Stochastic spreading on complex networks

Complex interacting systems are ubiquitous in nature and society. Computational modeling of these systems is, therefore, of great relevance for science and engineering. Complex networks are common representations of these systems (e.g., friendship networks or road networks). Dynamical processes (e.g., virus spreading, traffic jams) that evolve on these networks are shaped and constrained by the underlying connectivity. This thesis provides numerical methods to study stochastic spreading processes on complex networks. We consider the processes as inherently probabilistic and analyze their behavior through the lens of probability theory. While powerful theoretical frameworks (like the SIS-epidemic model and continuous-time Markov chains) already exist, their analysis is computationally challenging. A key contribution of the thesis is to ease the computational burden of these methods. Particularly, we provide novel methods for the efficient stochastic simulation of these processes. Based on different simulation studies, we investigate techniques for optimal vaccine distribution and critically address the usage of mathematical models during the Covid-19 pandemic. We also provide model-reduction techniques that translate complicated models into simpler ones that can be solved without resorting to simulations. Lastly, we show how to infer the underlying contact data from node-level observations.Komplexe, interagierende Systeme sind in Natur und Gesellschaft allgegenwärtig. Die computergestützte Modellierung dieser Systeme ist daher von immenser Bedeutung für Wissenschaft und Technik. Netzwerke sind eine gängige Art, diese Systeme zu repräsentieren (z. B. Freundschaftsnetzwerke, Straßennetze). Dynamische Prozesse (z. B. Epidemien, Staus), die sich auf diesen Netzwerken ausbreiten, werden durch die spezifische Konnektivität geformt. In dieser Arbeit werden numerische Methoden zur Untersuchung stochastischer Ausbreitungsprozesse in komplexen Netzwerken entwickelt. Wir betrachten die Prozesse als inhärent probabilistisch und analysieren ihr Verhalten nach wahrscheinlichkeitstheoretischen Fragestellungen. Zwar gibt es bereits theoretische Grundlagen und Paradigmen (wie das SIS-Epidemiemodell und zeitkontinuierliche Markov-Ketten), aber ihre Analyse ist rechnerisch aufwändig. Ein wesentlicher Beitrag dieser Arbeit besteht darin, die Rechenlast dieser Methoden zu verringern. Wir erforschen Methoden zur effizienten Simulation dieser Prozesse. Anhand von Simulationsstudien untersuchen wir außerdem Techniken für optimale Impfstoffverteilung und setzen uns kritisch mit der Verwendung mathematischer Modelle bei der Covid-19-Pandemie auseinander. Des Weiteren führen wir Modellreduktionen ein, mit denen komplizierte Modelle in einfachere umgewandelt werden können. Abschließend zeigen wir, wie man von Beobachtungen einzelner Knoten auf die zugrunde liegende Netzwerkstruktur schließt

Topology Reconstruction of Dynamical Networks via Constrained Lyapunov Equations

The network structure (or topology) of a dynamical network is often unavailable or uncertain. Hence, we consider the problem of network reconstruction. Network reconstruction aims at inferring the topology of a dynamical network using measurements obtained from the network. In this technical note we define the notion of solvability of the network reconstruction problem. Subsequently, we provide necessary and sufficient conditions under which the network reconstruction problem is solvable. Finally, using constrained Lyapunov equations, we establish novel network reconstruction algorithms, applicable to general dynamical networks. We also provide specialized algorithms for specific network dynamics, such as the well-known consensus and adjacency dynamics.Comment: 8 page

Current Perspectives on Viral Disease Outbreaks

The COVID-19 pandemic has reminded the world that infectious diseases are still important. The last 40 years have experienced the emergence of new or resurging viral diseases such as AIDS, ebola, MERS, SARS, Zika, and others. These diseases display diverse epidemiologies ranging from sexual transmission to vector-borne transmission (or both, in the case of Zika). This book provides an overview of recent developments in the detection, monitoring, treatment, and control of several viral diseases that have caused recent epidemics or pandemics

