Inferring country-specific import risk of diseases from the world air transportation network.

Disease propagation between countries strongly depends on their effective distance, a measure derived from the world air transportation network (WAN). It reduces the complex spreading patterns of a pandemic to a wave-like propagation from the outbreak country, establishing a linear relationship to the arrival time of the unmitigated spread of a disease. However, in the early stages of an outbreak, what concerns decision-makers in countries is understanding the relative risk of active cases arriving in their country-essentially, the likelihood that an active case boarding an airplane at the outbreak location will reach them. While there are data-fitted models available to estimate these risks, accurate mechanistic, parameter-free models are still lacking. Therefore, we introduce the 'import risk' model in this study, which defines import probabilities using the effective-distance framework. The model assumes that airline passengers are distributed along the shortest path tree that starts at the outbreak's origin. In combination with a random walk, we account for all possible paths, thus inferring predominant connecting flights. Our model outperforms other mobility models, such as the radiation and gravity model with varying distance types, and it improves further if additional geographic information is included. The import risk model's precision increases for countries with stronger connections within the WAN, and it reveals a geographic distance dependence that implies a pull- rather than a push-dynamic in the distribution process.

Evidence for positive long- and short-term effects of vaccinations against COVID-19 in wearable sensor metrics.

Vaccines are among the most powerful tools to combat the COVID-19 pandemic. They are highly effective against infection and substantially reduce the risk of severe disease, hospitalization, ICU admission, and death. However, their potential for attenuating long-term changes in personal health and health-related wellbeing after a SARS-CoV-2 infection remains a subject of debate. Such effects can be effectively monitored at the individual level by analyzing physiological data collected by consumer-grade wearable sensors. Here, we investigate changes in resting heart rate, daily physical activity, and sleep duration around a SARS-CoV-2 infection stratified by vaccination status. Data were collected over a period of 2 years in the context of the German Corona Data Donation Project with around 190,000 monthly active participants. Compared to their unvaccinated counterparts, we find that vaccinated individuals, on average, experience smaller changes in their vital data that also return to normal levels more quickly. Likewise, extreme changes in vitals during the acute phase of the disease occur less frequently in vaccinated individuals. Our results solidify evidence that vaccines can mitigate long-term detrimental effects of SARS-CoV-2 infections both in terms of duration and magnitude. Furthermore, they demonstrate the value of large-scale, high-resolution wearable sensor data in public health research.

Enhancing global preparedness during an ongoing pandemic from partial and noisy data.

As the coronavirus disease 2019 spread globally, emerging variants such as B.1.1.529 quickly became dominant worldwide. Sustained community transmission favors the proliferation of mutated sub-lineages with pandemic potential, due to cross-national mobility flows, which are responsible for consecutive cases surge worldwide. We show that, in the early stages of an emerging variant, integrating data from national genomic surveillance and global human mobility with large-scale epidemic modeling allows to quantify its pandemic potential, providing quantifiable indicators for pro-active policy interventions. We validate our framework on worldwide spreading variants and gain insights about the pandemic potential of BA.5, BA.2.75, and other sub- and lineages. We combine the different sources of information in a simple estimate of the pandemic delay and show that only in combination, the pandemic potentials of the lineages are correctly assessed relative to each other. Compared to a country-level epidemic intelligence, our scalable integrated approach, that is pandemic intelligence, permits to enhance global preparedness to contrast the pandemic of respiratory pathogens such as SARS-CoV-2.

Modeling the impact of the Omicron infection wave in Germany.

