Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Collective behavior may be elicited or can spontaneously emerge by a combination of interactions with the physical environment and conspecifics moving within that environment. To investigate the relative contributions of these factors in a small millimeter-scale swimming organism, we observed larval zebrafish, interacting at varying densities under circular confinement. Our aim was to understand the biological and physical mechanisms acting on these larvae as they swim together inside circular confinements. If left undisturbed, larval zebrafish swim intermittently in a burst and coast manner and are socially independent at this developmental stage, before shoaling behavioral onset. We report here our analysis of a new observation for this well-studied species: in circular confinement and at sufficiently high densities, the larvae collectively circle rapidly alongside the boundary. This is a new physical example of self-organization of mesoscale living active matter driven by boundaries and environment geometry. We believe this is a step forward toward using a prominent biological model system in a new interdisciplinary context to advance knowledge of the physics of social interactions.

With over 2 million people in the UK suffering from chronic wounds, understanding the biochemistry and pharmacology that underpins these wounds and wound healing is of high importance. Chronic wounds are characterised by high levels of matrix metalloproteinases (MMPs), which are necessary for the modification of healthy tissue in the healing process. Overexposure of MMPs, however, adversely affects healing of the wound by causing further destruction of the surrounding extracellular matrix. In this work, we propose a mathematical model that focuses on the interaction of MMPs with dermal cells using a system of partial differential equations. Using biologically realistic parameter values, this model gives rise to travelling waves corresponding to a front of healthy cells invading a wound. From the arising travelling wave analysis, we observe that deregulated apoptosis results in the emergence of chronic wounds, characterised by elevated MMP concentrations. We also observe hysteresis effects when both the apoptotic rate and MMP production rate are varied, providing further insight into the management (and potential reversal) of chronic wounds.

This study proposes using accumulated neurotoxicity, defined as the time integral of A{beta} oligomer concentration, as a biomarker for neuronal aging. A relationship between biological age and accumulated neurotoxicity is proposed. Numerical analysis guided the development of a new analytical solution linking the biological and calendar ages of neurons. The effects of A{beta} monomer and oligomer half-lives--key indicators of proteolytic efficiency--on biological age are examined. Both constant and age-dependent (exponentially increasing) half-life scenarios are considered. The findings indicate that increasing the half-life of A{beta} monomers and oligomers with age accelerates biological aging. Reducing A{beta} monomer production is shown to slow biological aging, with a linear relationship established between these two quantities. Additionally, biological age is found to depend linearly on the half-deposition time of A{beta} oligomers into senile plaques. The model demonstrates that biological age is irreversible, providing a theoretical explanation for why plaque-clearing therapies cannot reverse established cognitive impairment. The model also demonstrates that biological age is path-dependent rather than state-dependent.

As the COVID-19 pandemic continues unabated, many governments and public-health bodies worldwide have ceased to implement concerted measures for limiting viral spread, placing the onus instead on the individual. In this paper, we examine the feasibility of this proposition using an agent-based model to simulate the impact of individual shielding behaviors on reinfection frequency. We derive estimates of heterogeneity in immune protection from a population pharmacokinetic (pop PK) model of antibody kinetics following infection and variation in contact rate based on published estimates. Our results suggest that individuals seeking to opt out of adverse outcomes upon SARS-CoV-2 infection will find it challenging to do so, as large reductions in contact rate are required to reduce the risk of infection. Our findings suggest the importance of a multilayered strategy for those seeking to reduce the risk of infection. This work also suggests the importance of public health interventions such as universal masking in essential venues and air quality standards to ensure individual freedom of choice regarding COVID-19.

Cetacean calves can get assistance in rapid swimming by drafting with the mothers. The hydrodynamic forces produced have been predicted to enable reducing the drag on the calf Using models in a wind tunnel, the similarity between motion in the air and submerged swimming is used to produce quantitative data on the reduction of drag due to drafting in accordance with the theoretical predictions.

The phenomenon of collective navigation has received considerable interest in recent years. A common line of thinking, backed by theoretical studies, is that collective navigation can improve navigation efficiency through the many-wrongs principle, whereby individual error is reduced by comparing the headings of neighbours. When navigation takes place in a flowing environment, each individuals trajectory is influenced by drift. Consequently, a potential discrepancy emerges between an individuals intended heading and its actual heading. In this study we develop a theoretical model to explore whether collective navigation benefits are altered according to the form of heading information transmitted between neighbours. Navigation based on each individuals intended heading is found to confer robust advantages across a wide spectrum of flows, via both a marked improvement in migration times and a capacity for a group to overcome flows unnavigable by solitary individuals. Navigation based on individuals actual headings is far less effective, only offering an improvement under highly favourable currents. For many currents, sharing actual heading information can even lead to journey times that exceed those of individual navigators.