PRIMARY AND SECONDARY PREVENTION OF HEPATITIS C VIRUS AMONG RURAL APPALACHIAN PEOPLE WHO USE DRUGS

Hepatitis C virus (HCV) remains a major cause of morbidity and mortality worldwide, with 3% of the global population chronically infected. Clinical impacts in the United States are projected to increase for two decades, and mortality attributed to HCV now exceeds HIV. Injection drug use (IDU) is the most common route of transmission in the developed world. Advances in treatment offer hope of mitigating HCV impacts, but substantial barriers obstruct people who inject drugs (PWID) from receiving care, particularly in medically underserved regions including Central Appalachia. This study assessed IDU paraphernalia sharing longitudinally over 24 months in a sample of 283 rural PWID recruited by respondent‐driven sampling. Medical follow‐up among 254 seropositive participants was also assessed using discrete‐time survival analysis. HCV‐positive screening was associated with reduced IDU sharing frequency 18 months after testing compared to seronegative participants (adjusted OR [aOR]=1.4, 95% confidence interval [CI]: 1.0‐1.9), but this effect was not sustained. HCV‐positive participants were less likely to cease IDU 6 months after testing (aOR=0.4, 95% CI: 0.2‐0.7). Predictors negatively associated with decreased IDU sharing included recent unprotected sex, sedative use, and frequency of prescription opioid IDU; protective associations included female gender and religious affiliation. IDU cessation was negatively associated with ever being incarcerated, recent unprotected sex with PWID, heavy alcohol use, lifetime use of OxyContin®, and baseline frequency of prescription opioid IDU; protective associations included number of dependents, receiving disability payments, and substance abuse treatment. Drug‐specific associations decreasing IDU cessation included recent illicit use of OxyContin®, other oxycodone, and cocaine. 150 of 254 (59%) seropositive participants saw a clinician after HCV‐positive screening and counseling, 35 (14%) sought treatment, and 21 (8%) received treatment. Positive predictors of following up with a clinician following testing and counseling included health insurance, internet access, past substance abuse treatment, generalized anxiety disorder, and recent marijuana use. Factors decreasing odds of follow‐up included major depression, lifetime illicit methadone use, and recent legal methadone. These analyses shed valuable light on determinants of behavior impacting primary and secondary HCV prevention. Integrated, multidisciplinary approaches are recommended to meaningfully impact epidemic levels of HCV among rural PWID in Eastern Kentucky

Structural Brain Network Degeneration and Functional Up-regulation In Huntington’s disease

Huntington’s disease (HD) is a neurodegenerative disorder caused by a CAG repeat expansion in the Huntingtin gene on chromosome 4. In recent years there have been significant advances in understanding both the cellular pathology and the macrostructural changes that occur in the striatum and cortical structures as the disease proceeds. However, it remains unclear how abnormalities at the cellular level lead to characteristic patterns of macrostructural change in the brains of HD patients. In this thesis I aim to link structural and functional brain network abnormalities with regional changes at the cellular level. Using diffusion tractography and resting state functional MRI in well characterised HD cohorts I examine the relationship between structural and functional brain network organisation. I link these changes in structure and function to the neuropsychiatric symptoms prevalent in HD, occurring years before the manifestation of motor symptoms. By characterising changes in white matter brain networks I reveal how the brain network breaks down as HD progresses and show how this network deterioration leads to the emergence of clinical deficits. Using characteristics of the healthy white matter brain network I demonstrate how it is possible to predict the atrophy of specific brain connections in HD over time. In doing so I highlight a hierarchy of white matter connection vulnerability showing cortico-striatal connections are the first to be affected. In order to link these macrostructural white matter changes to cellular level abnormalities I utilise data from the Allen Institute transcription atlas and show how differences in regional gene expression in the healthy brain can account for the selective vulnerability of specific white matter connections in HD. The work presented in this thesis demonstrates how linking systems and cellular pathobiology in HD can inform us about disease mechanisms that drive brain atrophy and ultimately lead to clinical deficits

High-Performance Modelling and Simulation for Big Data Applications

This open access book was prepared as a Final Publication of the COST Action IC1406 “High-Performance Modelling and Simulation for Big Data Applications (cHiPSet)“ project. Long considered important pillars of the scientific method, Modelling and Simulation have evolved from traditional discrete numerical methods to complex data-intensive continuous analytical optimisations. Resolution, scale, and accuracy have become essential to predict and analyse natural and complex systems in science and engineering. When their level of abstraction raises to have a better discernment of the domain at hand, their representation gets increasingly demanding for computational and data resources. On the other hand, High Performance Computing typically entails the effective use of parallel and distributed processing units coupled with efficient storage, communication and visualisation systems to underpin complex data-intensive applications in distinct scientific and technical domains. It is then arguably required to have a seamless interaction of High Performance Computing with Modelling and Simulation in order to store, compute, analyse, and visualise large data sets in science and engineering. Funded by the European Commission, cHiPSet has provided a dynamic trans-European forum for their members and distinguished guests to openly discuss novel perspectives and topics of interests for these two communities. This cHiPSet compendium presents a set of selected case studies related to healthcare, biological data, computational advertising, multimedia, finance, bioinformatics, and telecommunications