Η έννοια των δικτύων εμφανίζεται πολύ συχνά με διάφορες μορφές. Δίκτυο μπορούμε να θεωρήσουμε ένα σύνολο υπολογιστών που συνδέονται μεταξύ τους υπακούοντας σε κάποιο πρωτόκολλο επικοινωνίας αλλά και μια ομάδα ανθρώ- πων που συνδέονται μέσω κάποιας κοινωνικής σχέσης, ενός εργασιακού χώρου αλλά και ως χρήστες ενός forum ή μίας πλατφόρμας κοινωνικής δικτύωσης. Σε οποιαδήποτε περίπτωση, ένα δίκτυο μπορεί να αναπαρασταθεί με τη μορφή ενός γράφηματος, όπου οι κόμβοι αναπαριστούν τα άτομα/υπολογιστές και οι ακμές τη μεταξύ τους σχέση ανάλογα με το πρόβλημα. Στα πλαίσια ενός τέτοιου δικτύου μας ενδιαφέρει η συμπεριφορά των κόμβων στην περίπτωση που συμβεί ένα γεγονός που αλλάζει την κατάστασή τους. Στην περίπτωση που αναφερόμαστε σε μία κοινωνική ομάδα ή μία πόλη, αυτό το φαι- νόμενο μπορεί να είναι το ξέσπασμα μίας επιδημίας που εξαπλώνεται στο δίκτυο αλλά και μίας είδησης/φήμης, όπου ενημερώνεται το δίκτυο. Στην πρώτη περί- πτωση, μας ενδιαφέρει να περιορίσουμε την επιδημία, αλλάζοντας τοπολογικά το δίκτυο ενώ στη δεύτερη περίπτωση, είναι επιθυμητό να διευκολύνουμε την εξά- πλωση της είδησης, έτσι ώστε να ενημερωθούν όσο το δυνατόν, περισσότεροι κόμβοι(χρήστες). Η συμπεριφορά του δικτύου σε ένα τέτοιο φαινόμενο, μπορεί να προσομοιωθεί από ένα δυναμικό σύστημα. Με τον όρο δυναμικό σύστημα αναφερόμαστε σε ένα σύστημα που έχει ένα σύνολο καταστάσεων, όπου κάθε κατάσταση, προκύπτει σε συνάρτηση με την προηγούμενη. Παραδείγματα εφαρμογής ενός δυναμικού συστήματος σε δίκτυο, εμφανίζονται σε διάφορους τομείς όπως στην οικολογία, τη διάχυση πληροφορίας, το viral marketing, την επιδημιολογία. Τα δυναμικά συστήματα που προσομοιώνουν τη συμπεριφορά του δικτύου σε τέτοια φαινόμενα, χρησιμοποιούν επιδημιολογικά μοντέλα για να περιγρά- ψουν τις δυνατές καταστάσεις στις οποίες μπορεί να περιέλθει ένας κόμβος. Στη συγκεκριμένη εργασία, χρησιμοποιήσαμε το μοντέλο SIS (Susceptible-Infected-Susceptible) [8].Το μοντέλο SIS δηλώνει ότι ένας κόμβος μπορεί να είναι είτε επιρρεπής στο να ασθενήσει (susceptible) είτε ασθενής (infected). Αυτό σημαί- νει πως ένας κόμβος δεν θεραπεύεται ποτέ πλήρως αλλά υπάρχει πιθανότητα να ασθενήσει πάλι. Με βάση τη βιβλιογραφία, σε ένα τέτοιο δυναμικό σύστημα, αναζητούμε κά- ποια σημεία (fixed points) στα οποία το σύστημα θα ισορροπεί. Υπάρχουν σημεία τα οποία είναι σημεία ισορροπίας αλλά δεν είναι σταθερά. Σε αυτά τα σημεία, το σύστημα μπορεί στιγμιαία να ισορροπήσει αλλά ξεφεύγει πολύ εύκολα από αυτό. Αναζητούμε συνεπώς, σταθερά σημεία ισορροπίας, τα λεγόμενα stable fixed points. Έχει αποδειχτεί [6] ότι μπορούμε σε αυτά στα σημεία να καθορίσουμε τις απαραίτητες συνθήκες για να είναι σταθερά, περιορίζοντας τη μέγιστη ιδιοτιμή του μητρώου γειτνίασης που περιγράφει το δίκτυο. Ορίζονται δηλαδή κατώφλια (thresholds) κατά περίπτωση, που περιορίζουν την μέγιστη ιδιοτιμή του δικτύου με τέτοιο τρόπο ώστε το σύστημα, να βρίσκεται σε κατάσταση ισορροπίας. Στην πε- ρίπτωση που αναφερόμαστε στο φαινόμενο της επιδημίας, στόχος είναι στο αντί- στοιχο σημείο ισορροπίας η μέγιστη ιδιοτιμή να είναι κάτω του κατωφλίου, έτσι ώστε να εξασφαλίσουμε τον περιορισμό εξάπλωσης της επιδημίας στο δίκτυο. Στην περίπτωση που αναφερόμαστε σε μία είδηση ή ένα ανταγωνιστικό προϊόν, η μέγιστη ιδιοτιμή θέλουμε να είναι άνω του αντίστοιχου κατωφλίου έτσι ώστε να έχουμε εξάπλωση στο δίκτυο. Επομένως ανάλογα με την περίπτωση, αντιμε- τωπίζουμε διαφορετικά τα κατώφλια που υπολογίζονται για το αντίστοιχο σημείο ισορροπίας. Στα πλαίσια της μεταπτυχιακής εργασίας, χρησιμοποιήσαμε το μοντέλο SIS για να περιγράψουμε το φαινόμενο όπου ένας ιός εξαπλώνεται σε ένα δίκτυο όπου οι κόμβοι του δικτύου, έχουν διαφορετική ευαισθησία απέναντί του. Πραγματο- ποιήσαμε μαθηματική περιγραφή του μοντέλου, ορίζοντας τα απαραίτητα κατώ- φλια έτσι ώστε το σύστημα να ισορροπεί ανάλογα με το σημείο ισορροπίας αλλά και το είδος του γραφήματος. Επίσης, πραγματοποιήσαμε προσομοίωση του μο- ντέλου σε συνθετικά γραφήματα (κλίκα, αυθαίρετο γράφημα κ.α), επαληθεύοντας τη συμπεριφορά που υποδεικνύει το μαθηματικό μοντέλο. / Which is the appropriate answer about the definition of a network? One could answer that a group of people who share a relationship (colleagues, students etc) could be referred to, as a network. Another possible definition, is a computer network. Consequently, it is obvious that the idea of a network can be found in various ways in our daily life. In the same terms, suppose we have one competing idea/product or a virus that propagates over a multiple profile social (or other) network. Can we predict what proportion of the network will actually get ”infected” (e.g., spread the idea or buy the competing product), when the nodes of the network appear to have different sensitivity based on their profile? For example, if there are two profiles A, B in a network and the nodes of profile A and profile B are susceptible to a highly spreading virus with probabilities βA and βB respectively, what percentage of both profiles will actually get infected from the virus in the end? The behavior of such a network, can be simulated using dynamical systems theory. We consider a dynamical system as a system with a set of possible states where each future state, is computed based on the previous state. Dynamical System Applications, can be found in many fields such as viral marketing, ecology, information diffusion and virus propagation. In order to simulate the rumor or virus which is spreading across the network, one has to use virus propagation models. The selection of the appropriate model, depends on the special attributes and characteristics of the spreading rumor/virus and it should cover all the possible states in which a node in the network can be (sick, healthy,susceptible, informed, not informed etc). According to Dynamical Systems Theory, we are looking for possible fixed points where the system is in equilibrium. In particular, we would require each fixed point to be a stable attractor and not lead the system far away from the equilibrium point due to opposing forces (stable fixed points). It has been proven that limiting the leading eigenvalue of the adjacency matrix of the graph, is the only condition required, in order for the system to be in equilibrium state, in the corresponding fixed point. In this paper, we assume an SIS propagation model [8] which is applied on a heterogeneous network. That is, we assume that there is no fair game using the terminology of [14, 3]. In the SIS model, each node can be either in a susceptible (S) state or in the infected state (I) and as result there is no permanent immunity and every node can get infected multiple times.Since this is the first theoretical treatment of heterogeneous environments for virus propagation, we choose to work in the simple model of SIS and not in other models. Suppose that we are given a social network and a rumor that spreads over it, where the nodes of the network represent people with high/low sensitivity to the rumor and the links represent the association of the nodes, how will the rumor propagate over the network? That is, can we determine whether all members of the network will reproduce the rumor to their neighbors and ”infect” them or the rumor will spread in a small group in the network and die out quickly? Similarly, which is the tipping point where such a rumor or infectious virus will take off? It would be very helpful if we could find the specific point when the ”virus” spreads all over the network and an epidemic occurs. Finally, what is the case when the nodes have different endurance/sensitivity to the ”virus” and have temporary or permanent immunity? Our basic assumption and innovation when compared to all previous approaches is that there is no fair-play and nodes have different profile against the virus. That is, the network is heterogeneous with respect to the virus, which means that nodes have different sensitivity to it. This is one of our main contributions in comparison with previous results where all nodes appear to have the same behavior towards the virus and the same model parameters. The propagation model which is followed, resembles the SIS (no immunity like flu) model where nodes are either susceptible or infected but with modifications. All nodes can get infected from one another, despite the difference of their profiles. We prove and present the tipping point where the virus is about to spread all over the network or the rumor ”infect” every member of the network and result in a ”viral” phenomenon. Our main contribution, is that we provide answers for the questions above, for special topologies such as the clique as well as arbitrary graphs of high or low connectivity. In particular, to the best of our knowledge, we are the first to provide theoretical and experimental findings on the propagation of a virus over a heterogeneous network. We prove that in the case of two profiles, if one profile has high sensitivity to the virus and the other one has low sensitivity, actually nodes from both profiles will get infected proportionally in the case where the network is a clique. For arbitrary networks, we prove necessary conditions for the virus to die out allowing for multiple profiles (not just two), while at the same time we give directions to prove other interesting cases. The problem has many applications in the field of viral marketing, medicine, ecology and other.

