Estimating emergency department crowding with stochastic population models.

Environments such as shopping malls, airports, or hospital emergency-departments often experience crowding, with many people simultaneously requesting service. Crowding highly fluctuates, with sudden overcrowding "spikes". Past research has either focused on average behavior, used context-specific models with a large number of parameters, or machine-learning models that are hard to interpret. Here we show that a stochastic population model, previously applied to a broad range of natural phenomena, can aptly describe hospital emergency-department crowding. We test the model using data from five-year minute-by-minute emergency-department records. The model provides reliable forecasting of the crowding distribution. Overcrowding is highly sensitive to the patient arrival-flux and length-of-stay: a 10% increase in arrivals triples the probability of overcrowding events. Expediting patient exit-rate to shorten the typical length-of-stay by just 20 minutes (8.5%) cuts the probability of severe overcrowding events by 50%. Such forecasting is critical in prevention and mitigation of breakdown events. Our results demonstrate that despite its high volatility, crowding follows a dynamic behavior common to many systems in nature.

Hair tourniquet syndrome: A retrospective study.

OBJECTIVE: Hair thread tourniquet syndrome (HTS) is a pediatric condition in which human hair or synthetic fiber encircles and strangulates a body appendage causing tissue necrosis. Few epidemiologic studies have been done. Our objective was to better define the demographics, clinical features, and predisposing factors for this condition. MATERIALS AND METHODS: Medical records of all infants up to 1 year old seen in the orthopedic emergency department of Galilee Medical Center were searched for the diagnosis of HTS or its ICD equivalent. RESULTS: Forty-one cases of hair tourniquet syndrome (HTS) were reviewed. Most cases (68%) occurred during the winter months (December to February). There were no reports between June to August (summer). The median age was 4 months and the male-to-female ratio was approximately 2:5. Toes were significantly more involved than fingers (97.5%) and the 3rd toe was the most affected (58%). Nine patients (21.9%) had more than one toe affected and only one case reported finger involvement. CONCLUSIONS: HTS in our population is a phenomenon that seems to occur mostly in winter. Infants between 3 and 5 months are at greater risk. Toes are more affected than fingers. The most involved toes are the 3rd and 4th.

Fluctuations and first-passage properties of systems of Brownian particles with reset.

We study, analytically and numerically, stationary fluctuations in two models involving N Brownian particles undergoing stochastic resetting in one dimension. We start with the well-known reset model where the particles reset to the origin independently (model A). Then we introduce nonlocal interparticle correlations by postulating that only the particle farthest from the origin can be reset to the origin (model B). At long times, models A and B approach nonequilibrium steady states. In the limit of N→∞, the steady-state particle density in model A has an infinite support, whereas in model B, it has a compact support, like the recently studied Brownian bees model. A finite system radius, which scales at large N as lnN, appears in model A when N is finite. In both models, we study stationary fluctuations of the center of mass of the system and of the radius of the system due to the random character of the Brownian motion and of the resetting events. In model A, we determine exact distributions of these two quantities. The variance of the center of mass for both models scales as 1/N. The variance of the radius is independent of N in model A and exhibits an unusual scaling (lnN)/N in model B. The latter scaling is intimately related to the 1/f noise in the radius autocorrelation. Finally, we evaluate the mean first-passage time (MFPT) to a distant target in model A, model B, and the Brownian bees model. For model A, we obtain an exact asymptotic expression for the MFPT which scales as 1/N. For model B and the Brownian bees model, we propose a sharp upper bound for the MFPT. The bound assumes an evaporation scenario, where the first passage requires multiple attempts of a single particle, which breaks away from the rest of the particles, to reach the target. The resulting MFPT for model B and the Brownian bees model scales exponentially with sqrt[N]. We verify this bound by performing highly efficient weighted-ensemble simulations of the first passage in model B.

Phase Transition in a Non-Markovian Animal Exploration Model with Preferential Returns.

We study a non-Markovian and nonstationary model of animal mobility incorporating both exploration and memory in the form of preferential returns. Exact results for the probability of visiting a given number of sites are derived and a practical WKB approximation to treat the nonstationary problem is developed. A mean-field version of this model, first suggested by Song et al., [Modelling the scaling properties of human mobility, Nat. Phys. 6, 818 (2010)NPAHAX1745-247310.1038/nphys1760] was shown to well describe human movement data. We show that our generalized model adequately describes empirical movement data of Egyptian fruit bats (Rousettus aegyptiacus) when accounting for interindividual variation in the population. We also study the probability of visiting any site a given number of times and derive a mean-field equation. Our analysis yields a remarkable phase transition occurring at preferential returns which scale linearly with past visits. Following empirical evidence, we suggest that this phase transition reflects a trade-off between extensive and intensive foraging modes.

