This thesis consists of two parts which are connected by the central theme of epidemics. In the first part, a website is designed for forecasting the number of cases of COVID-19 in the Netherlands. The forecasting is performed using the Network-Inference-Based Prediction Algorithm (NIPA). The first part of the thesis documents the design process and some of the challenges faced along the way. An explanation of the NIPA algorithm is presented, and its implementation on the website is discussed. The second part of this thesis shifts the focus to the modeling of mobility processes. Human-to-human transmission is often the dominant viral transmission vector, and therefore the spreading of the virus is inextricably linked to human mobility. The Markov-modulated process (MMP) model has recently been proposed as a novel method for modeling mobility processes. Yang has developed a so-called "aggregated MMP model" which is able to capture several key dynamics of mobility processes with high accuracy. This research builds on Yang's results and proposes the "quantized MMP model" as an extension of Yang's aggregated MMP model. Compared to the aggregated MMP model, the quantized MMP model reduces the number of required states by a factor equal to the quantization step size q, improving the efficiency of the model. The behavior of the quantized MMP model for different step sizes q is compared with the aggregated MMP model. The results show that the quantization error has zero mean, allowing the quantized MMP model to achieve similarly high model accuracy. The SIR dynamics of the quantized MMP model for different step sizes are tested extensively and the disease spreading performance is compared with the mobility process. The suitability of the MMP model for forecasting the evolution of epidemics is evaluated and discussed.

Since the first introduction of 4G in the early 2010s, mobile data traffic has increased significantly, mainly because 4G networks can support more devices, services and applications, as well as greater cellular network coverage. With the advent of the 5G era, the mobile communication system will be further developed. Today, most countries and regions are already implementing their own 5G plans. Compared with China, South Korea and the United States, the three leading countries in the 5G market, the EU’s 5G plans are relatively slow. The focus of this thesis is to explore various 5G deployment and migration options, as well as the current 5G status in different countries and regions. We start with current network technologies, compare and analyze various 5G deployment and migration options. Then we compare the 5G status of the EU with China, South Korea and the United States, and analyze the internal and external factors faced by the EU in the development of 5G. In these two analysis, we will consider several communication services that are currently used in the mobile network, including, but not limited to, voice/video calling and messaging, for both home usage and roaming usage. Finally, based on the above two analysis, suggestions for EU operators in 5G deployment and development are provided, along with recommendations for future research.

As new technologies continue to find their way into everyday life, the world becomes more and more connected. Airplanes and other means of transportation provide global connections in the physical world, while the omnipresence of the Internet means that information is shared around the globe, easier than ever before. But not only these man-made systems are distinctly connected, other complex systems like the human brain, or metabolic networks are successfully being studied from the perspective of their constituting connections. The combining concept in all these examples is the structure of the problem at hand: each system consists of interacting elementary components at the lowest level, from which a network structure emerges at the global level. The study of such networked systems, their observed features and the wide range of related analysis tools is commonly referred to as Network Science. In this thesis, the specific problem of how diseases spread over networks is addressed. Better understanding this spreading behavior has significant practical importance, i.e. for the prediction and control of disease prevalence, and poses many interesting theoretical challenges. In the context of modeling epidemics on networks, we formulate the Universal Mean-Field Framework. This new and theoretically well-founded framework unifies and generalizes a number of existing approximate models, and brings forth new approaches to bound the approximations. Apart from the work on epidemics, some new insights are explored in the context of the connections between electrical circuits, networks and simplices (higher-dimensional triangles). These deep theoretical equivalences allow the tools and intuitions from electrical circuits and geometry to be used in the study of networks. A comprehensive introduction and discussion of the equivalent representations and their connections is given. Additionally, we derive a new formula for the volume of a hyperacute simplex and propose to use this volume as a network-robustness measure.

