Journal of The Royal Society Interface

1Cranial sutures are important structures associated with skull growth, and it is widely known that the cranial sutures have a fractal nature. However, the measurement conditions and analytical procedures have varied among studies, making direct comparison and interpretation difficult. In addition, the mechanisms by which such fractal-like patterns arise remain incompletely understood. In this study, we established and validated a standardized box-counting protocol for quantifying the fractal dimension (FD) of cranial sutures. Using this protocol, we quantified FD in 45 digitized images of human lambda sutures and in eight structure-formation model variants designed to generate fractal-like patterns via distinct kernel designs (step, Gaussian, Mexican-hat, and time-dependent/dual-stage), spatially inhomogeneous inhibition (Fbase), low-frequency noise, and different initial conditions (including sine-curve initialization). We show that FD estimates are strongly affected by preprocessing (including skeletonization) and the selected scale range, explaining discrepancies across previous studies. Crucially, under the matched preprocessing and scale-range criteria, three of the eight model variants reproduce the FD of real sutures within predefined equivalence margins, supporting the notion that appropriate dynamics can produce the observed fractal-like suture behavior and providing testable hypotheses for how such patterns may emerge.

Standard differentiation assays sample cell states only at discrete time points, while the underlying progression unfolds continuously and heterogeneously across cells. As a result, different combinations of proliferation, commitment, and maturation dynamics can converge to similar endpoint measurements. This many-to-one mapping between latent trajectories and observable readouts constitutes a partially observed inverse problem that limits mechanistic interpretation. Although this ambiguity is inherent to many experimental systems, it is rarely examined using models that connect cell-state dynamics to assay-level quantities. We present OsteoMin, a coarse-grained cellular automaton that links stochastic transitions between pre-osteoblast and osteoblast states to experimentally measurable readouts of alkaline phosphatase activity, collagen deposition, and mineralization. Model parameters were constrained using literature-reported kinetics and evaluated against dexamethasone and menaquinone-4 perturbations. The frame-work reproduces qualitative assay trends and enables systematic analysis of how cell-state progression, matrix maturation, and external perturbations shape differentiation outcomes. Using this framework, we quantify the identifiability limits of endpoint assays and test whether standard measurements can distinguish underlying differentiation mechanisms. Distinct perturbation families often produce similar endpoint responses (macro-F1 {approx} 0.42), indicating limited discriminative power. Incorporating temporal trajectories improves separability (macro-F1 {approx} 0.78), demonstrating that most identifiable information resides in marker dynamics rather than terminal measurements. Sobol analysis shows early markers depend on proliferation timing, whereas late mineralization is governed by nonlinear matrix maturation and parameter interactions. Together, these results show that endpoint assays constrain overall progression but do not uniquely identify underlying mechanisms. OsteoMin provides a framework linking differentiation dynamics to assay observables and a basis for assessing identifiability in endpoint-driven systems.