Imagine you walk in a plane. You move by making a step of a certain length per time interval in a chosen direction. Repeating this process by randomly sampling step length and turning angle defines a two-dimensional random walk in what we call comoving frame coordinates. This is precisely how Ross and Pearson proposed to model the movements of organisms more than a century ago. Decades later their concept was generalised by including persistence leading to a correlated random walk, which became a popular model in Movement Ecology. In contrast, Langevin equations describing cell migration and used in active matter theory are typically formulated by position and velocity in a fixed Cartesian frame. In this article, we explore the transformation of stochastic Langevin dynamics from the Cartesian into the comoving frame. We show that the Ornstein-Uhlenbeck process for the Cartesian velocity of a walker can be transformed exactly into a stochastic process that is defined self-consistently in the comoving frame, thereby profoundly generalising correlated random walk models. This approach yields a general conceptual framework how to transform stochastic processes from the Cartesian into the comoving frame. Our theory paves the way to derive, invent and explore novel stochastic processes in the comoving frame for modelling the movements of organisms. It can also be applied to design novel stochastic dynamics for autonomously moving robots and drones.

Occupational and residential segregation and other manifestations of social and economic inequity drive of racial and socioeconomic inequities in infection, severe disease, and death from a wide variety of infections including SARS-CoV-2, influenza, HIV, tuberculosis, and many others. Despite a deep and long-standing quantitative and qualitative literature on infectious disease inequity, mathematical models that give equally serious attention to the social and biological dynamics underlying infection inequity remain rare. In this paper, we develop a simple transmission model that accounts for the mechanistic relationship between residential segregation on inequity in infection outcomes. We conceptualize segregation as a high-level, fundamental social cause of infection inequity that impacts both who-contacts-whom (separation or preferential mixing) as well as the risk of infection upon exposure (vulnerability). We show that the basic reproduction number, [R]0, and epidemic dynamics are sensitive to the interaction between these factors. Specifically, our analytical and simulation results and that separation alone is insufficient to explain segregation-associated differences in infection risks, and that increasing separation only results in the concentration of risk in segregated populations when it is accompanied by increasing vulnerability. Overall, this work shows why it is important to carefully consider the causal linkages and correlations between high-level social determinants - like segregation - and more-proximal transmission mechanisms when either crafting or evaluating public health policies. While the framework applied in this analysis is deliberately simple, it lays the groundwork for future, data-driven explorations of the mechanistic impact of residential segregation on infection inequities.

Withdrawal StatementThe authors have withdrawn their manuscript owing to errors in the experimental design that affect the integrity of the results. Therefore, the authors do not wish this work to be cited as reference for the project. If you have any questions, please contact the corresponding author

AO_SCPLOWBSTRACTC_SCPLOWThe COVID-19 pandemic has brought into sharp focus the need to understand respiratory virus transmission mechanisms. In preparation for an anticipated influenza pandemic, a substantial body of literature has developed over the last few decades showing that the short-range aerosol route is an important, though often neglected transmission path. We develop a simple mathematical model for COVID-19 transmission via aerosols, apply it to known outbreaks, and present quantitative guidelines for ventilation and occupancy in the workplace.

We examine the plausibility, scope and risks of aerial transmission of pathogens (including the SARS-CoV-2 virus) through respiratory droplets carried by exhaled e-cigarette aerosol (ECA). Given the lack of empiric evidence, we consider cigarette smoking and mouth breathing through a mouthpiece as convenient proxies to infer the respiratory mechanics and droplets sizes and their rate of emission that should result from vaping. To quantify direct exposure distance we model exhaled ECA flow as an intermittent turbulent jet evolving into an unstable puff, estimating for low intensity vaping (practiced by 80-90% of vapers) the emission of 6-200 (mean 79.82, standard deviation 74.66) respiratory submicron droplets per puff a horizontal distance spread of 1-2 meters, with intense vaping possibly emitting up to 1000 droplets per puff in the submicron range a distance spread over 2 meters. Since exhaled ECA acts effectively as a visual tracer of its expiratory flow, bystanders become instinctively aware that possible direct contagion might occur only in the direction and scope of the jet.

A long-standing question in animal behaviour is how organisms solve complex tasks. Here we explore how the dynamics of animal behaviour in the ubiquitous tasks of mate-search and competition can arise from a physics-based model of effective interactions. Male orb-weaving spiders of the genus Trichonephila are faced with the daunting challenge of entering the web of a much larger and potentially cannibalistic female, approaching her, and fending off rival males. The interactions that govern the dynamics of males within the confined two-dimensional arena of the females web are dominated by seismic vibrations. This unifying modality allows us to describe the spiders as interacting active particles, responding only to effective forces of attraction and repulsion due to the female and rival males. Our model is based on a detailed analysis of experimental spider trajectories, obtained during the approach of males towards females, and amidst their interactions with rival males of different sizes. The dynamics of spider particles that emerges from our theory allows us to explain a puzzling relationship between the density of males on the web and the reproductive advantages of large males. Our results provide strong evidence that the simple physical rules at the basis of our model can give rise to complex fitness related behaviours in this system.