With the proliferating networks, resource allocation based on Quality of Service (QoS) constraints mapping has been one of the difficulties faced by Internet Service Providers (ISP). The advent of new technologies such as virtualization and cloud computing have enabled the users to access content from anywhere around the world. This results in a need for an efficient and fast resource allocation method based on demand acting on the network. Many researchers have developed various algorithms to address this issue. However, they have considered only flow-based network properties, while the contemporary networks communicate mostly through path-based communication using the shortest paths. Inverse shortest path algorithm (ISPA) is a graph-theory based heuristic developed to solve this network resource allocation problem which considers both flow-based communication properties through Effective resistance matrix and path-based communication properties through shortest path matrix. Nevertheless, ISPA is so far implemented only for unweighted graphs. This study aims at assessing the feasibility of ISPA for weighted graphs by understanding the nature of Inverse shortest path problem (ISPP) bounds in weighted random graphs and implementing ISPA for weighted graphs. ISPP bounds behaviour is studied for weighted graphs by analyses of Q-norm distributions, probability of failure distributions and hopcount distributions. A feasibility condition verifying ISPP bounds is derived in relation with the input parameters of the weighted random graph. The solutions obtained through hop count distribution analysis are observed to be Poissonian in nature. Finally, ISPA is implemented for weighted graphs such that demand matrix can be resolved into a simple distance matrix to obtain solution which is a non-negative weighted Adjacency matrix and feasibility conditions are verified for the solutions obtained through ISPA.

Freight transport is an essential component of the economy, as among other things it ensures the availability of finished goods to consumers. Synchromodal transport is a new transport method that aims to use real-time and flexible switching among different modes of transport according to the latest logistics information, to utilise the different modes of transport efficiently. But what are the effects of disruptions of the infrastructure used by synchromodal transport on freight transport? As some recent disruptions in the Netherlands have shown, the negative effects can be considerable. The effects of disruptions on the functioning of multimodal transport networks have scarcely been researched. This research gap is addressed in this thesis, by analysing the robustness of the Dutch synchromodal freight network, comprising of the inland waterway, road, railway and container terminal infrastructure. First an overview is given of the elements of the synchromodal transport infrastructure. Apart from the infrastructure elements of each mode of transport, two important characteristics are identified: the interconnection and the interdependence. Container terminals are the interconnection between different modes of transport, as they facilitate the transshipment of containers. Infrastructure elements whose functioning influences multiple modes of transport (e.g. bridges) are the interdependence between different modes of transport. Subsequently, this overview of infrastructure elements is used to make a macroscopic graph model in which all relevant infrastructure elements are represented. Using the random removal of graph elements, the robustness of the synchromodal network is analysed. Three case studies are used to study the Dutch synchromodal network: the corridor between Rotterdam and Antwerp, the corridor Rotterdam and Duisburg, and the domestic freight transport in the Netherlands. The robustness analysis of the three case studies lead to the following conclusions. Of the three modes of transport, the modality road is the most robust. The inland waterway modality is less robust and the rail modality is the least robust. It should be noted that the rail modality provides a relatively cheap alternative and offers the capabilities to transport containers further into Europe than the inland waterways. The ability to transship containers between different modes of transport (i.e. interconnection) has a significant positive effect on the robustness. The interdependence has a smaller negative effect on the robustness. Generally, the new alternative paths offered by the addition of a mode of transport (even without interconnection) outweigh the negative effects of the interdependence. These findings make it clear that the use of the synchromodal transport method, increases the robustness of the freight transport network. During this research, many possibilities for future research were identified. As the research gap for analysing the robustness of a synchromodal transport network was very large at the start of this research, many things can still be researched after this research. The importance of freight transport warrants additional research on this topic. According to this research, due to mode-free booking and the real-time and flexible switching among different modalities, synchromodal transport offers a robust freight transport method.