This dissertation investigates the public response to HIV/AIDS in Sweden in the 1980s and early 1990s. The analysis focuses on the National Commission on AIDS (NCA,“Aidsdelegationen”). The NCA was appointed by the government in 1985, led by the Minister of Social Affairs and mandated to initiate and coordinate the national response to the epidemic and in function until 1992. The dissertation’s theoretical framework is based on the understanding of an epidemic as a cultural and historical concept, emphasizing that health policy in the late twentieth century must be analyzed as a complex process of problematization.  The study includes four parts. The first part covers the years 1982 to 1985, an era characterized by small scale action, based mainly on voluntary initiatives with small resources. The second part examines the period 1985-1989, when the NCA formed an official national policy based on both strong legislation (enabling quarantine of recalcitrants, registration, contact tracing etc.) and massive nationwide information efforts (through mass media campaigns). This highly active phase was followed by a period of consolidation, from 1989 to 1992, examined in the third part of the study. This period included a new infectious disease act focused on HIV/AIDS as well as official campaigns with stronger focus on the individuals’ responsibility for their own health. In the last part, covering the years 1992-1996, I show how the HIV/AIDS problem was institutionalized as a disease and health topic alongside many others. The national campaigns continued through the 1990s, focusing on empowerment and individualization. As in many similar countries, the main aim of the Swedish strategy was to educate and encourage people to act with caution and responsibility towards themselves and their fellow citizens. In addition to this cooperation and inclusion approach, a strategy of contain and control was also implemented. This second strategy can, as I show, be explained by the strong connection made between HIV/AIDS and drug users. Through this connection, the Swedish drug policy had a decisive influence on the Swedish HIV/AIDS policy.

