Developing measures for rapid and early detection of disease re-emergence is important to perform science-based risk assessment of epidemic threats. In the past few years, several early warning signals (EWS) from complex systems theory have been introduced to detect impending critical transitions and extend the set of indicators. However, it is still debated whether they are generically applicable or potentially sensitive to some dynamical characteristics such as system noise and rates of approach to critical parameter values. Moreover, testing on empirical data has, so far, been limited. Hence, verifying EWS performance remains a challenge. In this study, we tackle this question by analyzing the performance of common EWS, such as increasing variance and autocorrelation, in detecting the emergence of COVID-19 outbreaks in various countries. Our work illustrates that these EWS might be successful in detecting disease emergence when some basic assumptions are satisfied: a slow forcing through the transitions and not-fat-tailed noise. In uncertain cases, we observe that noise properties or commensurable time scales may obscure the expected early warning signals. Overall, our results suggest that EWS can be useful for active monitoring of epidemic dynamics, but that their performance is sensitive to certain features of the underlying dynamics. Our findings thus pave a connection between theoretical and empirical studies, constituting a further step towards the application of EWS indicators for informing public health policies.

Against the COVID-19 pandemic, non-pharmaceutical interventions have been widely applied and vaccinations have taken off. The upcoming question is how the interplay between vaccinations and social measures will shape infections and hospitalizations. Hence, we extend the Susceptible-Exposed-Infectious-Removed (SEIR) model including these elements. We calibrate it to data of Luxembourg, Austria and Sweden until 15 December 2020. Sweden results having the highest fraction of undetected, Luxembourg of infected and all three being far from herd immunity in December. We quantify the level of social interaction, showing that a level around 1/3 of before the pandemic was still required in December to keep the effective reproduction number $R_{\mathit{eff}}\left(t\right)$ below 1, for all three countries. Aiming to vaccinate the whole population within 1 year at constant rate would require on average 1,700 fully vaccinated people/day in Luxembourg, 24,000 in Austria and 28,000 in Sweden, and could lead to herd immunity only by mid summer. Herd immunity might not be reached in 2021 if too slow vaccines rollout speeds are employed. The model thus estimates which vaccination rates are too low to allow reaching herd immunity in 2021, depending on social interactions. Vaccination will considerably, but not immediately, help to curb the infection; thus limiting social interactions remains crucial for the months to come.

Deep brain stimulation (DBS) is a surgical therapy to alleviate symptoms of certain brain disorders by electrically modulating neural tissues. Computational models predicting electric fields and volumes of tissue activated are key for efficient parameter tuning and network analysis. Currently, we lack efficient and flexible software implementations supporting complex electrode geometries and stimulation settings. Available tools are either too slow (e.g. finite element method-FEM), or too simple, with limited applicability to basic use-cases. This paper introduces FastField, an efficient open-source toolbox for DBS electric field and VTA approximations. It computes scalable electric field approximations based on the principle of superposition, and VTA activation models from pulse width and axon diameter. In benchmarks and case studies, FastField is solved in about 0.2 s, ~ 1000 times faster than using FEM. Moreover, it is almost as accurate as using FEM: average Dice overlap of 92%, which is around typical noise levels found in clinical data. Hence, FastField has the potential to foster efficient optimization studies and to support clinical applications.

Models and theories in behaviour change science are not in short supply, but they almost exclusively pertain to a particular facet of behaviour, such as automaticity or reasoned action, or to a single scale of observation such as individuals or communities. We present a highly generalisable conceptual model which is widely used in complex systems research from biology to physics, in an accessible form to behavioural scientists. The proposed model of attractor landscapes can be used to understand human behaviour change on different levels, from individuals to dyads, groups and societies. We use the model as a tool to present neglected ideas in contemporary behaviour change science, such as hysteresis and nonlinearity. The model of attractor landscapes can deepen understanding of well-known features of behaviour change (research), including short-livedness of intervention effects, problematicity of focusing on behavioural initiation while neglecting behavioural maintenance, continuum and stage models of behaviour change understood within a single accommodating framework, and the concept of resilience. We also demonstrate potential methods of analysis and outline avenues for future research.

From the flashing of fireflies to autonomous robot swarms, synchronization phenomena are ubiquitous in nature and technology. They are commonly described by the Kuramoto model that, in this paper, we generalise to networks over n-dimensional spheres. We show that, for almost all initial conditions, the sphere model converges to a set with small diameter if the model parameters satisfy a given bound. Moreover, for even n, a special case of the generalized model can achieve phase synchronization with nonidentical frequency parameters. These results contrast with the standard n = 1 Kuramoto model, which is multistable (i.e., has multiple equilibria), and converges to phase synchronization only if the frequency parameters are identical. Hence, this paper shows that the generalized network Kuramoto models for n ≥ 2 displays more coherent and predictable behavior than the standard n = 1 model, a desirable property both in flocks of animals and for robot control.

Abrupt shifts between alternative regimes occur in complex systems, from cell regulation to brain functions to ecosystems. Several model-free early warning signals (EWS) have been proposed to detect impending transitions, but failure or poor performance in some systems have called for better investigation of their generic applicability. Notably, there are still ongoing debates whether such signals can be successfully extracted from data in particular from biological experiments. In this work, we systematically investigate properties and performance of dynamical EWS in different deteriorating conditions, and we propose an optimized combination to trigger warnings as early as possible, eventually verified on experimental data from microbiological populations. Our results explain discrepancies observed in the literature between warning signs extracted from simulated models and from real data, provide guidance for EWS selection based on desired systems and suggest an optimized composite indicator to alert for impending critical transitions using distribution data.