An individual-based dynamic model to assess interventions to mitigate opioid overdose risk.

BACKGROUND: Illicit opioid overdose continues to rise in North America and is a leading cause of death. Mathematical modeling is a valuable tool to investigate the epidemiology of this public health issue, as it can characterize key features of population outcomes and quantify the broader effect of structural and interventional changes on overdose mortality. The aim of this study is to quantify and predict the impact of key harm reduction strategies at differing levels of scale-up on fatal and nonfatal overdose among a population of people engaging in unregulated opioid use in Toronto. METHODS: An individual-based model for opioid overdose was built featuring demographic and behavioural variation among members of the population. Key individual attributes known to scale the risk of fatal and nonfatal overdose were identified and incorporated into a dynamic modeling framework, wherein every member of the simulated population encompasses a set of distinct characteristics that govern demographics, intervention usage, and overdose incidence. The model was parametrized to fatal and nonfatal overdose events reported in Toronto in 2019. The interventions considered were opioid agonist therapy (OAT), supervised consumption sites (SCS), take-home naloxone (THN), drug-checking, and reducing fentanyl in the drug supply. Harm reduction scenarios were explored relative to a baseline model to examine the impact of each intervention being scaled from 0% use to 100% use on overdose events. RESULTS: Model simulations resulted in 3690.6 nonfatal and 295.4 fatal overdoses, coinciding with 2019 data from Toronto. From this baseline, at full scale-up, 290 deaths were averted by THN, 248 from eliminating fentanyl from the drug supply, 124 from SCS use, 173 from OAT, and 100 by drug-checking services. Drug-checking and reducing fentanyl in the drug supply were the only harm reduction strategies that reduced the number of nonfatal overdoses. CONCLUSIONS: Within a multi-faceted harm reduction approach, scaling up take-home naloxone, and reducing fentanyl in the drug supply led to the largest reduction in opioid overdose fatality in Toronto. Detailed model simulation studies provide an additional tool to assess and inform public health policy on harm reduction.

Speed-mediated properties of schooling.

Collectively moving animals often display a high degree of synchronization and cohesive group-level formations, such as elongated schools of fish. These global patterns emerge as the result of localized rules of interactions. However, the exact relationship between speed, polarization, neighbour positioning and group structure has produced conflicting results and is largely limited to modelling approaches. This hinders our ability to understand how information spreads between individuals, which may determine the collective functioning of groups. We tested how speed interacts with polarization and positional composition to produce the elongation observed in moving groups of fish as well as how this impacts information flow between individuals. At the local level, we found that increases in speed led to increases in alignment and shifts from lateral to linear neighbour positioning. At the global level, these increases in linear neighbour positioning resulted in elongation of the group. Furthermore, mean pairwise transfer entropy increased with speed and alignment, implying an adaptive value to forming faster, more polarized and linear groups. Ultimately, this research provides vital insight into the mechanisms underlying the elongation of moving animal groups and highlights the functional significance of cohesive and coordinated movement.

Groups clapping in unison undergo size-dependent error-induced frequency increase.

Humans clapping together in unison is a familiar and robust example of emergent synchrony. We find that in experiments, such groups (from two to a few hundred) always increase clapping frequency, and larger groups increase more quickly. Based on single-person experiments and modeling, an individual tendency to rush is ruled out as an explanation. Instead, an asymmetric sensitivity in aural interactions explains the frequency increase, whereby individuals correct more strongly to match neighbour claps that precede their own clap, than those that follow it. A simple conceptual coupled oscillator model based on this interaction recovers the main features observed in experiments, and shows that the collective frequency increase is driven by the small timing errors in individuals, and the resulting inter-individual interactions that occur to maintain unison.

Familiarity affects collective motion in shoals of guppies (Poecilia reticulata).

The coordinated and synchronized movement of animals in groups often referred to as collective motion emerges through the interactions between individual animals within the group. Factors which affect these interactions have the potential to shape collective movement. One such factor is familiarity, or the tendency to bias behaviour towards individuals as a result of social recognition. We examined the effect of familiarity on the expression of collective motion in small shoals of female guppies (Poecilia reticulata). Groups comprising familiar individuals were more strongly polarized than groups of unfamiliar individuals, particularly when in novel surroundings. The ability to form more strongly polarized shoals potentially promotes information transfer and enhances the anti-predator benefits of grouping.

Goal-dependent current compensation and drift in surf scoter flocks.

BACKGROUND: Animals moving through air or water toward a goal frequently must contend with fluid currents, which can drift the actual path of the animal away from the direction of heading. Whether, and to what degree, animals compensate for currents depends on the species and environmental context, but plays an important role in the movement ecology of the species. In this paper, flocks of surf scoters (Melanitta perspicillata), an aquatic diving duck, were individually tracked during collective foraging in the presence of sideward water currents to assess the individual compensatory response while moving from open water toward the foraging location versus return to open water. RESULTS: During short-range movement toward the foraging location, surf scoters moved more slowly, and compensated for currents by orienting diagonally into the current to maintain a perpendicular track to the goal. In contrast, during return to open water, surf scoters moved faster, and maintained a perpendicular orientation away from the foraging location, and allowed the sideward current to drift their track diagonally. CONCLUSIONS: Surf scoters show a behavioural flexibility in response to currents, alternately using compensation and drift as the movement goal and consequent cost of accuracy change.

Additional Navigational Strategies Can Augment Odor-Gated Rheotaxis for Navigation under Conditions of Variable Flow.