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 of reduced vaccine efficacy (VE) against infections with this variant. The potential threat posed by its rapid spread in Germany was, at the time, difficult to predict. We developed a variant-dependent population-averaged susceptible-exposed-infected-recovered infectious-disease model that included information about variant-specific and waning VEs based on empirical data available at the time. Compared to other approaches, our method aimed for minimal structural and computational complexity and therefore enabled us to respond to changes in the situation in a more agile manner while still being able to analyze the potential influence of (non-)pharmaceutical interventions (NPIs) on the emerging crisis. Thus, the model allowed us to estimate potential courses of upcoming infection waves in Germany, focusing on the corresponding burden on intensive care units (ICUs), the efficacy of contact reduction strategies, and the success of the booster vaccine rollout campaign. We expected a large cumulative number of infections with the VOC Omicron in Germany with ICU occupancy likely remaining below capacity, nevertheless, even without additional NPIs. The projected figures were in line with the actual Omicron waves that were subsequently observed in Germany with respective peaks occurring in mid-February and mid-March. Most surprisingly, our model showed that early, strict, and short contact reductions could have led to a strong 'rebound' effect with high incidences after the end of the respective NPIs, despite a potentially successful booster campaign. The results presented here informed legislation in Germany. The methodology developed in this study might be used to estimate the impact of future waves of COVID-19 or other infectious diseases.

Estimating the share of SARS-CoV-2-immunologically naïve individuals in Germany up to June 2022.

After the winter of 2021/2022, the coronavirus disease 2019 (COVID-19) pandemic had reached a phase where a considerable number of people in Germany have been either infected with a severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variant, vaccinated or both, the full extent of which was difficult to estimate, however, because infection counts suffer from under-reporting, and the overlap between the vaccinated and recovered subpopulations is unknown. Yet, reliable estimates regarding population-wide susceptibility were of considerable interest: Since both previous infection and vaccination reduce the risk of severe disease, a low share of immunologically naïve individuals lowers the probability of further severe outbreaks, given that emerging variants do not escape the acquired susceptibility reduction. Here, we estimate the share of immunologically naïve individuals by age group for each of the sixteen German federal states by integrating an infectious-disease model based on weekly incidences of SARS-CoV-2 infections in the national surveillance system and vaccine uptake, as well as assumptions regarding under-ascertainment. We estimate a median share of 5.6% of individuals in the German population have neither been in contact with vaccine nor any variant up to 31 May 2022 (quartile range [2.5%-8.5%]). For the adult population at higher risk of severe disease, this figure is reduced to 3.8% [1.6%-5.9%] for ages 18-59 and 2.1% [1.0%-3.4%] for ages 60 and above. However, estimates vary between German states mostly due to heterogeneous vaccine uptake. Excluding Omicron infections from the analysis, 16.3% [14.1%-17.9%] of the population in Germany, across all ages, are estimated to be immunologically naïve, highlighting the large impact the first two Omicron waves had until the beginning of summer in 2022. The method developed here might be useful for similar estimations in other countries or future outbreaks of other infectious diseases.

Germany's fourth COVID-19 wave was mainly driven by the unvaccinated.

Background: While the majority of the German population was fully vaccinated at the time (about 65%), COVID-19 incidence started growing exponentially in October 2021 with about 41% of recorded new cases aged twelve or above being symptomatic breakthrough infections, presumably also contributing to the dynamics. So far, it remained elusive how significant this contribution was and whether targeted non-pharmaceutical interventions (NPIs) may have stopped the amplification of the crisis. Methods: We develop and introduce a contribution matrix approach based on the next-generation matrix of a population-structured compartmental infectious disease model to derive contributions of respective inter- and intragroup infection pathways of unvaccinated and vaccinated subpopulations to the effective reproduction number and new infections, considering empirical data of vaccine efficacies against infection and transmission. Results: Here we show that about 61%-76% of all new infections were caused by unvaccinated individuals and only 24%-39% were caused by the vaccinated. Furthermore, 32%-51% of new infections were likely caused by unvaccinated infecting other unvaccinated. Decreasing the transmissibility of the unvaccinated by, e. g. targeted NPIs, causes a steeper decrease in the effective reproduction number R than decreasing the transmissibility of vaccinated individuals, potentially leading to temporary epidemic control. Reducing contacts between vaccinated and unvaccinated individuals serves to decrease R in a similar manner as increasing vaccine uptake. Conclusions: A minority of the German population-the unvaccinated-is assumed to have caused the majority of new infections in the fall of 2021 in Germany. Our results highlight the importance of combined measures, such as vaccination campaigns and targeted contact reductions to achieve temporary epidemic control.

COVID-19 lockdown induces disease-mitigating structural changes in mobility networks.

