Detecting critical slowing down in high-dimensional epidemiological systems

Application of early warning signs to physiological contexts: a comparison of multivariate indices in patients on long-term hemodialysis

Early warnings signs (EWSs) can anticipate abrupt changes in system state, known as "critical transitions," by detecting dynamic variations, including increases in variance, autocorrelation (AC), and cross-correlation. Numerous EWSs have been proposed; yet no consensus on which perform best exists. Here, we compared 15 multivariate EWSs in time series of 763 hemodialyzed patients, previously shown to present relevant critical transition dynamics. We calculated five EWSs based on AC, six on variance, one on cross-correlation, and three on AC and variance. We assessed their pairwise correlations, trends before death, and mortality predictive power, alone and in combination. Variance-based EWSs showed stronger correlations (r = 0.663 ± 0.222 vs. 0.170 ± 0.205 for AC-based indices) and a steeper increase before death. Two variance-based EWSs yielded HR95 > 9 (HR95 standing for a scale-invariant metric of hazard ratio), but combining them did not improve the area under the receiver-operating curve (AUC) much compared to using them alone (AUC = 0.798 vs. 0.796 and 0.791). Nevertheless, the AUC reached 0.825 when combining 13 indices. While some indicators did not perform overly well alone, their addition to the best performing EWSs increased the predictive power, suggesting that indices combination captures a broader range of dynamic changes occurring within the system. It is unclear whether this added benefit reflects measurement error of a unified phenomenon or heterogeneity in the nature of signals preceding critical transitions. Finally, the modest predictive performance and weak correlations among some indices call into question their validity, at least in this context.

Spatio-temporal surveillance and early detection of SARS-CoV-2 variants of concern: a retrospective analysis

The SARS-CoV-2 pandemic has been characterized by the repeated emergence of genetically distinct virus variants of increased transmissibility and immune evasion compared to pre-existing lineages. In many countries, their containment required the intervention of public health authorities and the imposition of control measures. While the primary role of testing is to identify infection, target treatment, and limit spread (through isolation and contact tracing), a secondary benefit is in terms of surveillance and the early detection of new variants. Here we study the spatial invasion and early spread of the Alpha, Delta and Omicron (BA.1 and BA.2) variants in England from September 2020 to February 2022 using the random neighbourhood covering (RaNCover) method. This is a statistical technique for the detection of aberrations in spatial point processes, which we tailored here to community PCR (polymerase-chain-reaction) test data where the TaqPath kit provides a proxy measure of the switch between variants. Retrospectively, RaNCover detected the earliest signals associated with the four novel variants that led to large infection waves in England. With suitable data our method therefore has the potential to rapidly detect outbreaks of future SARS-CoV-2 variants, thus helping to inform targeted public health interventions.

The potential of resilience indicators to anticipate infectious disease outbreaks, a systematic review and guide

To reduce the consequences of infectious disease outbreaks, the timely implementation of public health measures is crucial. Currently used early-warning systems are highly context-dependent and require a long phase of model building. A proposed solution to anticipate the onset or termination of an outbreak is the use of so-called resilience indicators. These indicators are based on the generic theory of critical slowing down and require only incidence time series. Here we assess the potential for this approach to contribute to outbreak anticipation. We systematically reviewed studies that used resilience indicators to predict outbreaks or terminations of epidemics. We identified 37 studies meeting the inclusion criteria: 21 using simulated data and 16 real-world data. 36 out of 37 studies detected significant signs of critical slowing down before a critical transition (i.e., the onset or end of an outbreak), with a highly variable sensitivity (i.e., the proportion of true positive outbreak warnings) ranging from 0.03 to 1 and a lead time ranging from 10 days to 68 months. Challenges include low resolution and limited length of time series, a too rapid increase in cases, and strong seasonal patterns which may hamper the sensitivity of resilience indicators. Alternative types of data, such as Google searches or social media data, have the potential to improve predictions in some cases. Resilience indicators may be useful when the risk of disease outbreaks is changing gradually. This may happen, for instance, when pathogens become increasingly adapted to an environment or evolve gradually to escape immunity. High-resolution monitoring is needed to reach sufficient sensitivity. If those conditions are met, resilience indicators could help improve the current practice of prediction, facilitating timely outbreak response. We provide a step-by-step guide on the use of resilience indicators in infectious disease epidemiology, and guidance on the relevant situations to use this approach.