Network performance is determined by the interplay of underlying structures and overlying dynamic processes on networks. This thesis mainly considers two types of collective dynamics on networks, spread and transport, which are ubiquitous in our daily lives, ranging from information propagation, disease spreading, to molecular motors on cytoskeleton and urban traffic. Exploring the approaches on optimizing the network performance is the fundamental motivation of this work, which helps to control processes on networks and to upgrade network-based services. Although the properties of phase transition in Susceptible-Infected-Susceptible (SIS) processes have been investigated intensively, the time-dependent behavior of epidemics is still an open question. This thesis starts with the investigation of the spreading time (Chapter 2), which is the time when the number of infected nodes in the metastable state is first reached, starting from the outbreak of the epidemics. We observe that the spreading time resembles a lognormal-like distribution both for the Markovian and the non-Markovian infection processes. As a follow-up work of Chapter 2, we identify the fastest initial spreaders with the shortest average spreading time in epidemics on a network, which helps to ensure an efficient spreading (Chapter 3). We show that the fastest spreader changes with the effective infection rate of a SIS epidemic process, which means that the time-dependent influence of a node is usually strongly coupled to the dynamic process and the underlying network. We propose the spreading efficiency as a metric to quantify the efficiency of a spreader and identify the fastest spreader, which is adaptive to different infection rates in general networks. For maximizing the utility of spread, we introduce induced spreading, which aims to maximize the infection probabilities of some target nodes by adjusting the nodal infection rates (Chapter 4). We assume that the adjustment of the nodal infection rates has an associated cost and formulate the induced spreading for SIS epidemics in networks as an optimization problem under a constraint on the total cost. We address both a static model and a dynamic model for the optimization of the induced SIS spreading. We show that the infection rate increment on each node is coupled to both the degree and the average hops to the target nodes in the static optimization method. In the dynamic method, the effective resistance is a good metric to indicate the minimum total cost for targeting a single node. The average fraction of infected nodes in the NIMFA steady state, also called the steady-state prevalence, in terms of the effective infection rate can be expanded into a power series around the NIMFA epidemic threshold. Practically, we can faster compute the nodal infection probability of the NIMFA steady-state by the truncated expansion with enough terms and an effective infection rate within the radius of convergence. Thus, we investigate the radius of convergence that validates the Taylor expansion of the steady-state prevalence in Chapter 5. We show that the radius of convergence of the steady-state prevalence expansion strongly depends upon the spectral gap of the adjacency matrix. The research on the robustness of transport on networks mainly encompasses two robustness assessment approaches, along with their applications in communication networks and freight transport networks, respectively. Network recoverability refers to the ability of a network to return to a desired performance level after suffering malicious attacks or random failures (Chapter 6). We propose a general topological approach and recoverability indicators to measure the network recoverability in two scenarios: 1) recovery of damaged connections and 2) any disconnected pair of nodes can be connected to each other. By applying the effective graph resistance and the network efficiency as robustness metrics, we employ the proposed approach to assess 10 real-world communication networks. For vehicle transport systems, Chapter 7 proposes a robustness assessment for multimodal transport networks. The representation of interdependent networks is an excellent proxy for the structure of multimodal transportation systems. We apply our robustness assessment model to the Dutch freight transport, taking into account three modalities: waterway, road and railway. The node criticality, defined as the impact of a node removal on the total travel cost, resembles a power-law distribution, which implies scale-free property of the robustness against infrastructure disruptions. Many transport processes have a similar objective that all nodes reach an agreement regarding a certain quantity of interest by exchanging the nodal states with their neighboring nodes, which are described by the consensus model in networks (Chapter 8). The robustness of consensus processes is related to the convergence speed to the stability under external perturbations. The (generalized) algebraic connectivity of a network characterizes the lower-bound of the exponential convergence rate of consensus processes. We investigate the problem of accelerating the convergence of consensus processes by adding links to the network. We propose a greedy strategy for undirected network and further extend our approach to directed networks. Numerical tests verify the better performance of our methods than other metric-based approaches. This thesis considers two dynamic processes on networks and covers performance analysis and optimizations, by means of problem proposal, theoretical analysis, case study and algorithm designing. The developed concepts related to network efficiency and robustness provide a better understanding of collective dynamics on complex networks. The applicability of our methodologies bridges theoretical network models and realistic applications, as well as demonstrates the promising efficacy of network science.@en