The European Unions Safety Gate Rapid Alert System (RAPEX) requires Hazard and Risk Assessment Methodology (HARM) evaluations addressing both injury lethality and long-term consequences (LTC). This paper developed a post-processing method to use AIS 2015-coded trauma data directly for RAPEX HARM assessments. AIS 2015 utilizes two metrics: the AIS Code (AIS-CD) for threat to life and the predicted Functional Capacity Index (pFCI) for LTC. While the AIS-CD has been validated on numerous datasets, the pFCI values are based on a theoretical framework that is pending validation. To counter coding variability and poor alignment with clinical diagnoses, initial AIS identifiers (AIS-IDs) were aggregated to a robust level of detail for both metrics. Individual injury severities (AIS-CD/FCI-CD) were aggregated to the person level using a conversion derived from the three most severe injuries (triples), mirroring the concept of the New Injury Severity Score (NISS). The final HARM Level is the most severe outcome derived independently from either the AIS-CD or FCI-CD triple conversion. Analysis showed over 70% of injuries in the aggregated codebook had no LTC. While AIS-CD dominated lower HARM scores, LTC became more defining with increasing HARM severity for the GIDAS sample. At HARM 4 (highest severity), AIS-CD accounted for 53% of cases, FCI-CD accounted for 16%, and both were equally severe in 31% of cases. This method successfully assigns HARM values to AIS 2015 injuries, providing a more holistic severity measure than the current AIS-CD-only approach. HighlightsO_LINovel method assigns RAPEX HARM values to AIS 2015-coded injuries. C_LIO_LICombines lethality (AIS-code) and long-term consequences (FCI-code) for injury severity assessment. C_LIO_LIAggregates injury severity using the three most severe injuries per person. C_LIO_LILong-term consequences account for 13% and 16% of the highest two HARM ratings, respectively. C_LI

The formation of amyloid beta (A{beta}) deposits (senile plaques) is one of the hallmarks of Alzheimers disease (AD). This study investigates what processes are primarily responsible for their formation. A model is developed to simulate the diffusion of amyloid beta (A{beta}) monomers, the production of free A{beta} aggregates through nucleation and autocatalytic processes, and the deposition of these aggregates into senile plaques. The model suggests that efficient degradation of A{beta} monomers alone may suffice to prevent the growth of senile plaques, even without degrading A{beta} aggregates and existing plaques. This is because the degradation of A{beta} monomers interrupts the supply of reactants needed for plaque formation. The impact of A{beta} monomer diffusivity is demonstrated to be small, enabling the application of the lumped capacitance approximation and the derivation of approximate analytical solutions for limiting cases with both small and large rates of A{beta} aggregate deposition into plaques. It is found that the rate of plaque growth is governed by two competing processes. One is the deposition rate of free A{beta} aggregates into senile plaques. If this rate is small, the plaque grows slowly. However, if the rate of deposition of A{beta} aggregates into senile plaques is very large, the free A{beta} aggregates are removed from the intracellular fluid by deposition into the plaques, leaving insufficient free A{beta} aggregates to catalyze the production of new aggregates. This suggests that under certain conditions, A{beta} plaques may offer neuroprotection and impede their own growth. Additionally, it indicates that there exists an optimal rate of deposition of free A{beta} aggregates into the plaques, at which the plaques attain their maximum size.

This paper introduces an optimal control strategy for choleras crossover mathematical model. The proposed model integrates {Psi}-Caputo fractal variable-order derivatives, fractal fractional-order derivatives, and integer-order derivatives across three distinct time intervals, utilizing a simple non-standard kernel function {Psi}(t). A comprehensive stability analysis of the models steady states is conducted. The models results are compared with real-world data from the cholera outbreak in Yemen. Following this, an optimal control problem is formulated within the crossover framework. To numerically solve the resulting optimality system, a discretized non-standard -finite difference method is developed. Numerical simulations and comparative studies are presented to demonstrate the methods applicability and the efficiency of the approximation approach. The key finding of this study highlights that the crossover-controlled system proves to be the most effective approach for mitigating and controlling the spread of cholera.

