A Dynamic Network Model of Societal Complexity and Resilience Inspired by Tainter's Theory of Collapse.

In recent years, several global events have severely disrupted economies and social structures, undermining confidence in the resilience of modern societies. Examples include the COVID-19 pandemic, which brought unprecedented health challenges and economic disruptions, and the emergence of geopolitical tensions and conflicts that have further strained international relations and economic stability. While empirical evidence on the dynamics and drivers of past societal collapse is mounting, a process-based understanding of these dynamics is still in its infancy. Here, we aim to identify and illustrate the underlying drivers of such societal instability or even collapse. The inspiration for this work is Joseph Tainter's theory of the "collapse of complex societies", which postulates that the complexity of societies increases as they solve problems, leading to diminishing returns on complexity investments and ultimately to collapse. In this work, we abstract this theory into a low-dimensional and stylized model of two classes of networked agents, hereafter referred to as "laborers" and "administrators". We numerically model the dynamics of societal complexity, measured as the fraction of "administrators", which was assumed to affect the productivity of connected energy-producing "laborers". We show that collapse becomes increasingly likely as the complexity of the model society continuously increases in response to external stresses that emulate Tainter's abstract notion of problems that societies must solve. We also provide an analytical approximation of the system's dominant dynamics, which matches well with the numerical experiments, and use it to study the influence on network link density, social mobility and productivity. Our work advances the understanding of social-ecological collapse and illustrates its potentially direct link to an ever-increasing societal complexity in response to external shocks or stresses via a self-reinforcing feedback.

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.

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.

Situational pathogen avoidance mediates the impact of social connectedness on preventive measures during the COVID-19 pandemic.

During the COVID-19 pandemic, physical distancing was one of the more important behaviours for reducing the spread of the virus. The present study investigated the influence on pathogen avoidance of familiarity with other people at private gatherings. Based on the social identity model of risk taking and the theory of the behavioural immune system, we assumed that greater familiarity with others would make people feel more connected with one another and decrease situational pathogen avoidance. This could result in lower perceptions of the risk of contracting COVID-19 and fewer protective behaviours. Two experiments (n1 = 1022, n2 = 994) showed that the negative influence of greater familiarity on the perceived risk of infection and protective behaviour is explained by an increased feeling of connectedness and less feeling of situational pathogen avoidance. In an additional survey, the participants (n = 23,023) rated the quality of their past social contacts. The correlational analyses showed that the familiarity of the other person was more important in explaining variance in protective behaviours than attitudes toward those behaviours or the pandemic situation itself. Understanding the process that result in an explosive increase in infection after social gatherings can improve infection control in the future.

Prevalence of Positive COVID-19 Test Results Collected by Digital Self-report in the US and Germany.

This cohort study examines traditional surveillance and self-reported COVID-19 test result data collected from independent smartphone app­based studies in the US and Germany.

From delta to omicron: The role of individual factors and social context in self-reported compliance with pandemic regulations and recommendations.

As SARS-CoV-2 spreads especially when larger groups gather (e.g., at the workplace), it is crucial to understand compliance with regulations and recommendations in such settings. Using data from adults in Germany (N = 29,355) assessed between October 2021 and February 2022, we investigated factors associated with self-reported compliance in both private and working life and how these relate to each other. The results indicate that private compliance was stronger among older individuals and females; among those who worried more about the pandemic situation and assumed that infection was more severe; among those who trusted the government more; and among those who did not perceive public health measures as exaggerated. Private compliance was also associated with personality traits; in particular, individuals who followed regulations and recommendations were likely to be more introverted, conscientious, open, and agreeable. Compliance at work related to both private compliance and colleagues' behaviors. Individuals whose private compliance was high also complied at work. However, when private compliance was low, compliance at work aligned with colleagues' behaviors; that is, compliance at work was high when colleagues complied and low when they did not. The observed effects were stable over time. In summary, they suggest that compliance with regulations and recommendations depends on individual risk perception, trust in government, perception of required or recommended measures, and social norms. To promote protective behaviors in contexts where larger groups gather (including workplaces), making positive social norms more salient (e.g., by supporting role models) may prove especially useful.

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.

Dose-response functions and surrogate models for exploring social contagion in the Copenhagen Networks Study.

Spreading dynamics and complex contagion processes on networks are important mechanisms underlying the emergence of critical transitions, tipping points and other non-linear phenomena in complex human and natural systems. Increasing amounts of temporal network data are now becoming available to study such spreading processes of behaviours, opinions, ideas, diseases and innovations to test hypotheses regarding their specific properties. To this end, we here present a methodology based on dose-response functions and hypothesis testing using surrogate data models that randomise most aspects of the empirical data while conserving certain structures relevant to contagion, group or homophily dynamics. We demonstrate this methodology for synthetic temporal network data of spreading processes generated by the adaptive voter model. Furthermore, we apply it to empirical temporal network data from the Copenhagen Networks Study. This data set provides a physically-close-contact network between several hundreds of university students participating in the study over the course of 3 months. We study the potential spreading dynamics of the health-related behaviour "regularly going to the fitness studio" on this network. Based on a hierarchy of surrogate data models, we find that our method neither provides significant evidence for an influence of a dose-response-type network spreading process in this data set, nor significant evidence for homophily. The empirical dynamics in exercise behaviour are likely better described by individual features such as the disposition towards the behaviour, and the persistence to maintain it, as well as external influences affecting the whole group, and the non-trivial network structure. The proposed methodology is generic and promising also for applications to other temporal network data sets and traits of interest.