Outbreak Size Distribution in Stochastic Epidemic Models.

Motivated by recent epidemic outbreaks, including those of COVID-19, we solve the canonical problem of calculating the dynamics and likelihood of extensive outbreaks in a population within a large class of stochastic epidemic models with demographic noise, including the susceptible-infected-recovered (SIR) model and its general extensions. In the limit of large populations, we compute the probability distribution for all extensive outbreaks, including those that entail unusually large or small (extreme) proportions of the population infected. Our approach reveals that, unlike other well-known examples of rare events occurring in discrete-state stochastic systems, the statistics of extreme outbreaks emanate from a full continuum of Hamiltonian paths, each satisfying unique boundary conditions with a conserved probability flux.

Big-data approaches lead to an increased understanding of the ecology of animal movement.

Understanding animal movement is essential to elucidate how animals interact, survive, and thrive in a changing world. Recent technological advances in data collection and management have transformed our understanding of animal "movement ecology" (the integrated study of organismal movement), creating a big-data discipline that benefits from rapid, cost-effective generation of large amounts of data on movements of animals in the wild. These high-throughput wildlife tracking systems now allow more thorough investigation of variation among individuals and species across space and time, the nature of biological interactions, and behavioral responses to the environment. Movement ecology is rapidly expanding scientific frontiers through large interdisciplinary and collaborative frameworks, providing improved opportunities for conservation and insights into the movements of wild animals, and their causes and consequences.

Susceptible-infected-susceptible model of disease extinction on heterogeneous directed population networks.

Understanding the spread of diseases through complex networks is of great interest where realistic, heterogeneous contact patterns play a crucial role in the spread. Most works have focused on mean-field behavior-quantifying how contact patterns affect the emergence and stability of (meta)stable endemic states in networks. On the other hand, much less is known about longer time scale dynamics, such as disease extinction, whereby inherent process stochasticity and contact heterogeneity interact to produce large fluctuations that result in the spontaneous clearance of infection. Here we show that heterogeneity in both susceptibility and infectiousness (incoming and outgoing degree, respectively) has a nontrivial effect on extinction in directed contact networks, both speeding up and slowing down extinction rates depending on the relative proportion of such edges in a network, and on whether the heterogeneities in the incoming and outgoing degrees are correlated or anticorrelated. In particular, we show that weak anticorrelated heterogeneity can increase the disease stability, whereas strong heterogeneity gives rise to markedly different results for correlated and anticorrelated heterogeneous networks. All analytical results are corroborated through various numerical schemes including network Monte Carlo simulations.

[HAIR TOURNIQUET SYNDROME - A DISCREPANCY BETWEEN INCIDENCE AND DOCUMENTATION AND A DISCREPANCY BETWEEN COMMON TERMINOLOGY AND THE ICD].

INTRODUCTION: Hair tourniquet syndrome, AKA hair thread tourniquet or hair strangulation occurs among infants. A human hair or a thread strangulates a body appendage, resulting in obstruction of blood and lymph flow. If not recognized early it may cause tissue necrosis and rarely, require amputation. AIMS: Revealing the discrepancy between incidence and documentation in practice. Understanding the challenges standing in the way of the clinician while admitting a patient. METHODS: A retrospective study. The hospital's archive was searched for the period between the years 2008 to 2018. According to the ICD9 system this phenomenon is termed "external constriction caused by hair". Upon questioning, doctors had admitted having trouble finding the right diagnosis while digitally documenting a patient. The archive was searched twice - firstly, by the correct ICD9 code. Secondly, a general search was performed reviewing all 0-1 year-old patients' files. RESULTS: By researching the ICD9 code, 7 files were found. On the second search, 41 files were found, among them only 5 files were documented properly according to the ICD9 system. CONCLUSIONS: The majority (87.8%) of patients suffered from hair strangulation syndrome were not documented properly. Lack of documentation is a result of the digital difficulty finding the right diagnosis. DISCUSSION: Hair strangulation syndrome is not as rare as may be concluded basing on existing data. Clinicians must include it in the differential diagnosis when admitting a patient with the relevant symptoms or an agitated infant with no clear cause. Adjusting the digital systems in Israeli hospitals should be considered.