Over the last two decades the field of network science has been evolving fast. Many useful applications in a wide variety of disciplines have been found. The application of network science to the brain initiated the interdisciplinary field of complex brain networks. On a macroscopic level, brain regions are taken as nodes in a network. The analysis of pairwise connections between the brain regions as links has provided a new perspective on many problems. The application of network science to neuroscience data helped, for example, to identify the disruptions due to different neurological disorders when comparing healthy and abnormal brain networks. In this dissertation, we focus on the macroscopic level of brain regions and analyze their pairwise connections from a network science perspective. We address different general research questions from network science and exploit their application possibilities towards brain networks. Due to different measurement techniques, one can construct many different representations of brain networks. We thereby distinguish between the structural and functional brain network. Structural brain networks map the anatomical connections between the regions, which we could interpret as the ’streets’ of the brain. On top of these streets, we can measure the traffic with techniques like e.g. magnetoencephalography (MEG) or functional Magnetic Resonance Imaging (fMRI) resulting in so-called functional brain networks. However, the relation between the structural and the functional brain networks is still insufficiently understood. The first main research question of this dissertation focuses on the functional network layer and tries to identify the most important links and motifs of these networks. For this purpose, we propose the union of shortest path trees (USPT) as a new sampling method extracting all the shortest paths of a network (Chapter 2 and 3). After constructing the USPT, we compare the individual functional brain networks of multiple sclerosis patients and healthy controls (Chapter 2). Furthermore, we generalize this sampling method and present a new ranking of all the links based on the USPT (Chapter 3). Regarding the higher-order building blocks of the functional brain networks, we analyze the so-called information flow motifs based on MEG data from different frequency bands (Chapter 4). After researching the local properties of the functional brain networks, we analyze the influence of the underlying structural connections on the emerging information flow. Thus, the second main research question concerns the relationship between the functional and the underlying structural connectivity. Specifically, we analyze which topological properties of the structural networks drive the functional interactions. First, this question is approached in a mathematical and straightforward manner by assuming that an analytic function between the two networks exists (Chapter 5). We investigate this mapping function and its reverse by evaluating empirical individual and group-averaged multimodal data sets. A second approach towards the structure-function relationship employs a simple model of activity spread. The epidemic spreading model is applied on the human connectome to investigate the global patterns of directional information flow in brain networks (Chapter 6). The main focus here lies on the pairwise measure of transfer entropy to investigate the influence of one brain region on another. We present the results for the local and global outcomes of the dynamic spreading process aiming to identify the driving structural properties behind the observed global patterns. @en

Failures of networks, such as power outages in power systems, congestions in transportation networks, paralyse our daily life and introduce a tremendous cascading effect on our society. Networks should be constructed and operated in a robust way against random failures or deliberate attacks. We study how to add a single link into an existing network such that the robustness of the network is maximally improved among all the possibilities. A graph metric, the effective graph resistance, is employed to quantify the robustness of the network. Though exhaustive search guarantees the optimal solution, the computational complexity is high and is not scalable with the increase of network size. We propose strategies that take into account the structural and spectral properties of networks and indicate links whose addition result in a high robustness level.@en

