The recent outbreak of coronavirus disease 2019 (COVID-19) in mainland China was characterized by a distinctive subexponential increase confirmed cases during the early phase epidemic, contrasting with an initial exponential growth expected for unconstrained outbreak. We show that this effect can be explained as direct consequence containment policies effectively deplete susceptible population. To end, we introduce parsimonious model captures both quarantine symptomatic infected individuals,...

In the wake of COVID-19 pandemic many countries implemented containment measures to reduce disease transmission. Studies using digital data sources show that mobility individuals was effectively reduced in multiple countries. However, it remains unclear whether these reductions caused deeper structural changes networks and how such may affect dynamic processes on network. Here we use movement mobile phone users Germany has not only been considerably: Lockdown substantial long-lasting We find...

The recent outbreak of COVID-19 in Mainland China is characterized by a distinctive algebraic, sub-exponential increase confirmed cases with time during the early phase epidemic, contrasting an initial exponential growth expected for unconstrained sufficiently large reproduction rate. Although case counts vary significantly between affected provinces China, scaling law t μ surprisingly universal, range exponents = 2.1 ± 0.3. universality this behavior indicates that, spite social, regional,...

We present an analytical method for computing the mean cover time of a discrete-time random walk process on arbitrary, complex networks. The is defined as walker requires to visit every node in network at least once. This quantity particularly important search processes and target localization structures. Based global first-passage nodes, we derive cumulative distribution function based statistics. Our viable networks which walks equilibrate quickly. show that it can be applied successfully...

Abstract Vaccines are among the most powerful tools to combat COVID-19 pandemic. They highly effective against infection and substantially reduce risk of severe disease, hospitalization, ICU admission, death. However, their potential for attenuating long-term changes in personal health health-related wellbeing after a SARS-CoV-2 remains subject debate. Such effects can be effectively monitored at individual level by analyzing physiological data collected consumer-grade wearable sensors....

Disease propagation between countries strongly depends on their effective distance, a measure derived from the world air transportation network (WAN). It reduces complex spreading patterns of pandemic to wave-like outbreak country, establishing linear relationship arrival time unmitigated spread disease. However, in early stages an outbreak, what concerns decision-makers is understanding relative risk active cases arriving country—essentially, likelihood that case boarding airplane at...

Network data sets are often constructed by some kind of thresholding procedure. The resulting networks frequently possess properties such as heavy-tailed degree distributions, clustering, large connected components and short average shortest path lengths. These considered typical complex appear in many contexts, prompting consideration their universality. Here we introduce a simple model for correlated relational study the network ensemble obtained it. We find that some, but not all,...

As the coronavirus disease 2019 spread globally, emerging variants such as B.1.1.529 quickly became dominant worldwide. Sustained community transmission favors proliferation of mutated sub-lineages with pandemic potential, due to cross-national mobility flows, which are responsible for consecutive cases surge We show that, in early stages an variant, integrating data from national genomic surveillance and global human large-scale epidemic modeling allows quantify its providing quantifiable...

Social networks shape individuals' lives, influencing everything from career paths to health. This paper presents a registry-based, multi-layer and temporal network of the entire Danish population 2008 2021. Our maps relationships formed through family, households, neighborhoods, colleagues classmates for approximately 7.2 million individuals with more than 1.4 billion relations between them over course decade. We outline key properties this multiplex network, introducing both an...

Vancomycin-resistant E. faecium (VRE) are an important cause of nosocomial infections, which rapidly transmitted in hospitals. To identify possible transmission routes, we applied combined genomics and contact-network modeling to retrospectively evaluate routine VRE screening data generated by the infection control program a hemato-oncology unit. Over 1 year, total 111 isolates from patients were collected anal swabs tertiary care hospital Southern Germany. All isolated whole-genome...

Network visualization is an effective way to illustrate properties of a complex system.It important tool for exploring and finding patterns, used by researchers practitioners across many fields industries.Currently, there exist number tools visualizing networks.Networkx (Hagberg, Schult, & Swart, 2008) popular Python package network analysis which provides limited functionality computing layouts plotting networks statically.Layout computations are done in or using the php-based software...

Abstract Background While the majority of German population was fully vaccinated at time (about 65%), COVID-19 incidence started growing exponentially in October 2021 with about 41% recorded new symptomatic cases aged twelve or above being breakthrough infections, presumably also contributing to dynamics. So far, it remained elusive how significant this contribution and whether targeted non-pharmaceutical interventions (NPIs) may have stopped amplification crisis. Methods We develop...