A survey on agents applications in healthcare: Opportunities, challenges and trends

BACKGROUND AND OBJECTIVE

The agent abstraction is a powerful one, developed decades ago to represent crucial aspects of artificial intelligence research. The meaning has transformed over the years and now there are different nuances across research communities. At its core, an agent is an autonomous computational entity capable of sensing, acting, and capturing interactions with other agents and its environment. This review examines how agent-based techniques have been implemented and evaluated in a specific and very important domain, i.e. healthcare research.

METHODS

We survey key areas of agent-based research in healthcare, e.g. individual and collective behaviours, communicable and non-communicable diseases, and social epidemiology. We propose a systematic search and critical review of relevant recent works, introduced by an exploratory network analysis.

RESULTS

Network analysis enables to devise out 5 main research clusters, the most active authors, and 4 main research topics.

CONCLUSIONS

Our findings support discussion of some future directions for increasing the value of agent-based approaches in healthcare.

Exploring the role of the potential surface in the behaviour of early warning signals

The theory of critical slowing down states that a system displays increasing relaxation times as it approaches a critical transition. These changes can be seen in statistics generated from timeseries data, which can be used as early warning signals of a transition. Such early warning signals would be of value for emerging infectious diseases or to understand when an endemic disease is close to elimination. However, in applications to a variety of epidemiological models there is frequent disagreement with the general theory of critical slowing down, with some indicators performing well on prevalence data but not when applied to incidence data. Furthermore, the alternative theory of critical speeding up predicts contradictory behaviour of early warning signals prior to some stochastic transitions. To investigate the possibility of observing critical speeding up in epidemiological models we characterise the behaviour of common early warning signals in terms of a system's potential surface and noise around a quasi-steady state. We then describe a method to obtain these key features from timeseries data, taking as a case study a version of the SIS model, adapted to demonstrate either critical slowing down or critical speeding up. We show this method accurately reproduces the analytic potential surface and diffusion function, and that these results can be used to determine the behaviour of early warning signals and correctly identify signs of both critical slowing down and critical speeding up.

Inferring the effective reproductive number from deterministic and semi-deterministic compartmental models using incidence and mobility data

The effective reproduction number (ℜt) is a theoretical indicator of the course of an infectious disease that allows policymakers to evaluate whether current or previous control efforts have been successful or whether additional interventions are necessary. This metric, however, cannot be directly observed and must be inferred from available data. One approach to obtaining such estimates is fitting compartmental models to incidence data. We can envision these dynamic models as the ensemble of structures that describe the disease’s natural history and individuals’ behavioural patterns. In the context of the response to the COVID-19 pandemic, the assumption of a constant transmission rate is rendered unrealistic, and it is critical to identify a mathematical formulation that accounts for changes in contact patterns. In this work, we leverage existing approaches to propose three complementary formulations that yield similar estimates for ℜt based on data from Ireland’s first COVID-19 wave. We describe these Data Generating Processes (DGP) in terms of State-Space models. Two (DGP1 and DGP2) correspond to stochastic process models whose transmission rate is modelled as Brownian motion processes (Geometric and Cox-Ingersoll-Ross). These DGPs share a measurement model that accounts for incidence and transmission rates, where mobility data is assumed as a proxy of the transmission rate. We perform inference on these structures using Iterated Filtering and the Particle Filter. The final DGP (DGP3) is built from a pool of deterministic models that describe the transmission rate as information delays. We calibrate this pool of models to incidence reports using Hamiltonian Monte Carlo. By following this complementary approach, we assess the tradeoffs associated with each formulation and reflect on the benefits/risks of incorporating proxy data into the inference process. We anticipate this work will help evaluate the implications of choosing a particular formulation for the dynamics and observation of the time-varying transmission rate.

Performance of early warning signals for disease re-emergence: A case study on COVID-19 data

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.