This thesis is a contribution to a deeper understanding of how information propagates and what this process entails. At its very core is the concept of the network: a collection of nodes and links, which describes the structure of the systems under investigation. The network is a mathematical model which allows to focus on a very fundamental property: the mutual relations (links) between information exchanging agents (nodes). This simplicity makes networks elegant, as no specifics of any supporting hardware are needed to reason on this high level of abstraction. The developing field of network science led to countless applications of the network model to all sorts of complex systems in nature and technology. Naturally, it became an essential part of many multi-disciplinary research projects. Therefore, understanding how information propagates in networks enables us to learn and conceivably control the intricate processes, which we observe in complex systems. Since complex systems are the driver for this research, the first three chapters of this thesis are studies based on data collected from vastly different application domains, after more fundamental research is addressed in the later parts. Chapter 2 deals with the interaction of players of a popular multiplayer online game. Due to the competitive design of the game, teams are formed ad-hoc and compete with each other for victory. Some of the players exhibit anti-social behavior towards their teammates, which is known as toxicity. We analyze how toxicity in player networks emerges by developing a toxicity detector, highlighting possible triggers and analyze the disposition of players towards toxic teammates. Furthermore, we show how toxicity is linked to game success. Chapter 3 continues with a study of the human brain as a functional network. Information processing in the brain is measurable with technologies like magnetoencephalography. From such measurements that were collected from a group of subjects, the phase transfer entropy is computed as a quantity that reflects information exchange. When associated with the links between brain regions, unusual high numbers of certain substructures are observed in this network. We find that one of these substructures, the bi-directional two-hop path, to be highly abundant and robust within different frequencies bands, which highlights its importance for the propagation of brain activity. A clustering of the network based on these frequent substructures reveals a spatially coherent organization of important brain regions. A common symbol of propagation is the virus, which is at the center of the third data-driven analysis of this thesis in Chapter 4. More precisely, we research the digital version of the virus, the computer worm, and analyze its propagation by epidemic network models. With epidemic models, the state of the nodes in a network can be described as susceptible or infected. An infection process and a curing process determine how the nodes are changing between those states. We extend on the standard epidemic models, the SIS model, by a time-dependent curing rate function to reflect the changes in the effectiveness of the active worm removal. Once we set the curing rate function, the empirical worm data are fitted and analyzed on multiple scales from the global over the country down to the autonomous system level. The fitted model explains how computer worms or similar self-replicating pieces of information might change in their effectiveness over long periods of time. The SIS model returns as a central piece in Chapter 5 again. Although spreading processes are frequently modeled in isolation, the dynamics of many real-world applications are often driven by the interaction of multiple of such processes. These interactions can range from viruses that compete for susceptible nodes to viruses that mutually reinforce their propagation. We study the special case of superinfection, in which one dominant virus spreads within the infected population of a weaker virus. We highlight the conditions for which a co-existence of both viruses is stable and show that extinction cycles become possible if the infection rate of the dominant virus becomes too strong. Furthermore, we show that some of the possible outcomes of a superinfection are difficult to approximate with common mean-field techniques. However, the second largest eigenvalue of the infinitesimal generator of the underlying Markov process is potentially linked to co-existence and thus stability. Chapter 6 is a study on the capabilities of symbolic regression for network properties. We develop an automated system based on Genetic Programming which is able to be trained by families of networks to learn the relations between several of their properties. These properties can be features of the networks like the eigenvalues of their adjacency or Laplacian matrices or network metrics like the network diameter or the isoperimetric number. We show that the system can generate approximate formulas for those metrics that often give better results than previously known analytic bounds. The evolved formulas for the network diameter are evaluated on a selection of real-world networks of different origins. The network diameter bounds hop-based information propagation and is thus of high importance for designing network algorithms. A careful selection of training networks and network features is crucial for evolving good approximate formulas for the network diameter and similar properties. Finally, the thesis concludes with Chapter 7 which revisits the concepts that were developed and provides some critical assessment on their potential and limitations.@en