The preferred stride ratio (PSR), defined as the ratio of step length to cadence, is approximately invariant across a wide range of walking speeds in healthy adults but breaks down at slow speeds. The lower speed boundary at which this constancy is broken was estimated by Murakami and Otaka (2017) to be approximately 62 m min-1 ({approx} 1.03 m s-1) on the basis of unstandardised K-means cluster analysis applied to data from 21 healthy adults at five speed conditions. The present report re-examines this estimate using the digitised individual-level scatter of Fig. 1-A and the published group-level statistics of Table 1 of that study, applying three breakpoint estimators in parallel: (i) unstandardised K-means (replicating the original method), (ii) a Gaussian mean-and-variance changepoint estimator, and (iii) a piecewise-linear regression on PSR. Applied directly to the digitised scatter (n = 84 resolved markers from a total of 105; 44 of 44 slow-walk markers, 40 of 61 normal-walk markers), the unstandardised K-means estimator returned 62.0 m min-1, matching the originally reported value to the reported precision; the mean-and-variance changepoint estimator returned 55 m min-1; and the piecewise-linear estimator was numerically unstable on the raw heteroscedastic data. To quantify uncertainty, 5 000 Monte Carlo realisations of synthetic individual-level data were generated from a bivariate truncated-normal model conditioned on the published condition means and standard deviations and on the published within-cluster speed-PSR correlations. The Monte Carlo distributions gave median estimates of 61 m min-1 (95 % MC interval 55-67) for unstandardised K-means, 39 m min-1 (29-53) for the mean-and-variance changepoint estimator, and 35 m min-1 (19-49) for piecewise-linear regression. Under a log-normal sensitivity model the corresponding intervals were 60 [55, 66], 34 [20, 58], and 19 [5, 42] m min-1. The likelihood-based estimator placed the central tendency substantially below 62 m min-1, and its Monte Carlo intervals did not include the original boundary under either marginal-distribution model. An additional robust heteroscedastic segmented profile-likelihood analysis on log-PSR yielded lower Monte Carlo median breakpoints across all model specifications, although the full-variance intervals overlapped the original K-means boundary. The qualitative finding of Murakami and Otaka -- that PSR constancy breaks down at slow walking speeds -- is supported by the present reanalysis. The original 62 m min-1 boundary is reproduced under the unstandardised K-means estimator, where it reflects the location of the largest density gap in the published five-condition speed sampling rather than a formally estimated changepoint; estimators formally designed for changepoint detection localise the joint PSR mean-and-variance transition substantially below this value. O_FIG O_LINKSMALLFIG WIDTH=162 HEIGHT=200 SRC="FIGDIR/small/720900v2_fig1.gif" ALT="Figure 1"> View larger version (41K): org.highwire.dtl.DTLVardef@2bb53dorg.highwire.dtl.DTLVardef@187d9bborg.highwire.dtl.DTLVardef@1e7a6a0org.highwire.dtl.DTLVardef@16c587b_HPS_FORMAT_FIGEXP M_FIG O_FLOATNOFigure 1.C_FLOATNO Reproduction and likelihood-based extension of the boundary reported in Murakami and Otaka [5]. (A) Digitised individual-level scatter from Fig. 1-A of [5] (n = 84 resolved markers from a total of 105: 44 of 44 slow-walk markers and 40 of 61 normal-walk markers). The dashed vertical line marks the value 62.4 m min-1 as drawn in the original figure. (B) PSR variance amplification across the five speed conditions, expressed as Var(PSR)/Var(PSR)Preferred, on a logarithmic vertical axis. (C) Distributions of the breakpoint estimates over N = 5 000 Monte Carlo realisations under the bivariate truncated-normal model with cluster-specific within-cluster correlations: unstandardised K-means (median 61 m min-1), the Gaussian mean-and-variance changepoint estimator (median 39 m min-1), and piecewise-linear regression on PSR (median 35 m min-1). The dashed vertical line marks 62.4 m min-1. (D) Sensitivity of each estimator to the choice of marginal-distribution model (truncated normal vs. log-normal); error bars are 95 % Monte Carlo simulation intervals. (E) PSR mean {+/-} SD across the five speed conditions (Table 1 of [5], height-adjusted). C_FIG O_TBL View this table: org.highwire.dtl.DTLVardef@24fe39org.highwire.dtl.DTLVardef@ae8fdborg.highwire.dtl.DTLVardef@66a473org.highwire.dtl.DTLVardef@b6ad84org.highwire.dtl.DTLVardef@139bca7_HPS_FORMAT_FIGEXP M_TBL O_FLOATNOTable 1.C_FLOATNO O_TABLECAPTIONSource data reproduced from Murakami and Otaka [5], height-adjusted, n = 21 per condition. C_TABLECAPTION C_TBL

The environments inhabited by flying insects demand a balance between flight efficiency and flight manoeuvrability. In structural oscillators such as the insect indirect flight motor, efficiency (arising from resonance) and manoeuvrability (arising from kinematic modulation) are typically quid pro quo, with modulation incurring penalties to efficiency. Band-type resonance is a phenomenon that offers, in theory, a strategy to lessen these penalties via careful navigation through a band of efficient kinematic states. However, identifying this band is challenging: no methods exist to identify the complete band in realistic motor models, involving elasticity distributed across thorax and wing. Nor are the effects of elasticity distribution on the band known. In this work, we address both open topics. We present a suite of numerical methods for identifying the complete resonance band in general systems. Applying them to models of the insect flight motor with distributed elasticity--thoracic and wing flexion--reveals that distributed elasticity is moderate-risk but high-reward morphological feature. Well-tuned distributions expand the resonance band over fourfold whereas poorly-tuned distributions completely extinguish the resonance band. These results indicate that distributing elasticity across the insect flight motor can have adaptive value, and motivate broader work identifying distributions across species.