Veterinarians often perform controlled experiments in which they inoculate animals with infectious diseases. They then monitor the transmission process in infected animals. The aim of such experiments can be to assess vaccine effects. The fitting of individual-level models (ILMs) to the infectious disease data, typically achieved by means of Markov Chain Monte Carlo (MCMC) methods, can be computationally burdensome. Here, we want to see if a vaccination effect can be identified using simpler regression-type models rather than the complex infectious disease models. We examine the use of various logistic growth curve models, via a series of simulated experiments in which the underlying true model is a mechanistic model of infectious disease spread. We want to investigate whether a vaccination effect can be identified when only partial epidemic curves are observed, and to assess the performance of these models when experiments are run with various sets of observational times.

We study some Hölderian functional central limit theorems for the polygonal partial sum processes built on a first order nearly nonstationary autoregressive process and its least squares residuals Innovations are i.i.d. centered and at least square-integrable innovations. Two types of models are considered. For the first type model we prove that the limiting process depends on Ornstein – Uhlenbeck one. In the second type model, the convergence to Brownian motion is established in Hölder space in terms of the rate of coefficient and the integrability of the residuals. We also investigate some epidemic change in the innovations of the first order nearly nonstationary autoregressive process . We build the alpha-Hölderian uniform increments statistics based on the observations and on the least squares residuals to detect the short epidemic change in the process under consideration. Under the assumptions for innovations we find the limit of the statistics under null hypothesis, some conditions of consistency and we perform a test power analysis. / Disertacijoje nagrinėjami dalinių sumų laužčių procesai sudaryti iš pirmos eilės beveik nestacionaraus proceso bei jo mažiausių kvadratų liekanų. Inovacijos yra nepriklausomi, vienodai pasiskirstę ir bent kvadratu integruojami atsitiktiniai dydžiai su nuliniu vidurkiu. Įrodomos funkcinės ribinės teoremos šiems laužčių procesams Hiolderio erdvėje. Nagrinėjami du beveik nestacionaraus proceso atvejai. Vienu atveju įrodoma, kad ribinis procesas priklauso nuo Ornsteino–Uhlenbecko proceso. Kitu atveju, įrodomas konvergavimas į Brauno judesį Hiolderio erdvėje, atsižvelgiant į koeficiento divergavimo greitį bei inovacijų integruojamumą. Toliau nagrinėjamas epideminio pasikeitimo modelis beveik nestacionaraus pirmos eilės autoregresinio proceso inovacijoms. Nagrinėjami du modeliai. Iš stebėjimų bei liekanų konstruojama tolydžiųjų prieaugių alpha-Hiolderio statistika. Remiantis prielaidomis inovacijoms, randama statistikos ribinis procesas prie nulinės hipotezės, suderinamumo sąlygos, atliekama galios analizė.