The concept of a network, defined as a collection of interconnected nodes or entities, has become a foundation for a new field of inquiry, namely network science. Despite the apparent simplicity of the concept, the pairwise representation of interconnecting nodes has enabled a plethora of insights into the structure of networks and the effects of interactions on dynamic processes. This generality of the network concept has paved the way for novel approaches with the aim of understanding complex systems, from social networks to biological pathways. It has opened up new avenues for research into the fundamental mechanisms underlying these systems. As such, network science has become a highly active and dynamic field, driving the development of new theoretical frameworks, computational tools, and empirical methods that continuously push the boundaries of knowledge and understanding in numerous science and engineering domains. The first part of this thesis centres on the structural properties of complex networks and their practical applications. We demonstrate that the orthogonal eigenvectors of the adjacency matrix of a simple, unweighted, and undirected graph are sufficient to recover that graph, albeit potentially not in a unique manner (Chapter 2). This observation led us to uncover co-eigenvector graphs, which are graphs that share the same eigenvectors while having distinct eigenvalues. Co-eigenvector graphs are the dual counterparts of cospectral graphs, which share identical eigenvalues but possess distinct eigenvectors. In an unweighted graph, the number of walks between node pairs of a particular length can be expressed in terms of the corresponding power of the adjacency matrix. However, deriving a similar solution for the number of paths is significantly more intricate (Chapter 3). We present three distinct analytical solutions in matrix form for computing the number of paths of any length between node pairs, utilising different types of walks and leveraging principles from the mathematical field of combinatorics. The computational complexity of these solutions varies depending on the sparsity of the graph. The effective resistance metric, which characterises the entire network as perceived from the vantage point of two given nodes, represents a powerful tool for addressing a wide range of challenges in network theory. In Chapter 4, we leverage the information contained in effective resistance to solve the inverse all shortest path problem, wherein a weighted graph satisfying given upper bounds on the shortest path weights between node pairs is sought, with sparsity being a critical consideration. Additionally, we propose a novel graph sparsification algorithm that selectively removes links from an unweighted graph in a stepwise manner, with the goal of either minimising or maximising the effective resistance of the resultant graph. The second part of this thesis pertains to linear processes on complex networks, exploring their properties and applications. Our research reveals that a simple process of attraction and repulsion between adjacent nodes on a one-dimensional line, based on the similarity of their neighbourhoods, can effectively group together nodes from the same community (Chapter 5). Our linear clustering process generally produces more accurate partitions than the most prevalent modularity-based clustering methods in the literature, requiring a comparable amount of computational complexity. An empirical part of our research on processes in complex networks became possible thanks to our network construction based on a unique data set containing each municipality’s area, population and its geographically adjacent neighbouring municipalities. Thanks to this network construction, research became possible on a dynamic network of connected municipal nodes at a national level over the period from 1830 to 2019 (Chapter 6). By connecting the population data, area data and municipal merger data of all Dutch municipalities, we discovered that the logarithm of the municipal area and population size yields an almost linear difference equation over time. Research into the municipal merger process over the period 1830-2019 has shown that 873 of the 1228 Dutch municipalities have merged into adjacent larger municipalities with a larger population. Our simulation of municipality mergers based on network effects caused by population growth by municipality resulted in a county-level predictive accuracy of 91.7 % over a 200-year period. Suppose every node within a network exhibits linear internal dynamics of a specific order, and the dynamic interactions between these nodes are also linear. In that case, the entire network conforms to a collection of linear differential equations (Chapter 7). Our study offers an analytical solution for the comprehensive network dynamics in state space form, achieved by merging the fundamental topology and internal linear dynamics of every individual node.@en

