rate for the system with heterogeneous user profiles. Then the transmission rates of the three schemes are compared with the lower bound to evaluate their gap to optimality, and also compared with each other to show that each scheme can outperform the other two when certain conditions are met. Finally, we propose a cache distribution method that results in a minimal peak rate and a minimal average rate for one of the schemes when the users’ storage is relatively small compared with the size of the library.</p><p dir="ltr">In Chapter 3, we examine a discrete-time networked SIR (susceptible-infected-recovered) epidemic model, where the infection, graph, and recovery parameters may be time-varying. We propose a stochastic framework to estimate the system states from observed testing data and provide an analytic expression for the error of the estimation algorithm. We validate some of our assumptions for the stochastic framework with real COVID-19 testing data. We identify the system parameters with the system states from our estimation algorithm. Employing the estimated system states, we provide a novel distributed eradication strategy that guarantees at least exponential convergence to the set of healthy states. We illustrate the results via simulations over northern Indiana, USA.</p><p dir="ltr">In Chapter 4, we propose a novel discrete-time multi-virus SIR model that captures the spread of competing SIR epidemics over a population network. First, we provide a sufficient condition for the infection level of all the viruses over the networked model to converge to zero in exponential time. Second, we propose an observation model which captures the summation of all the viruses’ infection levels in each node, which represents the individuals who are infected by different viruses but share similar symptoms. We present a sufficient condition for the model to be strongly locally observable. We propose a distributed Luenberger observer for the system state estimation. We demonstrate how to calculate the observer gain for the estimator and prove that the estimation error of our proposed estimator converges to zero asymptotically with the observer gain found. We also propose a distributed feedback controller which guarantees that all viruses are eradicated at an exponential rate. We then show via simulations that the estimation error of the Luenberger observer converges to zero before the viruses die out.</p><p dir="ltr">We conclude in Chapter 5, where we summarize the findings of this thesis and introduce several challenging open research questions that arise from its results. These questions encompass a range of topics, including the design of optimal testing strategies for large populations, the investigation of estimation techniques in the presence of noisy measurement models, the extension of the SIR epidemic model to more complex models like SEIR and SAIR, and the exploration of efficient vaccine allocation schemes.</p>

Master of Science / Department of Electrical and Computer Engineering / William H. Hsu / Caterina M. Scoglio / Early detection of livestock diseases and development of cost optimal mitigation strategies are becoming a global necessity. Foot and Mouth Disease (FMD) is considered one of the most serious livestock diseases owing to its high rate of transmission and extreme economic consequences. Thus, it is imperative to improve parameterized mathematical models for predictive and preventive purposes. In this work, a meta-population based stochastic model is implemented to assess the FMD infection dynamics and to curb economic losses in countries with underdeveloped livestock disease surveillance databases. Our model predicts the spatio-temporal evolution of FMD over a weighted contact network where the weights are characterized by the effect of wind and movement of animals and humans. FMD incidence data from countries such as Turkey, Iran and Thailand are used to calibrate and validate our model, and the predictive performance of our model is compared with that of baseline models as well. Additionally, learning-based prediction models can be utilized to detect the time of onset of an epidemic outbreak. Such models are computationally simple and they may be trained to predict infection in the absence of background data representing the dynamics of disease transmission, which is otherwise necessary for predictions using spatio-temporal models. Thus, we comparatively study the predictive performance of our spatio-temporal against neural networks and autoregressive models. Also, Bayesian networks combined with Monte-Carlo simulations are used to determine the gold standard by approximation. Next, cost-effective mitigation strategies are simulated using the theoretical concept of infection network fragmentation. Based on the theoretical reduction in the total number of infected animals, several simulative mitigation strategies are proposed and their cost-effectiveness measures specified by the percentage reduction in the total number of infected animals per million US dollars, are also analyzed. We infer that the cost-effectiveness measures of mitigation strategies implemented using our spatio-temporal predictive model have a narrower range and higher granularity than those for mitigation strategies formulated using learning-based prediction models. Finally, we coin optimal mitigation strategies using Fuzzy Dominance Genetic Algorithms (FDGA). We use the concept of hierarchical fuzzy dominance to minimize the total number of infected animals, the direct cost incurred due to the implementation of mitigation strategies, the number of animals culled, and the number of animals vaccinated to mitigate an epidemic. This method has the potential to aid in economic policy development for countries that have lost their FMD-free status.