Overlapping timescales obscure early warning signals of the second COVID-19 wave

Early warning indicators based on critical slowing down have been suggested as a model-independent and low-cost tool to anticipate the (re)emergence of infectious diseases. We studied whether such indicators could reliably have anticipated the second COVID-19 wave in European countries. Contrary to theoretical predictions, we found that characteristic early warning indicators generally decreased rather than increased prior to the second wave. A model explains this unexpected finding as a result of transient dynamics and the multiple timescales of relaxation during a non-stationary epidemic. Particularly, if an epidemic that seems initially contained after a first wave does not fully settle to its new quasi-equilibrium prior to changing circumstances or conditions that force a second wave, then indicators will show a decreasing rather than an increasing trend as a result of the persistent transient trajectory of the first wave. Our simulations show that this lack of timescale separation was to be expected during the second European epidemic wave of COVID-19. Overall, our results emphasize that the theory of critical slowing down applies only when the external forcing of the system across a critical point is slow relative to the internal system dynamics.

Application of the method of parallel trajectories on modeling the dynamics of COVID-19 third wave

In this paper, we present a new method for successfully simulating the dynamics of COVID-19, experimentally focusing on the third wave. This method, namely, the Method of Parallel Trajectories (MPT), is based on the recently introduced self-organized diffusion model. According to this method, accurate simulation of the dynamics of the COVID-19 infected population evolution is accomplished by considering not the total data for the infected population, but successive segments of it. By changing the initial conditions with which each segment of the simulation is produced, we achieve close and detailed monitoring of the evolution of the pandemic, providing a tool for evaluating the overall situation and the fine-tuning of the restrictive measures. Finally, the application of the proposed MPT on simulating the pandemic's third wave dynamics in Greece and Italy is presented, verifying the method's effectiveness.

Eco-epidemiological scaling of Leptospirosis: Vulnerability mapping and early warning forecasts

Infectious disease epidemics are plaguing the world and a lot of research is focused on the development of models to reproduce disease dynamics for eco-environmental and biological investigation, and disease management. Leptospirosis is an example of a neglected zoonosis strongly mediated by ecohydrological dynamics with emerging endemic and epidemic patterns worldwide in both animal and human populations. By accounting for large heterogeneities of affected areas we show how exponential endemics and scale-free epidemics are largely predictable and linked to common socio-environmental features via scaling laws with different exponents that inform about vulnerability factors. This led to the development of a novel pattern-oriented integrated model that can be used as an early-warning signal (EWS) tool for endemic-epidemic regime classification, risk determinant attribution, and near real-time forecast of outbreaks. Forecasts are grounded on expected outbreak recurrence time dependent on exceedance probabilities and statistical EWS that sense outbreak onset. A stochastic spatially-explicit model is shown to comprehensively predict outbreak dynamics (early sensing, timing, magnitude, decay, and eco-environmental determinants) and derive a spreading factor characterizing endemics and epidemics, where average over maximum rainfall is the critical factor characterizing disease transitions. Dynamically, case cross-correlation considering neighboring communities senses 2-weeks in advance outbreaks. Eco-environmental scaling relationships highlight how predicted host suitability and topographic index can be used as epidemiological footprints to effectively distinguish and control Leptospirosis regimes and areas dependent on hydro-climatological dynamics as the main trigger. The spatio-temporal scale-invariance of epidemics - underpinning persistent criticality and neutrality or independence among areas - is emphasized by the high accuracy in reproducing sequence and magnitude of cases via reliable surveillance. Further investigations of robustness and universality of eco-environmental determinants are required; nonetheless a comprehensive and computationally simple EWS method for the full characterization of Leptospirosis is provided. The tool is extendable to other climate-sensitive zoonoses to define vulnerability factors and predict outbreaks useful for optimal disease risk prevention and control.

Early warning signal reliability varies with COVID-19 waves

Early warning signals (EWSs) aim to predict changes in complex systems from phenomenological signals in time series data. These signals have recently been shown to precede the emergence of disease outbreaks, offering hope that policymakers can make predictive rather than reactive management decisions. Here, using a novel, sequential analysis in combination with daily COVID-19 case data across 24 countries, we suggest that composite EWSs consisting of variance, autocorrelation and skewness can predict nonlinear case increases, but that the predictive ability of these tools varies between waves based upon the degree of critical slowing down present. Our work suggests that in highly monitored disease time series such as COVID-19, EWSs offer the opportunity for policymakers to improve the accuracy of urgent intervention decisions but best characterize hypothesized critical transitions.