Electric power has become an essential part of daily life: we plug our electronic devices in, switch our lights on, and expect to have power. As the availability of power is usually taken for granted in modern societies, we mostly feel annoyed at its absence and perceive the importance of power during outages which have severe effects on the public order. Blackouts have had disastrous consequences for many countries and they continue to occur frequently. Such examples demonstrate the necessity for careful analysis and planning of power grids, to ultimately increase the reliability of power grids. The power grids have evolved due to economic, environmental and human-caused factors. In addition to the contingency analysis, nowadays, the operation and planning of power grids are facing many other challenges (such as demand growth, targeted attacks, cascading failures, and renewable energy integration). Thus, many questions arise, including: which buses (nodes) to connect with a new line (link)? What are the impacts of malicious attacks on power grids? How may an initial failure result in a cascade of failures? How to prepare for the integration of renewable energy? Answering such questions requires developing new concepts and tools for analysing and planning of power grids. Power grids are one of the largest and the most complex man-made systems on earth. The complex nature of power grids and its underlying structure make it possible to analyse power grids relying on network science. The applications of network science on power grids have shown the promising potential to capture the interdependencies between components and to understand the collective emergent behaviour of complex power grids. This thesis is motivated by the increasing need of reliable power grids and the merits of network science on the investigation of power grids. In this context, relying on network science, we model and analyse the power grid and its near-future challenges in terms of line removals/additions, malicious attacks, cascading failures, and renewable integration.@en

The field of epidemiology encompasses a broad class of spreading phenomena, ranging from the seasonal influenza and the dissemination of fake news on online social media to the spread of neural activity over a synaptic network. The propagation of viruses, fake news and neural activity relies on the contact between individuals, social media accounts and brain regions, respectively. The contact patterns of the whole population result in a network. Due to the complexity of such contact networks, the understanding of epidemics is still unsatisfactory. In this dissertation, we advance the theory of epidemics and its applications, with a particular emphasis on the impact of the contact network. Our first contribution focusses on the analysis of the N-Intertwined Mean-Field Approximation (NIMFA) of the Susceptible-Infected-Susceptible (SIS) epidemic process on networks. We propose a geometric approach to clustering for epidemics on networks, which reduces the number of NIMFA differential equations from the network size N to the number m << N of clusters (Chapter 2). Specifically, we show that exact clustering is possible if and only if the contact network has an equitable partition, and we propose an approximate clustering method for arbitrary networks. Furthermore, for arbitrary contact networks, we derive the closed-form solution of the nonlinear NIMFA differential equations around the epidemic threshold (Chapter 3). Our solution reveals that the topology of the contact network is practically irrelevant for the epidemic outbreak around the epidemic threshold. Lastly, we study a discrete-time version of the NIMFA epidemic model (Chapter 4). We derive that the viral state is (almost always) monotonically increasing, the steady state is exponentially stable, and the viral dynamics is bounded by linear time-invariant systems. In the second part, we consider the reconstruction of the contact network and the prediction of epidemic outbreaks. We show that, for the stochastic SIS epidemic process on an individual level, the exact reconstruction of the contact network is impractical. Specifically, the maximum-likelihood SIS network reconstruction is NP-hard, and an accurate reconstruction requires a tremendous number of observations of the epidemic outbreak (Chapter 5). For epidemic models between groups of individuals, we argue that, in the presence of model errors, accurate long-term predictions of epidemic outbreaks are not possible, due to a severely ill-conditioned problem (Chapter 6). Nonetheless, short-term forecasts of epidemics are valuable, and we propose a prediction method which is applicable to a plethora of epidemic models on networks (Chapter 7). As an intermediate step, our prediction method infers the contact network from observations of the epidemic outbreak. Our key result is paradoxical: even though an accurate network reconstruction is impossible, the epidemic outbreak can be predicted accurately. Lastly, we apply our network-inference-based prediction method to the outbreak of COVID-19 (Chapter 8). The third part focusses on spreading phenomena in the human brain. We study the relation between two prominent methods for relating structure and function in the brain: the eigenmode approach and the series expansion approach (Chapter 9). More specifically, we derive closed-form expressions for the optimal coefficients of both approaches, and we demonstrate that the eigenmode approach is preferable to the series expansion approach. Furthermore, we study cross-frequency coupling in magnetoencephalography (MEG) brain networks (Chapter 10). By employing a multilayer network reconstruction method, we show that there are strong one-to-one interactions between the alpha and beta band, and the theta and gamma band. Furthermore, our results show that there are many cross-frequency connections between distant brain regions for theta-gamma coupling.@en