Βασικό χαρακτηριστικό της σύγχρονης εποχής αποτελεί η ραγδαία αύξηση του Διαδικτύου τόσο σε επίπεδο χρηστών όσο και σε επίπεδο παρεχόμενων υπηρεσιών. Συνεπώς, είναι επιτακτική η ανάγκη της προστασίας των δικτυακών και υπολογιστικών συστημάτων από διάφορες απειλές οι οποίες μπορούν να τα καταστήσουν τρωτά. Για την πλήρη προστασία όμως αυτών των συστημάτων, απαιτείται πρώτα η κατανόηση του είδους, της ταυτότητας και του τρόπου διάδοσης της απειλής. Ιδιαίτερη χρήσιμη έχει αποδειχθεί η ανάπτυξη και αναζήτηση αξιόπιστων μοντέλων ικανών να περιγράψουν αρκετά αποτελεσματικά τον τρόπο διάδοσης μιας απειλής. Η αναζήτηση τέτοιων μοντέλων αποτελεί πλέον ένα σημαντικό τομέα έρευνας στην ακαδημαϊκή και όχι μόνο κοινότητα. Σκοπός της παρούσας διπλωματικής εργασίας είναι η προσομοίωση και μελέτη των βασικών επιδημιολογικών μοντέλων SI, SIR, SIS και SIRS. Τα μοντέλα αυτά είναι εμπνευσμένα από την επιστήμη της Βιολογίας, και πλέον τη σημερινή εποχή χρησιμοποιούνται ευρέως για τη μοντελοποίηση της διάδοσης αρκετών απειλών στα δίκτυα υπολογιστών, όπως πχ. οι ιοί και τα σκουλήκια (viruses and worms). Η εργασία αποτελείται από πέντε κεφάλαια. Στο πρώτο κεφάλαιο, γίνεται και η παρουσίαση των ασυρμάτων δικτύων αισθητήρων περιγράφοντας επίσης τόσο τη δομή όσο και τα βασικά χαρακτηριστικά αυτών. Στο δεύτερο κεφάλαιο γίνεται μια παρουσίαση των βασικών ειδών του κακόβουλου λογισμικού που μπορούν να πλήξουν ένα υπολογιστικό σύστημα. Γίνεται επίσης αναφορά στα χαρακτηριστικά των κακόβουλων λογισμικών τα οποία επηρεάζουν την εξάπλωσή του. Το τρίτο κεφάλαιο επιχειρεί να εισάγει την έννοια της επιδημιολογίας στα συστήματα υπολογιστών με την ανάλυση κυρίως των ιδιαιτεροτήτων οι οποίες την χαρακτηρίζουν. Επίσης αυτό το κεφάλαιο παρουσιάζει κάποια βασικά επιδημιολογικά μοντέλα κάνοντας μια αναφορά τόσο στα βασικά χαρακτηριστικά αυτών, όσο επίσης και στον τρόπο λειτουργίας τους. Το τέταρτο κεφάλαιο το οποίο είναι και το πιο σημαντικό της εργασίας αυτής, αφιερώνεται στην παρουσίαση του εργαλείου OPNET Modeler που χρησιμοποιήσαμε και στην εκτενή περιγραφή της προσομοίωσης των μοντέλων SI, SIS, SIR και SIRS που διεξήγαμε για ένα ασύρματο δίκτυο αισθητήρων. Γίνεται παρουσίαση της λειτουργίας του δικτύου με ταυτόχρονη επεξήγηση του κώδικα που αναπτύχθηκε. Επιπλέον παρουσιάζονται και αναλύονται τα αποτελέσματα της προσομοίωσης ενώ παράλληλα περιγράφονται και τα συμπεράσματα στα οποία μας οδήγησε η εν λόγω προσομοίωση. Τέλος, στο πέμπτο κεφάλαιο, γίνεται μια αναφορά σε κάποια βασικά συμπεράσματα στα οποία οδηγηθήκαμε, ενώ περιγράφονται και πεδία πάνω στη μελέτη της διάδοσης ενός κακόβουλου λογισμικού σε ένα υπολογιστικό δίκτυο, τα οποία μπορούν να μελετηθούν εκτενέστερα μελλοντικά. / A basic characteristic of contemporary days is the boom of the Internet either in terms of users or in terms of services rendered. Therefore, there is an imperative need to protect the network and computational systems from various threats which can render them vulnerable. However, for the full protection of these systems, it is required in the first place to get to know the type, the identity and the propagation mode of the threat. Of significant use has proved to be the development and the pursuit of models capable of describing quite effectively the way a threat is spread. The pursuit of such models constitutes nowadays a significant sector of research, including, but not limited to the academic community. The intention of the present diploma thesis is the simulation and study of the basic epidemic models SI, SIR, SIS and SIRS. These models are inspired from the science of Biology, and they are widely used nowadays for the modeling of the spread of various threats in computer networks such as viruses and worms. This dissertation consists of five chapters. In the first chapter, there is taking place the presentation of wireless sensor networks and there is also a description of their structure and their basic characteristics. In the second chapter there is a presentation of the basic types of malicious software that can hit a computational system. There is also reference to the characteristics of malicious software that affect their propagation. The third chapter attempts to introduce the concept on epidemiology in computer systems, analyzing mainly the particularities characterizing her. In addition, this chapter presents some basic epidemic models, referring both to their basic characteristics and their mode of operation. The fourth chapter, which is also the most significant one of the present thesis, is dedicated to the presentation of the tool OPNET Modeler that we used too in the thorough description of the simulation of the models SI, SIR, SIS and SIRS that we carried out for a wireless sensor network. It is taking place the presentation of the network’s operation mode with a simultaneous explanation of the code that was developed. Moreover, there are presented and analyzed the results of the simulation when at the same time are also described the conclusions that were derived from the present simulation. Finally, in the fifth chapter, there is a reference to some basic conclusions in which we were led, where there are also described fields concerning the study of malicious software propagation in a computational network, which can studied further in the future.