The navigation strategies animals use to find sources of odor depend on the olfactory stimuli, the properties of flowing fluids, and the locomotory capabilities of the animal. In high Reynolds number environments, animals typically use odor-gated rheotaxis to find the source of turbulent odor plumes. This strategy succeeds because, although turbulence creates an intermittent chemical cue, the animal follows the (continuous) directional cue created by the flow that is transporting the chemical. However, in nature, animals may lose all contact with an odor plume as variations in the direction of bulk flow cause the plume to be rotated away before the animal reaches the source of the odor. Our goal was to use a mathematical model to test the hypothesis that strategies that augment odor-gated rheotaxis would be beneficial for finding the source of an odor plume in such variable flow. The model links a stochastic variable-direction odor plume with a turbulence-based intermittent chemical signal and four different movement strategies, including: odor-gated rheotaxis alone (as a control), odor-gated rheotaxis augmented by further rheotaxis in the absence of odor, odor-gated rheotaxis augmented by a random walk, and odor-gated rheotaxis augmented by movement actively guided by the heading of the flow when the odor was still present. We found that any of the three augmented strategies could improve on strict odor-gated rheotaxis. Moreover, variations in performance caused the best strategy to depend on the speed of movement of the animal and the magnitude of the variation in flow, and more subtly on the duration over which the augmented strategy was performed. For most combinations of parameters in the model, either augmenting with a random walk or following the last-known heading were the best-performing strategies. Overall, our results suggest that marine animals that rely on odor cues to navigate in turbulent environments may augment odor-gated rheotaxis with additional movements that will increase the probability of finding the sources of odors. Moreover, we believe our approach to modeling odor plumes in variable flows is a valuable step toward mathematically capturing the key conditions experienced by animals navigating on the basis of odors carried by flows.

Ordering dynamics in collectively swimming Surf Scoters.

One striking feature of collective motion in animal groups is a high degree of alignment among individuals, generating polarized motion. When order is lost, the dynamic process of reorganization, directly resulting from the individual interaction rules, provides significant information about both the nature of the rules, and how these rules affect the functioning of the collective. By analyzing trajectories of collectively swimming Surf Scoters (Melanitta perspicillata) during transitions between order and disorder, I find that individual speed and polarization are positively correlated in time, such that individuals move more slowly in groups exhibiting lower alignment. A previously validated zone-based model framework is used to specify interactions that permit repolarization while maintaining group cohesion and avoiding collisions. Polarization efficiency is optimized under the constraints of cohesion and collision-avoidance for alignment-dominated propulsion (versus autonomous propulsion), and for repulsion an order of magnitude larger than attraction and alignment. The relative strengths of interactions that optimize polarization also quantitatively recover the speed-polarization dependence observed in the data. Parameters determined here through optimizing polarization efficiency are essentially the same as those determined previously from a different approach: a best-fit model for polarized Surf Scoter movement data. The rules governing these flocks are therefore robust, accounting for behavior across a range of order and structure, and also highly responsive to perturbation. Flexibility and efficient repolarization offers an adaptive explanation for why specific interactions in such animal groups are used.

Inferring individual rules from collective behavior.

Social organisms form striking aggregation patterns, displaying cohesion, polarization, and collective intelligence. Determining how they do so in nature is challenging; a plethora of simulation studies displaying life-like swarm behavior lack rigorous comparison with actual data because collecting field data of sufficient quality has been a bottleneck. Here, we bridge this gap by gathering and analyzing a high-quality dataset of flocking surf scoters, forming well-spaced groups of hundreds of individuals on the water surface. By reconstructing each individual's position, velocity, and trajectory, we generate spatial and angular neighbor-distribution plots, revealing distinct concentric structure in positioning, a preference for neighbors directly in front, and strong alignment with neighbors on each side. We fit data to zonal interaction models and characterize which individual interaction forces suffice to explain observed spatial patterns. Results point to strong short-range repulsion, intermediate-range alignment, and longer-range attraction (with circular zones), as well as a weak but significant frontal-sector interaction with one neighbor. A best-fit model with such interactions accounts well for observed group structure, whereas absence or alteration in any one of these rules fails to do so. We find that important features of observed flocking surf scoters can be accounted for by zonal models with specific, well-defined rules of interaction.

A conceptual model for milling formations in biological aggregates.

Collective behavior of swarms and flocks has been studied from several perspectives, including continuous (Eulerian) and individual-based (Lagrangian) models. Here, we use the latter approach to examine a minimal model for the formation and maintenance of group structure, with specific emphasis on a simple milling pattern in which particles follow one another around a closed circular path.We explore how rules and interactions at the level of the individuals lead to this pattern at the level of the group. In contrast to many studies based on simulation results, our model is sufficiently simple that we can obtain analytical predictions. We consider a Newtonian framework with distance-dependent pairwise interaction-force. Unlike some other studies, our mill formations do not depend on domain boundaries, nor on centrally attracting force-fields or rotor chemotaxis.By focusing on a simple geometry and simple distant-dependent interactions, we characterize mill formations and derive existence conditions in terms of model parameters. An eigenvalue equation specifies stability regions based on properties of the interaction function. We explore this equation numerically, and validate the stability conclusions via simulation, showing distinct behavior inside, outside, and on the boundary of stability regions. Moving mill formations are then investigated, showing the effect of individual autonomous self-propulsion on group-level motion. The simplified framework allows us to clearly relate individual properties (via model parameters) to group-level structure. These relationships provide insight into the more complicated milling formations observed in nature, and suggest design properties of artificial schools where such rotational motion is desired.