A network-based microfoundation of Granovetter's threshold model for social tipping.

Social tipping, where minorities trigger larger populations to engage in collective action, has been suggested as one key aspect in addressing contemporary global challenges. Here, we refine Granovetter's widely acknowledged theoretical threshold model of collective behavior as a numerical modelling tool for understanding social tipping processes and resolve issues that so far have hindered such applications. Based on real-world observations and social movement theory, we group the population into certain or potential actors, such that - in contrast to its original formulation - the model predicts non-trivial final shares of acting individuals. Then, we use a network cascade model to explain and analytically derive that previously hypothesized broad threshold distributions emerge if individuals become active via social interaction. Thus, through intuitive parameters and low dimensionality our refined model is adaptable to explain the likelihood of engaging in collective behavior where social-tipping-like processes emerge as saddle-node bifurcations and hysteresis.

Mapping and discrimination of networks in the complexity-entropy plane.

Complex networks are usually characterized in terms of their topological, spatial, or information-theoretic properties and combinations of the associated metrics are used to discriminate networks into different classes or categories. However, even with the present variety of characteristics at hand it still remains a subject of current research to appropriately quantify a network's complexity and correspondingly discriminate between different types of complex networks, like infrastructure or social networks, on such a basis. Here we explore the possibility to classify complex networks by means of a statistical complexity measure that has formerly been successfully applied to distinguish different types of chaotic and stochastic time series. It is composed of a network's averaged per-node entropic measure characterizing the network's information content and the associated Jenson-Shannon divergence as a measure of disequilibrium. We study 29 real-world networks and show that networks of the same category tend to cluster in distinct areas of the resulting complexity-entropy plane. We demonstrate that within our framework, connectome networks exhibit among the highest complexity while, e.g., transportation and infrastructure networks display significantly lower values. Furthermore, we demonstrate the utility of our framework by applying it to families of random scale-free and Watts-Strogatz model networks. We then show in a second application that the proposed framework is useful to objectively construct threshold-based networks, such as functional climate networks or recurrence networks, by choosing the threshold such that the statistical network complexity is maximized.

Zealotry effects on opinion dynamics in the adaptive voter model.

The adaptive voter model has been widely studied as a conceptual model for opinion formation processes on time-evolving social networks. Past studies on the effect of zealots, i.e., nodes aiming to spread their fixed opinion throughout the system, only considered the voter model on a static network. Here we extend the study of zealotry to the case of an adaptive network topology co-evolving with the state of the nodes and investigate opinion spreading induced by zealots depending on their initial density and connectedness. Numerical simulations reveal that below the fragmentation threshold a low density of zealots is sufficient to spread their opinion to the whole network. Beyond the transition point, zealots must exhibit an increased degree as compared to ordinary nodes for an efficient spreading of their opinion. We verify the numerical findings using a mean-field approximation of the model yielding a low-dimensional set of coupled ordinary differential equations. Our results imply that the spreading of the zealots' opinion in the adaptive voter model is strongly dependent on the link rewiring probability and the average degree of normal nodes in comparison with that of the zealots. In order to avoid a complete dominance of the zealots' opinion, there are two possible strategies for the remaining nodes: adjusting the probability of rewiring and/or the number of connections with other nodes, respectively.

Spatial network surrogates for disentangling complex system structure from spatial embedding of nodes.

Networks with nodes embedded in a metric space have gained increasing interest in recent years. The effects of spatial embedding on the networks' structural characteristics, however, are rarely taken into account when studying their macroscopic properties. Here, we propose a hierarchy of null models to generate random surrogates from a given spatially embedded network that can preserve certain global and local statistics associated with the nodes' embedding in a metric space. Comparing the original network's and the resulting surrogates' global characteristics allows one to quantify to what extent these characteristics are already predetermined by the spatial embedding of the nodes and links. We apply our framework to various real-world spatial networks and show that the proposed models capture macroscopic properties of the networks under study much better than standard random network models that do not account for the nodes' spatial embedding. Depending on the actual performance of the proposed null models, the networks are categorized into different classes. Since many real-world complex networks are in fact spatial networks, the proposed approach is relevant for disentangling the underlying complex system structure from spatial embedding of nodes in many fields, ranging from social systems over infrastructure and neurophysiology to climatology.

Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package.

We introduce the pyunicorn (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. pyunicorn is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics, or network surrogates. Additionally, pyunicorn provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis, recurrence networks, visibility graphs, and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology.

Macroscopic description of complex adaptive networks coevolving with dynamic node states.

In many real-world complex systems, the time evolution of the network's structure and the dynamic state of its nodes are closely entangled. Here we study opinion formation and imitation on an adaptive complex network which is dependent on the individual dynamic state of each node and vice versa to model the coevolution of renewable resources with the dynamics of harvesting agents on a social network. The adaptive voter model is coupled to a set of identical logistic growth models and we mainly find that, in such systems, the rate of interactions between nodes as well as the adaptive rewiring probability are crucial parameters for controlling the sustainability of the system's equilibrium state. We derive a macroscopic description of the system in terms of ordinary differential equations which provides a general framework to model and quantify the influence of single node dynamics on the macroscopic state of the network. The thus obtained framework is applicable to many fields of study, such as epidemic spreading, opinion formation, or socioecological modeling.