Disertacijoje nagrinėjami dalinių sumų laužčių procesai sudaryti iš pirmos eilės beveik nestacionaraus proceso bei jo mažiausių kvadratų liekanų. Inovacijos yra nepriklausomi, vienodai pasiskirstę ir bent kvadratu integruojami atsitiktiniai dydžiai su nuliniu vidurkiu. Įrodomos funkcinės ribinės teoremos šiems laužčių procesams Hiolderio erdvėje. Nagrinėjami du beveik nestacionaraus proceso atvejai. Vienu atveju įrodoma, kad ribinis procesas priklauso nuo Ornsteino–Uhlenbecko proceso. Kitu atveju, įrodomas konvergavimas į Brauno judesį Hiolderio erdvėje, atsižvelgiant į koeficiento divergavimo greitį bei inovacijų integruojamumą. Toliau nagrinėjamas epideminio pasikeitimo modelis beveik nestacionaraus pirmos eilės autoregresinio proceso inovacijoms. Nagrinėjami du modeliai. Iš stebėjimų bei liekanų konstruojama tolydžiųjų prieaugių alpha-Hiolderio statistika. Remiantis prielaidomis inovacijoms, randama statistikos ribinis procesas prie nulinės hipotezės, suderinamumo sąlygos, atliekama galios analizė. / We study some Hölderian functional central limit theorems for the polygonal partial sum processes built on a first order nearly nonstationary autoregressive process and its least squares residuals Innovations are i.i.d. centered and at least square-integrable innovations. Two types of models are considered. For the first type model we prove that the limiting process depends on Ornstein – Uhlenbeck one. In the second type model, the convergence to Brownian motion is established in Hölder space in terms of the rate of coefficient and the integrability of the residuals. We also investigate some epidemic change in the innovations of the first order nearly nonstationary autoregressive process . We build the alpha-Hölderian uniform increments statistics based on the observations and on the least squares residuals to detect the short epidemic change in the process under consideration. Under the assumptions for innovations we find the limit of the statistics under null hypothesis, some conditions of consistency and we perform a test power analysis.

There are some new challenges in system administration and design to optimize the resource management for a cloud based application. Some applications demand stringent performance requirements (e.g. delay and jitter bounds), while some applications exhibit bursty (volatile) workloads. This thesis proposes an epidemic model inspired (and continuous time Markov Chain based) framework, which can reproduce workload volatility namely the "buzz effects" (when there is a sudden increase of a content popularity) of a Video on Demand (VoD) system. Two estimation procedures (heuristic and a Markov Chain Monte Carlo (MCMC) based approach) have also been proposed in this work to calibrate the model against workload traces. Obtained model parameters from the calibration procedures reveal some interesting property of the model. Based on numerical simulations, precisions of both procedures have been analyzed, which show that both of them perform reasonably. However, the MCMC procedure outperforms the heuristic approach. This thesis also compares the proposed model with other existing models examining the goodness-of-fit of some statistical properties of real workload traces. Finally this work suggests a probabilistic resource provisioning approach based on a Large Deviation Principle (LDP). LDP statistically characterizes the buzz effects that causeextreme workload volatility. This analysis exploits the information obtained using the LDP of the VoD system for defining resource management policies. These policies may be of some interest to all stakeholders in the emerging context of cloud networking.