The ability of chemotactic populations to localize and track targets in fluctuating environments depends critically on the temporal structure of environmental signals. Using a minimal agent-based framework of non-interacting run-and-tumble cells implementing an E. coli-inspired temporal sensing strategy, populations are exposed to static and moving chemoattractant fields perturbed by noise with controlled temporal structure, spanning white, pink (1/f), and correlated Ornstein-Uhlenbeck processes. Chemotactic populations are found to act as temporal filters, robustly suppressing fast fluctuations while remaining highly sensitive to slowly varying perturbations. As a consequence, chemotactic performance is governed not by noise amplitude, but by its temporal correlations. By continuously varying the noise correlation time, a critical regime emerges at{tau} c [~]{tau} run, where aggregates lose stability, tracking errors increase sharply, and spatial dispersion rises. Power spectral analysis further shows that the low-frequency power fraction of the signal provides a strong predictor of failure, outperforming total signal variance and establishing a direct link between environmental noise spectra and collective behavior. Introducing external flow reveals that advective transport amplifies noise-induced destabilization when it overlaps the chemotactic capture region, defining a combined spatiotemporal constraint on robustness. Together, these results identify temporal correlations and spectral structure as fundamental control parameters for chemotactic organization and provide a quantitative framework for predicting and designing collective behavior in fluctuating environments.

Conventional diagonal stride skiing traditionally includes a glide phase, characterised by a period of relatively passive gliding on one ski. While the glide phase may take advantage of low ski-snow friction, it does not exhibit the same whole-cycle mechanical energy fluctuations seen in running or walking on foot. A new sub-technique, known as running style, substantially reduces the glide phase and may alter the role of elastic tissues, making the movement pattern more similar to uphill running on foot in its temporal organisation. We examined knee extensor and plantar flexor muscle-tendon behaviour in eight competitive skiers performing conventional diagonal and running techniques on a treadmill inclined at 10{degrees}. Using synchronised ultrasonography, 3D kinematics, ski forces and EMG, we quantified gastrocnemius medialis and vastus lateralis fascicle and muscle-tendon unit (MTU) dynamics in both the running (RUN) and conventional (CON) styles. Shorter glide and total cycle durations during RUN shifted MTU peak length and velocity earlier during the kick phase. Fascicles in both muscles operated at similar velocities across techniques, showing MTU-fascicle decoupling. Vastus lateralis fascicles shortened at higher absolute peak velocities than gastrocnemius in both conditions, while normalised velocities were similar. RUN increased preactivation and advanced EMG timing, while integrated EMG during the kick was lower compared to CON. These findings suggest that, despite large shifts in external mechanics between glide-based and more running-like skiing, elastic tissues may help stabilise fascicle behaviour and preserve a similar contractile strategy across muscles and techniques.

Patient-derived tumour spheroids are increasingly used as engineered three-dimensional tissue models for studying tumour growth, nutrient limitation, and therapeutic response. However, extracting quantitative, mechanistically interpretable information from longitudinal imaging data remains challenging. Here, we present a three-dimensional phase-field framework for modelling patient-derived tumour spheroids as continuum, self-organising tissues. The model captures the coupled evolution of viable and necrotic cell fractions through nutrient-limited growth, death, and mechanically and thermodynamically mediated motion, using seven biologically interpretable effective parameters. Key experimental observables emerge naturally from nutrient-growth coupling, without imposing explicit species interfaces or quiescent layers. The framework was quantitatively calibrated against longitudinal imaging data from melanoma spheroids across two cell lines and three initial seeding densities. Across all conditions, simulations reproduced the temporal evolution of all measured observables with low relative error ({approx} 3{sigma} of experimental data), and direct comparison with an established Greenspan-type ODE model demonstrated comparable or improved predictive accuracy. Parameter identifiability analysis revealed weak individual parameter constraints, yet model predictions remained robust, a profile consistent with biological models. We demonstrate that a general PDE-based growth framework can match or outperform a dedicated spheroid model while remaining fully biologically interpretable. Beyond predictive accuracy, the phase-field formulation naturally resolves internal mechanical structure, providing access to quantities that are not directly experimentally observable. These results establish that mechanistically grounded continuum models can be quantitatively calibrated to routine spheroid imaging data, offering a foundation for integrating spatial and mechanical information into the interpretation of organoid-based assays. Graphical Abstract O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=77 SRC="FIGDIR/small/717345v1_ufig1.gif" ALT="Figure 1"> View larger version (21K): org.highwire.dtl.DTLVardef@12eddb2org.highwire.dtl.DTLVardef@1dce430org.highwire.dtl.DTLVardef@1091fc2org.highwire.dtl.DTLVardef@4055e_HPS_FORMAT_FIGEXP M_FIG C_FIG