Early warning signals of infectious disease transitions: a review

Early warning signals (EWSs) are a group of statistical time-series signals which could be used to anticipate a critical transition before it is reached. EWSs are model-independent methods that have grown in popularity to support evidence of disease emergence and disease elimination. Theoretical work has demonstrated their capability of detecting disease transitions in simple epidemic models, where elimination is reached through vaccination, to more complex vector transmission, age-structured and metapopulation models. However, the exact time evolution of EWSs depends on the transition; here we review the literature to provide guidance on what trends to expect and when. Recent advances include methods which detect when an EWS becomes significant; the earlier an upcoming disease transition is detected, the more valuable an EWS will be in practice. We suggest that future work should firstly validate detection methods with synthetic and historical datasets, before addressing their performance with real-time data which is accruing. A major challenge to overcome for the use of EWSs with disease transitions is to maintain the accuracy of EWSs in data-poor settings. We demonstrate how EWSs behave on reported cases for pertussis in the USA, to highlight some limitations when detecting disease transitions with real-world data.

Self-driven criticality in a stochastic epidemic model

We present a generic epidemic model with stochastic parameters in which the dynamics self-organize to a critical state with suppressed exponential growth. More precisely, the dynamics evolve into a quasi-steady state, where the effective reproduction rate fluctuates close to the critical value 1 for a long period, as indeed observed for different epidemics. The main assumptions underlying the model are that the rate at which each individual becomes infected changes stochastically in time with a heavy-tailed steady state. The critical regime is characterized by an extremely long duration of the epidemic. Its stability is analyzed both numerically and analytically in different models.

Criticality in epidemic spread: An application in the case of COVID19 infected population

Recently, it has been successfully shown that the temporal evolution of the fraction of COVID-19 infected people possesses the same dynamics as the ones demonstrated by a self-organizing diffusion model over a lattice, in the frame of universality. In this brief, the relevant emerging dynamics are further investigated. Evidence that this nonlinear model demonstrates critical dynamics is scrutinized within the frame of the physics of critical phenomena. Additionally, the concept of criticality over the infected population fraction in epidemics (or a pandemic) is introduced and its importance is discussed, highlighting the emergence of the critical slowdown phenomenon. A simple method is proposed for estimating how far away a population is from this "singular" state, by utilizing the theory of critical phenomena. Finally, a dynamic approach applying the self-organized diffusion model is proposed, resulting in more accurate simulations, which can verify the effectiveness of restrictive measures. All the above are supported by real epidemic data case studies.

Detecting Early-Warning Signals in Time Series of Visits to Points of Interest to Examine Population Response to COVID-19 Pandemic

The objective of this paper is to examine population response to COVID-19 and associated policy interventions through detecting early-warning signals in time series of visits to points of interest (POIs). Complex systems, such as cities, would demonstrate early-warning signals (e.g., increased autocorrelation and standard deviation) when they approach phase transitions responding to external perturbation, such as crises, policy changes, and human behavior changes. In urban systems, population visits to POIs, such as restaurants, museums, and hospitals, represent a state of cities as complex systems. These states may undergo phase transitions due to population response to pandemic risks and intervention policies (e.g., social distancing and shelter-in-place orders). In this study, we conducted early-warning signal detection on population visits to POIs to examine population response to pandemic risks, and we evaluated time lags between detected early-warning dates and dates of first cases and policy interventions. We examined two early-warning signals, the increase of autocorrelation at-lag-1 and standard deviation, in time series of population visits to POIs in 17 metropolitan cities in the United States of America. We examined visits to grouped POIs according to two categories of essential services and non-essential services. The results show that: (1) early-warning signals for population response to COVID-19 were detected between February 14 and March 11, 2020 in 17 cities; (2) detected population response had started prior to shelter-in-place orders in 17 cities; (3) early-warning signals detected from the essential POIs visits appeared earlier than those from non-essential POIs; and 4) longer time lags between detected population response and shelter-in-place orders led to a less decrease in POI visits. The results show the importance of detecting early-warning signals during crises in cities as complex systems. Early-warning signals could provide important insights regarding the timing and extent of population response to crises to inform policymakers.