AA amyloidosis is a severe complication of chronic inflammatory diseases characterized by fibrillar protein deposition in the kidneys, leading to progressive organ failure. This study presents a mathematical model coupling SAA-HDL binding dynamics with renal amyloid aggregation kinetics to elucidate disease pathogenesis. Under normal conditions, Serum Amyloid A (SAA) circulates bound to high-density lipoprotein (HDL), which acts as a molecular chaperone preventing misfolding. However, during chronic inflammation, SAA production exceeds HDL binding capacity, resulting in free SAA that undergoes renal filtration. The model calculates free SAA concentration from reversible binding equilibrium and incorporates renal filtration, mesangial accumulation, and conversion to amyloid fibrils through primary nucleation and autocatalytic growth mechanisms. A central contribution of this work is quantifying accumulated nephrotoxicity arising from AA oligomers, which inflict cumulative cytotoxic damage to mesangial and tubular cells over time. Because oligomers are continuously generated during ongoing aggregation, their toxic burden integrates across the entire duration of the disease. Combined nephrotoxicity, encompassing both oligomer-mediated cellular injury and fibril-driven mechanical disruption of renal architecture, therefore reflects not merely the current disease state but the full inflammatory trajectory of the patient. This cumulative damage defines renal biological age, a measure of functional deterioration whose portion attributable to accumulated nephrotoxicity is irreversible. Renal biological age is also path-dependent: two patients with identical present-day SAA levels may carry different renal damage burdens depending on the duration, timing, and severity of their prior inflammatory episodes. Sensitivity analysis reveals that HDL concentration and SAA cleavage rate are critical determinants of amyloid burden.

Understanding the health outcomes of military exposures is a critical effort for Veterans, their health care team, and national leaders. Veterans Affairs providers receive reports of military exposure related concerns from 43% of Veterans. Understanding the causal influences of environmental exposures on health is a complex task advancement in exposure science and may require interpreting multiple data sources; particularly when exposure pathways and multi-exposure interactions are ill-defined, as is the case for complex and emerging military service-related exposures. Thus, there is a need to standardize clinically meaningful exposure metrics from different data sources to guide clinicians and researchers with a consistent model for investigating and communicating exposure risk profiles. The Linked Exposures Across Databases (LEAD) framework provides a unifying model for characterizing exposure from different exposure datatypes and databases with a focus on providing clinically relevant exposure metrics. Application of LEAD is demonstrated through comparison of different military exposure data sources: Veteran Military Occupational and Environmental Exposure Assessment Tool (VMOAT), Individual Longitudinal Exposure Record (ILER) database and a military incident report database, the Explosive Ordnance Disposal Information Management System (EODIMS). This cohesive method for evaluating military exposures leverages established information with new sources of data and has the potential to influence how military exposure data is integrated into exposure health care and investigational models.

Understanding and monitoring the major influences on SARS-CoV-2 prevalence is essential to inform policy making and devise appropriate packages of non-pharmaceutical interventions (NPIs). Through evaluating community level influences on the prevalence of SARS-CoV-2 infection and their spatiotemporal variations in England, this study aims to provide some insights into the most important risk parameters. We used spatial clusters developed in Jahanshahi and Jin, 2021 as geographical areas with distinct land use and travel patterns. We also segmented our data by time periods to control for changes in policies or development of the disease over the course of the pandemic. We then used multivariate linear regression to identify influences driving infections within the clusters and to compare the variations of those between the clusters. Our findings demonstrate the key roles that workplace and commuting modes have had on some of the sections of the working population after accounting for several interrelated influences including mobility and vaccination. We found communities of workers in care homes and warehouses and to a lesser extent textile and ready meal industries and those who rely more on public transport for commuting tend to carry a higher risk of infection across all residential area types and time periods.

While modelling and simulation are powerful techniques for exploring complex phenomena, if they are not coupled with suitable real-world data any results obtained are likely to require extensive validation. We consider this problem in the context of search game modelling, and suggest that both demographic and behaviour data are used to configure certain model parameters. We show this integration in practice by using a combined dataset of over 150,000 individuals to configure a specific search game model that captures the environment, population, interventions and individual behaviours relating to winter health service pressures. The presence of this data enables us to more accurately explore the potential impact of service pressure interventions, which we do across 33,000 simulations using a computational version of the model. We find government advice to be the best-performing intervention in simulation, in respect of improved health, reduced health inequalities, and thus reduced pressure on health service utilisation.

Using a modified form of the SIR model, we show that, under general conditions, all pandemics exhibit certain scaling rules. Using only daily data for symptomatic, confirmed cases, these scaling rules can be used to estimate: (i) reff, the effective pandemic R-parameter; (ii) ftot, the fraction of exposed individuals that were infected (symptomatic and asymptomatic); (iii) Leff, the effective latency, the average number of days an infected individual is able to infect others in the pool of susceptible individuals; and (iv) , the probability of infection per contact between infected and susceptible individuals. We validate the scaling rules using an example and then apply our method to estimate reff, ftot, Leff and for the first phase of the SARS-Cov-2, Covid-19 pandemic for several countries where there was a well separated first peak in identified infected daily cases after the outbreak of the pandemic in early 2020. Our results are general and can be applied to any pandemic.