Large commercial and military aircraft can operate in a wide range of turbulent conditions, except during extreme weather events such as cyclones. Smaller man-made vehicles, such as micro aerial vehicles (MAVs) and nano aerial vehicles (NAVs), are significantly more sensitive to routine environmental wind fluctuations, making them difficult to control. In contrast, insects exhibit remarkable stability in naturally gusty conditions. Despite this, few studies have systematically investigated the impact of gusts and turbulence on insect flight performance. To address this gap and to gain fundamental insights into insect flight stability under gusty conditions, we examined the flight of freely flying black soldier flies subjected to a discrete head-on aerodynamic gust in a controlled laboratory environment. Flight motions were recorded using two high-speed cameras, and body and wing kinematics were analyzed across 14 distinct cases. In response to the gust, we observed consistent features across the cases: (1) asymmetry in wing stroke amplitude, (2) large changes in body roll angle--up to 160{degrees}--occurring over approximately two wing beats ([~]20 ms) with recovery over [~]9 wing beats, (3) transient pitch-down attitude, and (4) deceleration in the flight direction. These rapid responses, combining passive and active control mechanisms, provide insight into the flight control strategies employed by insects. The findings offer valuable guidance for the design of MAVs and NAVs capable of robustly responding to gusts and unsteady airflow in natural environments.

Network-based epidemic models have been instrumental in understanding how contact structure shapes infectious disease dynamics, yet widely used frameworks such as Erd[o]s-Renyi, configuration-model, and stochastic block networks do not explicitly capture the combination of fully accessible (saturated) within-group interactions and constrained between-group connectivity characteristic of many real-world settings. Here, we introduce the Multi-Clique (MC) network model, a generative framework in which individuals are organised into fully connected cliques representing stable contact groups (e.g., households, classrooms, or workplaces), with a limited number of external connections governing inter-group transmission. Using stochastic susceptible-infectious-recovered (SIR) simulations on degree-matched networks, we compare epidemic dynamics on MC networks with those on classical random graph models. Despite having an identical mean degree, MC networks exhibit systematically distinct behaviour, including slower epidemic growth, reduced peak prevalence, increased fade-out probability, and delayed time to peak. These effects arise from rapid within but constrained between clique transmission, creating structural bottlenecks that standard models do not capture. The MC framework provides an interpretable, data-driven representation of recurrent contact structure, with parameters that map directly to observable quantities such as household and classroom sizes. By isolating the role of intergroup connectivity, the model offers a basis for evaluating targeted intervention strategies that reduce between-group mixing while preserving within-group interactions. Our results highlight the importance of explicitly representing the real-life clique-based network structure in epidemic models and suggest that classical degree-matched networks may systematically overestimate epidemic speed and intensity in structured populations.

Movement is costly, and animals are under strong selective pressure to move efficiently, yet, in patchy, dynamic landscapes, decision-making is inherently uncertain. We quantify the energetic savings achieved by using up-to-date information presented within social cues for reducing movement costs. We use an agent-based model, founded on realistic aeronautical rules and parametrised on the Andean condor (Vultur gryphus), to study movement in patchy landscapes. By explicitly considering altitude, flight results in a sequence of soaring and gliding in the 3D space. We investigate how the cost of movement to an overall goal varies when birds use social information from others that are either fixed in space or moving collectively to the common goal, and under different risk-taking speed strategies, from slow and cautious to fast and risky. The value of social information is operationalised as energetic savings in units of basal metabolic rate. Under low predictability, agents with intermediate risk and high social-information use exhibit lowest movement costs, with up to 41% energy savings over asocial movement. By extending classical aeronautical theory to social and variable environments we demonstrate the adaptive value of social information for efficient movement in patchy, unpredictable landscapes.