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

Thresholding normally distributed data creates complex networks.

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 properties are considered typical of complex networks and appear in many contexts, prompting consideration of their universality. Here we introduce a simple model for correlated relational data and study the network ensemble obtained by thresholding it. We find that some, but not all, of the properties associated with complex networks can be seen after thresholding the correlated data, even though the underlying data are not "complex." In particular, we observe heavy-tailed degree distributions, a large numbers of triangles, and short path lengths, while we do not observe nonvanishing clustering or community structure.

Comprehensive integrated NGS-based surveillance and contact-network modeling unravels transmission dynamics of vancomycin-resistant enterococci in a high-risk population within a tertiary care hospital.

Vancomycin-resistant E. faecium (VRE) are an important cause of nosocomial infections, which are 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 of a hemato-oncology unit. Over 1 year, a total of 111 VRE isolates from 111 patients were collected by anal swabs in a tertiary care hospital in Southern Germany. All isolated VRE were whole-genome sequenced, followed by different in-depth bioinformatics analyses including genotyping and determination of phylogenetic relations, aiming to evaluate a standardized workflow. Patient movement data were used to overlay sequencing data to infer transmission events and strain dynamics over time. A predominant clone harboring vanB and exhibiting genotype ST117/CT469 (n = 67) was identified. Our comprehensive combined analyses suggested intra-hospital spread, especially of clone ST117/CT469, despite of extensive screening, single room placement, and contact isolation. A new interactive tool to visualize these complex data was designed. Furthermore, a patient-contact network-modeling approach was developed, which indicates both the periodic import of the clone into the hospital and its spread within the hospital due to patient movements. The analyzed spread of VRE was most likely due to placement of patients in the same room prior to positivity of screening. We successfully demonstrated the added value for this combined strategy to extract well-founded knowledge from interdisciplinary data sources. The combination of patient-contact modeling and high-resolution typing unraveled the transmission dynamics within the hospital department and, additionally, a constant VRE influx over time.

Effective containment explains subexponential growth in recent confirmed COVID-19 cases in China.

The recent outbreak of coronavirus disease 2019 (COVID-19) in mainland China was characterized by a distinctive subexponential increase of confirmed cases during the early phase of the epidemic, contrasting with an initial exponential growth expected for an unconstrained outbreak. We show that this effect can be explained as a direct consequence of containment policies that effectively deplete the susceptible population. To this end, we introduce a parsimonious model that captures both quarantine of symptomatic infected individuals, as well as population-wide isolation practices in response to containment policies or behavioral changes, and show that the model captures the observed growth behavior accurately. The insights provided here may aid the careful implementation of containment strategies for ongoing secondary outbreaks of COVID-19 or similar future outbreaks of other emergent infectious diseases.

Publisher Correction: Generalization of the small-world effect on a model approaching the Erdos-Rényi random graph.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Generalization of the small-world effect on a model approaching the Erdos-Rényi random graph.

The famous Watts-Strogatz (WS) small-world network model does not approach the Erdos-Rényi (ER) random graph model in the limit of total randomization which can lead to confusion and complicates certain analyses. In this paper we discuss a simple alternative which was first introduced by Song and Wang, where instead of rewiring, edges are drawn between pairs of nodes with a distance-based connection probability. We show that this model is simpler to analyze, approaches the true ER random graph model in the completely randomized limit, and demonstrate that the WS model and the alternative model may yield different quantitative results using the example of a random walk temporal observable. An efficient sampling algorithm for the alternative model is proposed. Analytic results regarding the degree distribution, degree variance, number of two-stars per node, number of triangles per node, clustering coefficient, and random walk mixing time are presented. Subsequently, the small-world effect is illustrated by showing that the clustering coefficient decreases much slower than an upper bound on the message delivery time with increasing long-range connection probability which generalizes the small-world effect from informed searches to random search strategies. Due to its accessibility for analytic evaluations, we propose that this modified model should be used as an alternative reference model for studying the influence of small-world topologies on dynamic systems as well as a simple model to introduce numerous topics when teaching network science.

Cover time for random walks on arbitrary complex networks.

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