This work describes the design and implementation of the Disease Control System DiCon (pronounced [ˈdaɪkɒn]), providing a general framework for solving optimization problems on distributed computer systems. The central aspects of DiCon are discussed, as are decisions made while realizing the system. Several implementation-specific details are highlighted. Real-world applications show the system's flexibility and demonstrate the potential impact DiCon has on public-health decision making. / text

The problem of changing scale in models of a system is relevant in many different fields. In this thesis we investigate the problem in models of biological systems, particularly infectious disease spread and population dynamics. We investigate this problem using the process algebra \emph{Weighted Synchronous Calculus of Communicating Systems} (WSCCS). In WSCCS we can describe the different types of individual in a population and study the population by placing many of these individuals in parallel. We present an algorithm that allows us to rigorously derive mean field equations (MFE) describing the average change in the population. The algorithm takes into account the Markov chain semantics of WSCCS such that as the system being considered becomes larger, the approximation offered by the MFE tends towards the mean of the Markov chain. The traditional approach to developing population level equations of a system involves making assumptions about the behaviour of the entire population. Our approach means that the population level dynamics explained by the MFE are a direct consequence of the behaviour of individuals, which is more readily observed and measured than the behaviour of the population. In this way we develop MFE models of several different systems and compare the equations obtained to the traditional mathematical models of the system.

The rates of opioid prescription and use have continued to increase over the last few decades. In turn, a greater number of patients suffer from opioid tolerance. Treatment of acute pain is a clinical challenge for these patients. Acute pain can arise from common occurrences like surgical pain and pain resulting from the injury. P-glycoprotein (p-gp) is a transporter at the blood-brain barrier (BBB) associated with a decrease in the analgesic efficacy of morphine. Peripheral inflammatory pain (PIP) is a pain state known to cause a change in p-gp trafficking at the BBB. P-gp traffics from the nucleus to the luminal surface of endothelial cells making up the BBB. This surface where circulating blood interfaces with the endothelial cell is where p-gp will efflux morphine back into circulation. Osmotic minipumps were used as a long-term delivery method in this model of opioid tolerance in female rats. PIP induced p-gp trafficking away from nuclear stores showed a 2-fold increase when animals were exposed to opioids for 6 days. This observation presents a possible relationship between p-gp trafficking and the challenges of treating post-surgical pain in opioid tolerant patients. This could reveal potential strategies for improving pain management in these patients.