During the past decade, South Africa has become the country with the highest number of HIV/AIDS infections in the world. In the wake of the widely spread HIV/AIDS epidemic in South Africa, hundreds of thousands of children are left parentless. Since limited research exists on the psycho-educational needs of children orphaned by AIDS in South Africa, the focus of this study was on their psycho-educational development. A literature study was conducted to investigate the HIV/AIDS epidemic in South Africa and its consequences for the psycho-educational development of AIDS orphans. A qualitative investigation was undertaken and interviews were conducted with caregivers of AIDS orphans at two care centres in rural KwaZulu-Natal. The aim of the investigation was to identify the psycho-educational needs of AIDS orphans as perceived by their caregivers. Moreover, the investigation also aimed at identifying factors that impede the psycho-educational development of AIDS orphans, and to determine the extent to which these day care centres meet the psycho-educational needs of these orphans. The following psycho-educational needs of AIDS orphans emerged from the investigation: - the need to socialise and communicate - the need to cope with parental death - the need for acceptance - the need for security and care - the need for love and belonging - the need to deal with negative emotions Physical and material needs were added to the above needs, since these were frequently mentioned during the course of the interviews. Factors that seriously impeded the psycho-educational development of AIDS orphans were abuse and neglect. The investigation also revealed that the care centres were to a large extent able to meet a broad spectrum of these orphans’ psycho-educational needs, especially at the care centre where the AIDS orphans were able to sleep over and received the full-time attention caregivers. Since the extended family system can no longer fully carry the burden of hundreds of thousands of AIDS orphans in South Africa, care centres situated in the affected communities can offer a viable alternative to traditional models of care. The study emphasised the need for further research on the needs of AIDS orphans as well as increased support of AIDS orphans on local, provincial and national levels. / MEd (Learner support), North-West University, Potchefstroom Campus, 2012

During the past decade, South Africa has become the country with the highest number of HIV/AIDS infections in the world. In the wake of the widely spread HIV/AIDS epidemic in South Africa, hundreds of thousands of children are left parentless. Since limited research exists on the psycho-educational needs of children orphaned by AIDS in South Africa, the focus of this study was on their psycho-educational development. A literature study was conducted to investigate the HIV/AIDS epidemic in South Africa and its consequences for the psycho-educational development of AIDS orphans. A qualitative investigation was undertaken and interviews were conducted with caregivers of AIDS orphans at two care centres in rural KwaZulu-Natal. The aim of the investigation was to identify the psycho-educational needs of AIDS orphans as perceived by their caregivers. Moreover, the investigation also aimed at identifying factors that impede the psycho-educational development of AIDS orphans, and to determine the extent to which these day care centres meet the psycho-educational needs of these orphans. The following psycho-educational needs of AIDS orphans emerged from the investigation: - the need to socialise and communicate - the need to cope with parental death - the need for acceptance - the need for security and care - the need for love and belonging - the need to deal with negative emotions Physical and material needs were added to the above needs, since these were frequently mentioned during the course of the interviews. Factors that seriously impeded the psycho-educational development of AIDS orphans were abuse and neglect. The investigation also revealed that the care centres were to a large extent able to meet a broad spectrum of these orphans’ psycho-educational needs, especially at the care centre where the AIDS orphans were able to sleep over and received the full-time attention caregivers. Since the extended family system can no longer fully carry the burden of hundreds of thousands of AIDS orphans in South Africa, care centres situated in the affected communities can offer a viable alternative to traditional models of care. The study emphasised the need for further research on the needs of AIDS orphans as well as increased support of AIDS orphans on local, provincial and national levels. / MEd (Learner support), North-West University, Potchefstroom Campus, 2012

This thesis investigates several uses of simulation methods to understand and control pandemic influenza in urban settings. An agent-based simulation, which models pandemic spread in a large metropolitan area, is used for two main purposes: to identify the shape of the distribution of pandemic outcomes, and to test for the presence of complex relationships between public health policy responses and underlying pandemic characteristics. The usefulness of pandemic simulation as a tool for assessing the cost-effectiveness of vaccination programs is critically evaluated through a rigorous comparison of three recent H1N1 vaccine cost-effectiveness studies. The potential for simulation methods to improve vaccine deployment is then demonstrated through a discrete-event simulation study of a mass immunization clinic.

This thesis investigates several uses of simulation methods to understand and control pandemic influenza in urban settings. An agent-based simulation, which models pandemic spread in a large metropolitan area, is used for two main purposes: to identify the shape of the distribution of pandemic outcomes, and to test for the presence of complex relationships between public health policy responses and underlying pandemic characteristics. The usefulness of pandemic simulation as a tool for assessing the cost-effectiveness of vaccination programs is critically evaluated through a rigorous comparison of three recent H1N1 vaccine cost-effectiveness studies. The potential for simulation methods to improve vaccine deployment is then demonstrated through a discrete-event simulation study of a mass immunization clinic.