Coccidioidomycosis (Valley fever) is an environmentally acquired fungal infection endemic to the arid Americas, presenting a growing public health challenge as changing environmental patterns threaten to amplify exposure risks across both established and newly recognized endemic zones. Historically, forecasting efforts have relied on statistical correlations with meteorological variables. These phenomenological models often fail to capture the complex, non-linear interactions between the saprobic (environmental) and parasitic (host) life cycles of Coccidioides, particularly under non-stationary climate conditions. Here, we present a hierarchy of mechanistic Ordinary Differential Equation (ODE) models that explicitly map environmental drivers to the distinct biological stages of the fungal life cycle. We developed successive model iterations, incrementally incorporating soil moisture retention, temperature-dependent growth rates, and wildlife reservoir dynamics, and calibrated them against human case data from various regions of Arizona. We derive a time-variant environmental reproduction number and test how transmission potential fluctuates dynamically with environmental forcing. The comparative forecasting analysis, utilizing various statistical tests, information criteria, Relative Root Mean Square Error, the Diebold-Mariano test, and the Modified Diebold-Mariano, shows how the models progress. Mechanistic models based solely on continuous fungal growth perform worse than statistical baselines. By integrating climate data, we increase predictive power to a level comparable to that of the statistical model. Explicitly incorporating a wildlife reservoir as a biological amplifier significantly improves model forecasting over statistical baselines. This framework offers public health officials a biologically grounded tool to predict disease burden and guide targeted interventions responding to changing climate patterns.

Pertussis remains an endemic and periodically resurgent vaccine-preventable disease despite long-standing immunisation programmes, reflecting complex interactions between transmission, waning immunity, vaccination history, and heterogeneous clinical presentation. We present a comprehensive age-structured mathematical model of pertussis transmission that explicitly represents infection heterogeneity, immunity dynamics, and detailed vaccination schedules across the life course. The model stratifies the population into 56 age groups and 29 epidemiological states, capturing four distinct infection types that differ by severity, symptoms, and infectiousness, including asymptomatic infection. Both naturally acquired and vaccine-derived immunity are modelled as non-lifelong, incorporating waning, partial protection, reinfection, and immune boosting following exposure without transmissible infection. Vaccination is represented at high resolution, including dose-specific primary series vaccination, booster doses in early childhood, childhood, and adolescence, and maternal immunisation during pregnancy, with differentiation between whole-cell and acellular pertussis vaccine formulations and historical changes in vaccine use and coverage. Periodicity and stochasticity are incorporated to reproduce observed multi-year epidemic cycles. A global sensitivity analysis using Latin hypercube sampling and partial rank correlation coefficients identifies immunity waning rates, immune boosting, and recovery from severe infection as key drivers of modelled incidence, mortality, and population protection. By integrating detailed immune processes with realistic vaccination histories, this model provides a flexible framework for evaluating pertussis epidemiology and assessing the population-level impact of alternative vaccination strategies, including booster and maternal immunisation policies.

Change point detection is critical for identifying structural transitions in time series data. While most existing methods focus on changes in statistical properties of the data such as the mean or variance, many real-world systems are governed by dynamical models in which changes occur in model parameters. We introduce MICA, an algorithm that detects change points by minimizing the discrepancy between model simulations with a given dynamical model and observed data. The method integrates binary segmentation with a genetic algorithm to identify both the timing and nature of model parameter changes. MICA simultaneously estimates segment-specific and global parameters alongside change points, offering enhanced flexibility and interpretability. We demonstrate its utility on synthetic datasets and real-world scenarios, including COVID-19 epidemiological modeling, under policy interventions, and the analysis of generator cooling systems in wind turbines to monitor operational status. While illustrated using differential and difference equation models, MICA is model-agnostic and applicable to any simulatable system, making it broadly useful for applications requiring accurate tracking of structural dynamics.