Reconstructing an epigenetic landscape using a genetic pulling approach.

Cells use genetic switches to shift between alternate stable gene expression states, e.g., to adapt to new environments or to follow a developmental pathway. Conceptually, these stable phenotypes can be considered as attractive states on an epigenetic landscape with phenotypic changes being transitions between states. Measuring these transitions is challenging because they are both very rare in the absence of appropriate signals and very fast. As such, it has proved difficult to experimentally map the epigenetic landscapes that are widely believed to underly developmental networks. Here, we introduce a nonequilibrium perturbation method to help reconstruct a regulatory network's epigenetic landscape. We derive the mathematical theory needed and then use the method on simulated data to reconstruct the landscapes. Our results show that with a relatively small number of perturbation experiments it is possible to recover an accurate representation of the true epigenetic landscape. We propose that our theory provides a general method by which epigenetic landscapes can be studied. Finally, our theory suggests that the total perturbation impulse required to induce a switch between metastable states is a fundamental quantity in developmental dynamics.

Population Dynamics in a Changing Environment: Random versus Periodic Switching.

Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment modeled by a carrying capacity switching either randomly or periodically between states of abundance and scarcity. The population dynamics is characterized by demographic noise (birth and death events) coupled to a varying environment. We elucidate the similarities and differences of the evolution subject to a stochastically and periodically varying environment. Importantly, the population size distribution is generally found to be broader under intermediate and fast random switching than under periodic variations, which results in markedly different asymptotic behaviors between the fixation probability of random and periodic switching. We also determine the detailed conditions under which the fixation probability of the slow strain is maximal.

Population switching under a time-varying environment.

We study the switching dynamics of a stochastic population subjected to a deterministically time-varying environment. Our approach is demonstrated on a problem of population establishment, which is important in ecology. At the deterministic level, the model we study gives rise to a critical population size beyond which the system experiences establishment. Notably the latter has been shown to be strongly influenced by the interplay between demographic and environmental variations. Here we consider two prototypical examples of a time-varying environment: a temporary change in the environment, and a periodically varying environment. By employing a semiclassical approximation we compute, within exponential accuracy, the change in the establishment probability and mean establishment time of the population, due to the environmental variability. Our analytical results are verified by using a modified Gillespie algorithm which accounts for explicitly time-dependent reaction rates. Importantly, our theoretical approach can also be useful in studying switching dynamics in gene regulatory networks under external variations.

Extinction risk of a metapopulation under bistable local dynamics.

We study the extinction risk of a fragmented population residing on a network of patches coupled by migration, where the local patch dynamics includes deterministic bistability. Mixing between patches is shown to dramatically influence the population's viability. We demonstrate that slow migration always increases the population's global extinction risk compared to the isolated case, while at fast migration synchrony between patches minimizes the population's extinction risk. Moreover, we discover a critical migration rate that maximizes the extinction risk of the population, and identify an early-warning signal when approaching this state. Our theoretical results are confirmed via the highly efficient weighted ensemble method. Notably, our theoretical formalism can also be applied to studying switching in gene regulatory networks with multiple transcriptional states.

Degree Dispersion Increases the Rate of Rare Events in Population Networks.

There is great interest in predicting rare and extreme events in complex systems, and in particular, understanding the role of network topology in facilitating such events. In this Letter, we show that degree dispersion-the fact that the number of local connections in networks varies broadly-increases the probability of large, rare fluctuations in population networks generically. We perform explicit calculations for two canonical and distinct classes of rare events: network extinction and switching. When the distance to threshold is held constant, and hence stochastic effects are fairly compared among networks, we show that there is a universal, exponential increase in the rate of rare events proportional to the variance of a network's degree distribution over its mean squared.

Demographic stochasticity and extinction in populations with Allee effect.

We study simple stochastic scenarios, based on birth-and-death Markovian processes, that describe populations with the Allee effect, to account for the role of demographic stochasticity. In the mean-field deterministic limit we recover well-known deterministic evolution equations widely employed in population ecology. The mean time to extinction is in general obtained by the Wentzel-Kramers-Brillouin (WKB) approximation for populations with the strong and weak Allee effects. An exact solution for the mean time to extinction can be found via a recursive equation for special cases of the stochastic dynamics. We study the conditions for the validity of the WKB solution and analyze the boundary between the weak and strong Allee effect by comparing exact solutions with numerical simulations.

