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

A backbone network is the central part of the communication network, which provides connectivity within the various systems across large distances. Disruptions in a backbone network would cause severe consequences which could manifest in the service outage on a large scale. Depending on the size and the importance of the network, its failure could leave a substantial impact on the area it is associated with. The failures of the network services could lead to a significant disturbance of human activities. Therefore, making backbone communication networks more resilient directly affects the resilience of the area. Contemporary urban and regional development overwhelmingly converges with the communication infrastructure expansion and their obvious mutual interconnections become more reciprocal. Spreading failures are of particular interest. They usually originate in a single network segment and then spread to the rest of network often causing a global collapse. Two types of spreading failures are given focus, namely: epidemics and cascading failures. How to make backbone networks more resilient against spreading failures? How to tune the topology or additionally protect nodes or links in order to mitigate an effect of the potential failure? Those are the main questions addressed in this thesis. First, the epidemic phenomena are discussed. The subjects of epidemic modeling and identification of the most influential spreaders are addressed using a proposed Linear Time-Invariant (LTI) system approach. Throughout the years, LTI system theory has been used mostly to describe electrical circuits and networks. LTI is suitable to characterize the behavior of the system consisting of numerous interconnected components. The results presented in this thesis show that the same mathematical toolbox could be used for the complex network analysis. Then, cascading failures are discussed. Like any system which can be modeled using an interdependence graph with limited capacity of either nodes or edges, backbone networks are prone to cascades. Numerical simulations are used to model such failures. The resilience of European National Research and Education Networks (NREN) is assessed, weak points and critical areas of the network are identified and the suggestions for its modification are proposed.

A backbone network is the central part of the communication network, which provides connectivity within the various systems across large distances. Disruptions in a backbone network would cause severe consequences which could manifest in the service outage on a large scale. Depending on the size and the importance of the network, its failure could leave a substantial impact on the area it is associated with. The failures of the network services could lead to a significant disturbance of human activities. Therefore, making backbone communication networks more resilient directly affects the resilience of the area. Contemporary urban and regional development overwhelmingly converges with the communication infrastructure expansion and their obvious mutual interconnections become more reciprocal. Spreading failures are of particular interest. They usually originate in a single network segment and then spread to the rest of network often causing a global collapse. Two types of spreading failures are given focus, namely: epidemics and cascading failures. How to make backbone networks more resilient against spreading failures? How to tune the topology or additionally protect nodes or links in order to mitigate an effect of the potential failure? Those are the main questions addressed in this thesis. First, the epidemic phenomena are discussed. The subjects of epidemic modeling and identification of the most influential spreaders are addressed using a proposed Linear Time-Invariant (LTI) system approach. Throughout the years, LTI system theory has been used mostly to describe electrical circuits and networks. LTI is suitable to characterize the behavior of the system consisting of numerous interconnected components. The results presented in this thesis show that the same mathematical toolbox could be used for the complex network analysis. Then, cascading failures are discussed. Like any system which can be modeled using an interdependence graph with limited capacity of either nodes or edges, backbone networks are prone to cascades. Numerical simulations are used to model such failures. The resilience of European National Research and Education Networks (NREN) is assessed, weak points and critical areas of the network are identified and the suggestions for its modification are proposed.

Die Covid-19 Pandemie hat gezeigt, wie stark die Ausbreitung von Infektionskrankheiten von der Dynamik der menschlichen Mobilität bestimmt wird. Gleichzeitig eröffnet die anhaltende Explosion an verfügbaren Mobilitätsdaten im 21. Jahrhundert einen viel genaueren Blick auf die menschliche Mobilität. In dieser Arbeit untersuchen wir verschiedene Ansätze, wie moderne Mobilitätsdaten zusammen mit Modellierung ein tieferes Verständnis des Zusammenspiels von menschlicher Mobilität und der Ausbreitung von Infektionskrankheiten ermöglichen. Wir verwenden Mobilitätsdaten um zu zeigen, dass landesweite Mobilitätsmuster während der Covid-19 Pandemie in Deutschland komplexe strukturelle Veränderungen durchlaufen haben. Wir stellen einen räumlich heterogenen Rückgang der Mobilität während Lockdown-Phasen fest. Vor allem beobachten wir, dass ein deutlicher Rückgang der Fernreisen während der Pandemie zu einem lokaleren Netzwerk und einer Abschwächung des “Small-World”-Effekts führt. Wir zeigen, dass diese strukturellen Veränderungen einen erheblichen Einfluss auf die Ausbreitungsdynamik von Epidemien haben, indem sie die epidemische Kurve abflachen und die Ausbreitung in geografisch weit entfernte Regionen verzögern. Des Weiteren entwickeln wir eine neue Methode zur Bestimmung des Ausbruchsursprungs anhand von hochaufgelösten geografischen Bewegungsdaten. Abschließend untersuchen wir, wie repräsentativ Mobilitätsdatensätze für das tatsächliche Reiseverhalten einer Bevölkerung sind. Wir identifizieren verschieden Arten von Verzerrungen, zeigen ihre Spuren in empirischen Datensätzen, und entwickeln einen mathematischen Rahmen um diese Verzerrungen abzuschwächen. Wir hoffen, dass unsere Studien in dieser Arbeit sich als hilfreiche Bausteine erweisen für ein einheitliches Verständnis von menschlicher Mobilität und der Dynamik von Infektionskrankheiten. / The Covid-19 pandemic demonstrated how strongly infectious disease spread is driven by the dynamics of human mobility. At the same time, the ongoing explosion of available mobility data in the 21st century opens up a much finer view of human mobility. In this thesis, we investigate several ways in which modern mobility data sources and modeling enable a deeper understanding of the interplay of human mobility and infectious disease spread. We use large-scale mobility data captured from mobile phones to show that country-wide mobility patterns undergo complex structural changes during the Covid-19 pandemic in Germany. Most prominently, we observe that a distinct reduction in long-distance travel during the pandemic leads to a more local, clustered network and a moderation of the “small-world” effect. We demonstrate that these structural changes have a considerable effect on epidemic spreading processes by “flattening” the epidemic curve and delaying the spread to geographically distant regions. Further, we show that high-resolution mobility data can be used for early outbreak detection. We develop a novel method to determine outbreak origins from geolocated movement data of individuals affected by the outbreak. We also present several practical applications that have been developed based on the above research. To further explore the question of applicability, we examine how representative mobility datasets are of the actual travel behavior of a population. We develop a mathematical framework to mitigate these biases, and use it to show that biases can severely impact outcomes of dynamic processes such as epidemic simulations, where biased data incorrectly estimates the severity and speed of disease transmission. We hope that our studies in this thesis will prove as helpful building blocks to assemble the emerging, unified understanding of mobility and infectious disease dynamics.