The classical concept of Critical Community Size (CCS) as formulated by Bartlett defines the minimum host population required for a pathogen to persist endemically without stochastic extinction. While this framework successfully described directly transmitted childhood infections in relatively isolated populations, it is increasingly inadequate for modern urban systems characterized by strong connectivity between cities. Pathogens circulating in highly connected urban networks can repeatedly re-emerge through spatial reintroduction even when local transmission temporarily fades out. In such systems, persistence is inherently probabilistic and influenced simultaneously by population size, environmental suitability, and network connectivity. In this study, we develop a generalization of the CCS concept, the Empirical Persistence Threshold (EPT), and apply it to three of the main arboviruses circulating in Brazil--dengue, chikungunya, and Zika--over the period 2017-2024. The Empirical Persistence Threshold generalizes the classical notion of critical community size by replacing a single deterministic threshold with a probabilistic, datadriven measure. Instead of asking for the minimum population at which persistence is guaranteed, EPT characterizes the lower tail of the population distribution among municipalities that empirically sustain transmission. Using weekly incidence data from thousands of municipalities, we transform temporal incidence series into binary sequences describing the presence or absence of reported transmission. For each municipality, we characterize persistence through the empirical distribution of run lengths of consecutive weeks with reported cases. Distances between run-length distributions are computed using the Wasserstein-1 metric, allowing a geometrically meaningful comparison between persistence profiles, and municipalities are grouped into epidemiological regimes using hierarchical clustering methods. Across all three arboviruses, we identify two robust regimes: one exhibiting sporadic and recurrent epidemic transmission, and the other exhibiting sustained persistent transmission. We then estimate the population scales associated with each persistence regime. The analysis is further extended to evaluate how persistence thresholds vary across climate regimes (Koppen classification) and urban hierarchy levels (REGIC). This framework allows the estimation of probabilistic persistence thresholds analogous to CCS, but adapted to connected urban systems. We define the Empirical Persistence Threshold as lower quantiles of the population distribution among municipalities in the persistent regime, and additionally estimate persistence thresholds based on regime membership probabilities. Results reveal strong interactions between population size, climate, and urban connectivity. Dengue exhibits the lowest persistence thresholds, Zika intermediate thresholds, and chikungunya the highest thresholds. These findings demonstrate that pathogen persistence in modern urban systems cannot be described by a single deterministic population threshold. Instead, persistence emerges from the joint effects of demographic scale, environmental suitability, and network position within metapopulation systems. Author SummaryInfectious diseases often require a minimum population size to persist locally, a concept known as the critical community size (CCS). This idea was developed for relatively isolated populations, but modern cities form highly connected networks where diseases can repeatedly reappear even after local transmission disappears. In this study, we introduce the Empirical Persistence Threshold (EPT), a data-driven approach that replaces the idea of a single fixed threshold with a probabilistic description of persistence. Instead of focusing on case counts, we analyze how long transmission persists over time in each municipality. Using weekly data for dengue, chikungunya, and Zika across Brazil from 2017 to 2024, we identify distinct patterns of transmission persistence and estimate the population levels associated with sustained transmission. We also examine how these thresholds vary with climate and urban structure. Our results show that persistence depends not only on population size, but also on environmental conditions and the position of cities within the urban network.

BackgroundHIV transmission is characterised by a low per-act probability, a relatively high proportion of multiple variant transmission events, and a plateauing of transmission risk at high viral loads. No existing mechanistic model can simultaneously recapitulate all of these observations, thereby limiting our ability to predict unobserved transmission phenomena and evaluate prevention strategies. MethodsWe developed a suite of mathematical models that encode an empirically plausible set of transmission mechanisms and then fit these models within a Bayesian framework to available epidemiological data to identify which set of mechanisms are sufficient to recapitulate the data. Following formal model comparison, we embedded the best-fit model into a phylodynamic framework and calibrated it using Approximate Bayesian Computation, to assess whether phylogenetic trees from individual transmission pairs were both consistent with the model and informative. Finally, we further validated our most likely model against two large prospective studies (PARTNER1 and STEP). ResultsOur calibrated model predicts that for each systemic infection, approximately four to five transient infections occur--exposure events in which viral replication occurs but is stochastically extinguished--consistent with indirect empirical evidence from the STEP vaccine trial. The model predicts a transmission rate of fewer than 0.05 systemic infections per 100 couple-years follow up from individuals with undetectable viral load, providing a mechanistic basis for the negligible risk observed in the PART-NER1 study. The model also predicts a strong link between the number of viral particles transmitted and the number of variants establishing infection, modulated by the transmitters infection stage. Recalibrating for men who have sex with men indicated that higher transmission rates in this population are explained by a single parameter: a greater probability of permissive conditions for infection. These predictions emerge from a model in which three mechanisms were needed to explain the epidemiological data: highly infrequent permissive conditions within the exposed partner, stage-dependent differences in the probability that infected cells establish systemic infection, and target cell limitation at the site of infection. The model was further validated against phylogenetic data from 48 transmission pairs, where combining mechanistic and phylogenetic information sharpened posterior estimates of time since infection in the majority of cases. ConclusionThree biologically grounded mechanisms are sufficient to explain the key features of HIV transmission. The resulting model provides a principled and mechanistic basis for estimating transmission risk and for designing interventions to reduce it.