The famous Watts-Strogatz (WS) small-world network model does not approach the Erd\H{o}s-R\'enyi (ER) random graph in limit of total randomization which can lead to confusion and complicates certain analyses. In this paper we discuss a simple alternative was first introduced by Song Wang, where instead rewiring, edges are drawn between pairs nodes with distance-based connection probability. We show that is simpler analyze, approaches true ER completely randomized limit, demonstrate WS may...

Digital contact tracing (DCT) applications have been introduced in many countries to aid the containment of COVID-19 outbreaks. Initially, enthusiasm was high regarding their implementation as a non-pharmaceutical intervention (NPI). However, no country able prevent larger outbreaks without falling back harsher NPIs. Here, we discuss results stochastic infectious-disease model that provide insights how progression an outbreak and key parameters such detection probability, app participation...

Abstract After the winter of 2021/2022, coronavirus disease 2019 (COVID-19) pandemic had reached a phase where considerable number people in Germany have been either infected with severe acute respiratory syndrome 2 (SARS-CoV-2) variant, vaccinated or both, full extent which was difficult to estimate, however, because infection counts suffer from under-reporting, and overlap between recovered subpopulations is unknown. Yet, reliable estimates regarding population-wide susceptibility were...

As an approach to describe the long-range properties of non-Abelian gauge theories at non-zero temperature T < T_c, we consider a non-interacting ensemble dyons (magnetic monopoles) with non-trivial holonomy. We show analytically, that quark-antiquark free energy from Polyakov loop correlator grows linearly distance, and how string tension scales dyon density. In numerical treatments, tails fields cause severe finite-volume effects. Therefore, demonstrate application Ewald's summation method...

Social networks shape individuals' lives, influencing everything from career paths to health. This paper presents a registry-based, multi-layer and temporal network of the entire Danish population in years 2008-2021 (roughly 7.2 mill. individuals). Our maps relationships formed through family, households, neighborhoods, colleagues classmates. We outline key properties this multiplex network, introducing both an individual-focused perspective as well bipartite representation. show how...

In November 2021, the first infection with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variant of concern (VOC) B.1.1.529 ('Omicron') was reported in Germany, alongside global reports reduced vaccine efficacy (VE) against infections this variant. The potential threat posed by its rapid spread Germany was, at time, difficult to predict. We developed a variant-dependent population-averaged susceptible-exposed-infected-recovered infectious-disease model that included...

Networks that are organized as a hierarchy of modules have been the subject much research, mainly focusing on algorithms can extract this community structure from data. The question why modular hierarchical organizations so ubiquitous in nature, however, has received less attention. One hypothesis is topologies may provide an optimal for certain dynamical processes. We revisit network model interpolates, using single parameter, between two known topologies: strong modularity to...

Digital contact tracing applications have been introduced in many countries to aid the containment of COVID-19 outbreaks. Initially, enthusiasm was high regarding their implementation as a non-pharmaceutical intervention (NPI). Yet, no country able prevent larger outbreaks without falling back harsher NPIs, and total effect digital remains elusive. Based on results empirical studies modeling efforts, we show that apps might prevented cases order single-digit percentages up until now, at...

Vaccines are among the most powerful tools used to combat COVID-19 pandemic. They highly effective against infection and substantially reduce risk of severe disease, hospitalization, ICU admission, death. However, their potential for attenuating long-term effects a SARS-CoV-2 infection, commonly denoted as Long COVID, remains elusive is still subject debate. Such can be effectively monitored at individual level by analyzing physiological data collected consumer-grade wearable sensors. Here,...

Abstract After having affected the population for two years, COVID-19 pandemic has reached a phase where considerable number of people in Germany have been either infected with SARS-CoV-2 variant, vaccinated, or both. Yet full extent to which contact virus vaccine remains elusive, particularly on regional level, because (a) infection counts suffer from under-reporting, and (b) overlap between vaccinated recovered subpopulations is unknown. Since previous infection, vaccination, especially...

Analyzing the spread of infectious diseases by means compartmental mathematical models has been an active area research for almost a century (Anderson & May, 2010;Keeling Rohani, 2011;Kermack McKendrick, 1991).Since emergence coronavirus disease 2019 pandemic in early 2020, field seen yet another considerable boost interest.Researchers have since working on large number different that are used to forecast case numbers, analyze implications contact structures between individual people, or...

Vaccines are the most powerful pharmaceutical tool to combat COVID-19 pandemic. While majority (about 65%) of German population were fully vaccinated, incidence started growing exponentially in October 2021 with about 41% recorded new cases aged twelve or above being symptomatic breakthrough infections, presumably also contributing dynamics. At time, it (i) remains elusive how significant this contribution is and (ii) whether targeted non-pharmaceutical interventions (NPIs) may stop...