Active probing to highlight approaching transitions to ictal states in coupled neural mass models

The extraction of electrophysiological features that reliably forecast the occurrence of seizures is one of the most challenging goals in epilepsy research. Among possible approaches to tackle this problem is the use of active probing paradigms in which responses to stimuli are used to detect underlying system changes leading up to seizures. This work evaluates the theoretical and mechanistic underpinnings of this strategy using two coupled populations of the well-studied Wendling neural mass model. Different model settings are evaluated, shifting parameters (excitability, slow inhibition, or inter-population coupling gains) from normal towards ictal states while probing stimuli are applied every 2 seconds to the input of either one or both populations. The correlation between the extracted features and the ictogenic parameter shifting indicates if the impending transition to the ictal state may be identified in advance. Results show that not only can the response to the probing stimuli forecast seizures but this is true regardless of the altered ictogenic parameter. That is, similar feature changes are highlighted by probing stimuli responses in advance of the seizure including: increased response variance and lag-1 autocorrelation, decreased skewness, and increased mutual information between the outputs of both model subsets. These changes were mostly restricted to the stimulated population, showing a local effect of this perturbational approach. The transition latencies from normal activity to sustained discharges of spikes were not affected, suggesting that stimuli had no pro-ictal effects. However, stimuli were found to elicit interictal-like spikes just before the transition to the ictal state. Furthermore, the observed feature changes highlighted by probing the neuronal populations may reflect the phenomenon of critical slowing down, where increased recovery times from perturbations may signal the loss of a systems' resilience and are common hallmarks of an impending critical transition. These results provide more evidence that active probing approaches highlight information about underlying system changes involved in ictogenesis and may be able to play a role in assisting seizure forecasting methods which can be incorporated into early-warning systems that ultimately enable closing the loop for targeted seizure-controlling interventions.

Hanias M, Kampitakis M, Papadopoulos P, Picos R, M. Potirakis S. A Universal Physics-Based Model Describing COVID-19 Dynamics in Europe

The self-organizing mechanism is a universal approach that is widely followed in nature. In this work, a novel self-organizing model describing diffusion over a lattice is introduced. Simulation results for the model's active lattice sites demonstrate an evolution curve that is very close to those describing the evolution of infected European populations by COVID-19. The model was further examined against real data regarding the COVID-19 epidemic for seven European countries (with a total population of 290 million) during the periods in which social distancing measures were imposed, namely Italy and Spain, which had an enormous spread of the disease; the successful case of Greece; and four central European countries: France, Belgium, Germany and the Netherlands. The value of the proposed model lies in its simplicity and in the fact that it is based on a universal natural mechanism, which through the presentation of an equivalent dynamical system apparently documents and provides a better understanding of the dynamical process behind viral epidemic spreads in general-even pandemics, such as in the case of COVID-19-further allowing us to come closer to controlling such situations. Finally, this model allowed the study of dynamical characteristics such as the memory effect, through the autocorrelation function, in the studied epidemiological dynamical systems.

Anticipating the Novel Coronavirus Disease (COVID-19) Pandemic

The COVID-19 outbreak was first declared an international public health, and it was later deemed a pandemic. In most countries, the COVID-19 incidence curve rises sharply over a short period of time, suggesting a transition from a disease-free (or low-burden disease) equilibrium state to a sustained infected (or high-burden disease) state. Such a transition is often known to exhibit characteristics of "critical slowing down." Critical slowing down can be, in general, successfully detected using many statistical measures, such as variance, lag-1 autocorrelation, density ratio, and skewness. Here, we report an empirical test of this phenomena on the COVID-19 datasets of nine countries, including India, China, and the United States. For most of the datasets, increases in variance and autocorrelation predict the onset of a critical transition. Our analysis suggests two key features in predicting the COVID-19 incidence curve for a specific country: (a) the timing of strict social distancing and/or lockdown interventions implemented and (b) the fraction of a nation's population being affected by COVID-19 at that time. Furthermore, using satellite data of nitrogen dioxide as an indicator of lockdown efficacy, we found that countries where lockdown was implemented early and firmly have been successful in reducing COVID-19 spread. These results are essential for designing effective strategies to control the spread/resurgence of infectious pandemics.