Spaceflight-Associated Neuro-ocular Syndrome (SANS) involves complex interactions between intracranial pressure (ICP), intraocular pressure (IOP), and cerebrospinal fluid (CSF) dynamics within the optic nerve subarachnoid space (ONSAS). While existing computational models address specific aspects of these interactions, they lack a comprehensive, system-level representation. To bridge this gap, we present the HEAD (Hemodynamic Eye-brain Associated Dynamics) model. By consistently integrating several previously proposed physiological sub-models, HEAD provides a unified lumped-parameter framework that fully couples cerebrovascular autoregulation, multi-territory ocular hemodynamics, and compartmentalized craniospinal-ONSAS CSF circulation under gravitational loading. This formulation enables the simultaneous analysis of eye-brain-CSF dynamics within a single computational tool. Model predictions were validated against experimental data from supine (0{degrees}) to head-down tilt (HDT, -30{degrees}) postures, accurately reproducing posture-dependent IOP increases and achieving an excellent ICP match against clinical benchmarks at the -6{degrees} HDT standard bed-rest angle. The coupled system predicts bed-specific ocular hemodynamic responses, with retinal blood flow exhibiting the largest relative increase under HDT compared to the ciliary and choroidal circulations. Crucially, explicitly modeling the ONSAS as a distinct compartment reveals a posture-dependent pressure drop of 1.89-3.69 mmHg between the intracranial and perioptic spaces. This compartmentalization yields a translaminar pressure profile that remains positive (8.05-11.83 mmHg) across all simulated conditions but is chronically reduced under sustained HDT. Ultimately, the HEAD model elucidates the physiological mechanisms linking gravitational stress to translaminar mechanics, providing a robust computational foundation to investigate SANS and supply boundary conditions for structural models of the optic nerve head.

Ordinary differential equation models of biochemical reactions are often formulated as stoichiometric systems in which the dynamics arise from a collection of interacting processes. A central challenge is that the functional form of each process is rarely known a priori and may be difficult to infer from data. We propose biochemically informed neural ordinary differential equations (BINODEs), a neural-ODE framework that retains the stoichiometric structure of mechanistic models while representing individual processes by neural networks. In BINODEs, the outputs of neural network processes (NNPs) are mapped to state derivatives through a linear layer analogous to a stoichiometric matrix. This architecture allows biological side information, such as process-specific inputs, sign constraints, and monotonicity assumptions, to be built directly into the model. We characterize the approximation properties of NNPs for several standard biochemical rate laws and show that the proposed framework recovers both trajectories and process-level structure in Monod, Lotka-Volterra, pharmacokinetic, and ultradian endocrine models. These results suggest that BINODEs offer a useful compromise between mechanistic interpretability and data-driven flexibility for modeling partially known biochemical or biological dynamical systems.