Population extinction under bursty reproduction in a time-modulated environment.

In recent years nondemographic variability has been shown to greatly affect dynamics of stochastic populations. For example, nondemographic noise in the form of a bursty reproduction process with an a priori unknown burst size, or environmental variability in the form of time-varying reaction rates, have been separately found to dramatically impact the extinction risk of isolated populations. In this work we investigate the extinction risk of an isolated population under the combined influence of these two types of nondemographic variation. Using the so-called momentum-space Wentzel-Kramers-Brillouin (WKB) approach and accounting for the explicit time dependence in the reaction rates, we arrive at a set of time-dependent Hamilton equations. To this end, we evaluate the population's extinction risk by finding the instanton of the time-perturbed Hamiltonian numerically, whereas analytical expressions are presented in particular limits using various perturbation techniques. We focus on two classes of time-varying environments: periodically varying rates corresponding to seasonal effects and a sudden decrease in the birth rate corresponding to a catastrophe. All our theoretical results are tested against numerical Monte Carlo simulations with time-dependent rates and also against a numerical solution of the corresponding time-dependent Hamilton equations.

Stochastic Model of Breakdown Nucleation under Intense Electric Fields.

A plastic response due to dislocation activity under intense electric fields is proposed as a source of breakdown. A model is formulated based on stochastic multiplication and arrest under the stress generated by the field. A critical transition in the dislocation population is suggested as the cause of protrusion formation leading to subsequent arcing. The model is studied using Monte Carlo simulations and theoretical analysis, yielding a simplified dependence of the breakdown rates on the electric field. These agree with experimental observations of field and temperature breakdown dependencies.

Reducing the extinction risk of stochastic populations via nondemographic noise.

We consider nondemographic noise in the form of uncertainty in the reaction step size and reveal a dramatic effect this noise may have on the stability of self-regulating populations. Employing the reaction scheme mA→kA but allowing, e.g., the product number k to be a priori unknown and sampled from a given distribution, we show that such nondemographic noise can greatly reduce the population's extinction risk compared to the fixed k case. Our analysis is tested against numerical simulations, and by using empirical data of different species, we argue that certain distributions may be more evolutionary beneficial than others.

A new minimally invasive surgical technique for medial retinaculum repair following traumatic patellar dislocation.

A new surgical method is introduced offering a less invasive approach to reattach the medial retinaculum following acute patellar dislocation. This retrospective analysis comprised 12 cases of medial retinacular repair in 10 patients. The surgical technique achieved reinforced reattachment of the torn region of the medial retinaculum for improved patellar support and stabilization. During follow-up, no recurrent patellar dislocations occurred, except where one patient reported a subjective feeling of patellar dislocation. The average Kujala score for our sample group after 2 years was 89.2. A plethora of methods are described in the literature to repair a tear to the medial patellofemoral ligament, which attaches at the superomedial patella. However, it is our contention that traumatic patellar dislocation invariably results in osteochondral avulsion at the inferomedial patella, refuting medial patellofemoral ligament involvement, and, rather, implicating the inferior aspect of the deep layer of medial retinaculum. Our surgical technique enables stable fixation of the region, decreasing the rate of recurrent dislocations. No grafts are used, permitting tendinous and ligamentous anatomy to remain intact. We further postulate that performing a CT examination preoperatively may reduce time between diagnosis and surgery, in addition to locating fracture sites more precisely.

Stochastic foundations in nonlinear density-regulation growth.

In this work we construct individual-based models that give rise to the generalized logistic model at the mean-field deterministic level and that allow us to interpret the parameters of these models in terms of individual interactions. We also study the effect of internal fluctuations on the long-time dynamics for the different models that have been widely used in the literature, such as the theta-logistic and Savageau models. In particular, we determine the conditions for population extinction and calculate the mean time to extinction. If the population does not become extinct, we obtain analytical expressions for the population abundance distribution. Our theoretical results are based on WKB theory and the probability generating function formalism and are verified by numerical simulations.

Publisher's Note: Effect of reaction-step-size noise on the switching dynamics of stochastic populations [Phys. Rev. E 93, 052117 (2016)].

This corrects the article DOI: 10.1103/PhysRevE.93.052117.