Doctor of Philosophy / Department of Electrical and Computer Engineering / Caterina Maria Scoglio / We have analytically discovered the existence of two global epidemic invasion thresholds in a directed meta-population network model of the United States cattle industry. The first threshold describes the outbreak of disease first within the core of the livestock system while the second threshold describes the invasion of the epidemic into a second class of locations where the disease would pose a risk for contamination of meat production. Both thresholds have been verified through extensive numerical simulations. We have further derived the relationship between the pair of thresholds and discovered a unique dependence on the network topology through the fractional compositions and the in-degree distributions of the transit and sink nodes. We then addressed a major challenge for epidemiologists and their efforts to model disease outbreaks in cattle. There is a critical shortfall in the availability of large-scale livestock movement data for the United States. We meet this challenge by developing a method to estimate cattle movement parameters from publicly available data. Across 10 Central States of the US, we formulated a large, convex optimization problem to predict the cattle movement parameters which, having minimal assumptions, provide the best fit to the US Department of Agriculture's Census database and follow constraints defined by scientists and cattle experts. Our estimated parameters can produce distributions of cattle shipments by head which compare well with shipment distributions also provided by the US Department of Agriculture. This dissertation concludes with a brief incorporation of the analytic models and the parameter estimation. We approximated the critical movement rates defined by the global invasion thresholds and compared them with the average estimated cattle movement rates to find a significant opportunity for epidemics to spread through US cattle populations.

Doctor of Philosophy / Department of Electrical and Computer Engineering / Caterina Scoglio / Society increasingly depends on networks for almost every aspect of daily life. Over the past decade, network science has flourished tremendously in understanding, designing, and utilizing networks. Particularly, network science has shed light on the role of the underlying network topology on the dynamic behavior of complex systems, including cascading failure in power-grids, financial contagions in trade market, synchronization, spread of social opinion and trends, product adoption and market penetration, infectious disease pandemics, outbreaks of computer worms, and gene mutations in biological networks. In the last decade, most studies on complex networks have been confined to a single, often homogeneous network. An extremely challenging aspect of studying these complex systems is that the underlying networks are often heterogeneous, composite, and interdependent with other networks. This challenging aspect has very recently introduced a new class of networks in network science, which we refer to as multilayer and interconnected networks. Multilayer networks are an abstract representation of interconnection among nodes representing individuals or agents, where the interconnection has a multiple nature. For example, while a disease can propagate among individuals through a physical contact network, information can propagate among the same individuals through an online information-dissemination network. Another example is viral information dissemination among users of online social networks; one might disseminate information received from a Facebook contact to his or her followers on Twitter. Interconnected networks are abstract representations where two or more simple networks, possibly with different dynamics over them, are interconnected to each other. For example, in zoonotic diseases, a virus can move from the network of animals, with some transmission dynamics, to a human network, with possibly very different dynamics. As communication systems are evolving more and more toward integration with computing, sensing, and control systems, the theory of multilayer and interconnected networks seems to be crucial to successful communication systems development in cyber-physical infrastructures. Among the most relevant dynamics over networks is epidemic spreading. Epidemic spreading dynamics over simple networks exhibit a clear example where interaction between non-complex dynamics at node level and the topology leads to a complex emergent behavior. A substantial line of research during the past decade has been devoted to capturing the role of the network on spreading dynamics, and mathematical tools such as spectral graph theory have been greatly useful for this goal. For example, when the network is a simple graph, the dominant eigenvalue and eigenvector of the adjacency matrix have been proven to be key elements determining spreading dynamics features, including epidemic threshold, centrality of nodes, localization of spreading sites, and behavior of the epidemic model close to the threshold. More generally, for many other dynamics over a single network, dependency of dynamics on spectral properties of the adjacency matrix, Laplacian matrix, or some other graph-related matrix, is well-studied and rigorously established, and practical applications have been successfully derived. In contrast, limited established results exist for dynamics on multilayer and interconnected networks. Yet, an understanding of spreading processes over these networks is very important to several realistic phenomena in modern integrated and composite systems, including cascading failure in power grids, financial contagions in trade market, synchronization, spread of social opinion and trends, product adoption and market penetration, infectious disease pandemics, and outbreak in computer worms. This dissertation focuses on spreading processes on multilayer and interconnected networks, organized in three parts. The first part develops a general framework for modeling epidemic spreading in interconnected and multilayer networks. The second part solves two fundamental problems: introducing the concept of an epidemic threshold curve in interconnected networks, and coexistence phenomena in competitive spreading over multilayer networks. The third part of this dissertation develops an epidemic model incorporating human behavior, where multi-layer network formulation enables modeling and analysis of important features of human social networks, such as an information-dissemination network, as well as contact adaptation. Finally, I conclude with some open research directions in the topic of spreading processes over multilayer and interconnected networks, based on the resulting developments of this dissertation.