Fuel availability and fuel dryness are consistently shown to be the primary drivers of wildfire intensity and burnt area. Here we hypothesise that differences in the timing of fuel build up and drying determine the optimal time for wildfire occurrence. We use gross primary production (GPP) as a measure of biomass production and hence fuel availability, and vapour pressure deficit (VPD) as a measure of fuel drying. We use the phase difference in the seasonal time course and magnitude of GPP and VPD to cluster regions that should therefore have distinct wildfire behaviour. We then show that each of the resultant clusters is distinctive in terms of one or more fire properties, specifically number of ignitions, burnt area, size, speed, duration, intensity, and length of the wildfire season. The emergence of distinct regimes as a function of two biophysical drivers reflects the fact that both vegetation and wildfire properties are a consequence of eco-evolutionary adaptions to environmental conditions. We then examine the degree to which human activities or vegetation properties modify these fire regimes within each of these clusters. Variability in GPP and VPD largely explains the within-cluster variation in fire properties. The type of vegetation cover has an influence on burnt area and carbon emissions in particular, while human activities are more important for fire properties such as size, rate of spread and duration largely through their influence of landscape fragmentation. Although both human activities and vegetation properties modify wildfire regimes, the ability to distinguish wildfire regimes using GPP and VPD alone emphasizes that land management, fire use and fire suppression are constrained by environmental conditions. This eco-evolutionary optimality approach to characterising wildfire regimes provides a basis for designing a simple fire model for Earth System modelling.

Coinfection of COVID-19 and malaria in endemic regions may generate complex epidemiological interactions that influence susceptibility patterns, disease burden, and outbreak risk. Although malaria-acquired immunity has been hypothesized to modulate host responses to other infections, its population-level implications for COVID-19 transmission under uncertainty remain insufficiently understood. In this study, we develop a deterministic-stochastic compartmental model for the coupled dynamics of COVID-19, malaria, and their co-infection. Malaria-acquired partial immunity is incorporated through a relative susceptibility parameter that reduces the risk of COVID-19 infection among malaria-recovered individuals. For the deterministic system, we establish positivity, boundedness, an invariant feasible region, and basic reproduction numbers for the COVID-19-only and malaria-only subsystems. We then use numerical simulations to examine how immunity-mediated reductions in susceptibility may influence COVID-19 incidence, peak burden, hospitalization, and cumulative mortality. To account for environmental and transmission variability, we extend the deterministic model to an Ito stochastic differential equation framework and use repeated realizations to characterize uncertainty in epidemic trajectories, peak distributions, and outbreak risk. In addition, global sensitivity analysis based on partial rank correlation coefficients (PRCCs) is performed to identify the parameters with the greatest influence on COVID-19 outcomes. Our results suggest that, under the assumed modeling framework, malaria-acquired partial immunity may reduce the peak infectious burden and cumulative mortality associated with COVID-19. The stochastic simulations further show substantial variability around deterministic trajectories and indicate a non-negligible probability of large outbreak events that are not fully captured by mean-field predictions alone. Overall, the proposed framework provides an uncertainty-aware, mechanistic basis for studying COVID-19-malaria co-dynamics and for assessing how interacting disease processes may shape epidemic outcomes in endemic settings.

There is growing recognition that host behavioral responses to disease risk are critical factors driving disease dynamics, but understanding how behavioral responses influence dynamics remains a major challenge. Coupled behavioral and epidemiological models commonly assume that hosts use population prevalence as an indicator of disease risk. However, real-world estimates of prevalence come from data aggregated over coarse spatial scales, while transmission occurs through fine-scale contacts. Fine-scale changes in movement behavior represent an important type of risk response because individuals must use proxies for infection risk, such as host density or environmental factors, whose relationship with actual transmission risk may vary across contexts. In this study, we examine the consequences of using diierent risk proxies to inform fine-scale movement and determine when and if relying on imperfect proxies can cause risk-averse behaviors to increase, rather than decrease, disease transmission relative to no behavioral change. We examine the effect of three risk proxies - local prevalence, local host density, and local transmission coefficient (i.e., "place") - in the context of "simple trips", where individuals may respond to disease risk by altering rates of travel from home to "away" locations and back. In one case, individuals stay home more frequently (an absolute risk response) and in the other case, individuals shift their travel to less risky, away locations (a relative risk response). Absolute responses were far more effective in reducing prevalence than relative responses, which were detrimental in some parameter regimes. Detrimental responses occurred when information used to perceive risk was mismatched with the mode of transmission (either density-dependent or frequency-dependent), such that individuals either failed to use pertinent information or used irrelevant information. Imperfect information thus plays a critical role in determining whether behavioral response reduces or elevates disease risk.