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

Buruli ulcer (BU) is a neglected tropical skin disease caused by infection with Mycobacterium ulcerans. The mode of its transmission into the skin has not been fully clarified, but it is believed to involve mechanical transfer, perhaps by insect bites. M. ulcerans secretes a toxin called mycolactone which causes necrosis of the skin and formation of large skin lesions. Understanding the development of these skin lesions over time is crucial to understand the pathogenesis of BU. We formulate a mathematical model to describe the space-time dynamics of M. ulcerans bacteria, mycolactone and skin cell densities as well as fibrin deposition. We investigate the relative contributions to ulcer formation of direct cytotoxicity of mycolactone and ischaemia following the loss of coagulation control. Our results are consistent with existing biological evidence that higher mycolactone concentrations accelerate cell death. Furthermore, the model indicates that the rate of wound expansion is primarily controlled by the diffusion and net birth rate of bacteria, which sets the overall scaling for the speed of wound expansion, along with two dimensionless constants that define the shape of the trajectory of wound edge position against time, namely the ratio of the mycolactone diffusion coefficient to the bacterial diffusion coefficient, and the ratio of the mycolactone degradation rate to the bacterial net birth rate. When mycolactone diffuses significantly faster than bacteria spread or when mycolactone degrades more slowly than bacteria reproduce, the initial development of the wound is faster. In contrast, the long-term wound expansion speed appears to be relatively unchanged across a wide range of the dimensionless parameters.

We develop a general geometrical framework for growth processes in which the growth rate depends exponentially on the number of active growth-supporting components. The framework separates the fraction of active components from the size of the accessible component space, allowing qualitatively different growth laws to arise from the same underlying construction. Bacterial population growth provides an example of a fixed-size component space controlled primarily by activation and deactivation, whereas examples such as human population growth or speciation provide an expanding component space in which interactions between individuals promote further growth. This motivates a Replicative geometrical law, dX/dt= X exp({beta} X^{gamma}), whose exponent characterizes the scaling of the effective growth-supporting component space and is tested against historical human-population regimes and eukaryotic lineage-through-time data. For innovation indicators such as patents and arXiv manuscript submissions, where an existing item need not itself reproduce, the same construction motivates a Direct Geometrical production law without the prefactor X. The framework therefore provides a common description of fixed and expanding component spaces while distinguishing Replicative from Direct Geometrical growth.

Healing of the gastrointestinal (GI) tract following surgical interventions is governed by coupled mechanobiological processes and may lead to severe complications such as perforation or stricture formation. A first comprehensive mechanobiological modeling framework of GI healing is herein proposed. The framework addresses two clinically relevant applications of bioprinting: endoscopic treatment of GI tissue defects and bioprinting-assisted surgical anastomosis. Tissue remodeling is based upon a hyperelastic material model with fiber dispersion coupling the spatiotemporal reaction diffusion dynamics of fibroblasts and cytokines with collagen deposition, reorientation, and plastic deformation. An active stress formulation drives fibroblasts and myofibroblast contraction while a multiplicative decomposition approach is adopted for collagen remodeling as a permanent change. The governing equations are discretised in time with an implicit Euler scheme, finite element in space and solved by a staggered algorithm implemented in the open-source platform FEniCS. Numerical simulations show that the initial collagen fibers content and orientation strongly influence fibroblast infiltration and scar contracture formation. The study quantifies the advantage of having a collagen bioprinted architecture aligned with tissue fibers, to reduce structural remodeling distortion. The model also predicts a strong correlation between collagen deposition and luminal burst pressure during the recovery of mechanical integrity in GI anastomosis.

Large shear deformation in cartilage can lead to tissue failure and injury, which are often precursors to diseases such as post-traumatic osteoarthritis. Under shear, cartilage strain-stiffens prior to failure, which makes stiffening an important indicator of changes to the loading of the extracellular matrix that gives rise to this tissue's properties. While a variety of stiffening mechanisms ranging from uncrimping to fiber-alignment have been explored, whether such mechanisms apply to the depth dependent shear strain stiffening in articular cartilage remains poorly understood. Here, we present experiments and theory that support the idea that the strain-stiffening behavior is caused by a mechanical phase transition from a random isotropic network whose mechanics arise primarily from bending-dominated modes to one where the mechanics arise from stretching-dominated modes. Indeed, consistent with network model predictions, we find that stress-strain data for all depths can be collapsed onto a single universal curve that diverges at a depth-dependent critical strain. These results show that increasing the local concentration of collagen, which constitutes the primary load-bearing network in cartilage, decreases the critical strain at which the strain-stiffening transition occurs, while increasing the low-strain elastic modulus. Furthermore, we demonstrate that bulk compression leads to a higher critical strain and decreased low-strain elastic modulus. Network simulations capture this rich behavior, and indicate that under compression the network collapses, which allows for larger strains before the transition from bending-dominated to stretching-dominated mechanics occurs. Collectively, these findings shed light on the roles that tissue composition and axial strain play in the mechanisms that organize how articular cartilage stiffens during the lead-up to injury.

Devireddy et al. [1] previously showed that an enthalpy-based, macroscale model simulated tissue freezing histories are in close agreement with a coupled model incorporating cellular water transport and intracellular ice formation (IIF). That comparison, however, was performed for a limited set of tissue geometries, cooling conditions, and biophysical parameters. Here, we revisit that conclusion by reimplementing the published model from its governing equations and systematically expanding the parameter space to determine when microscale processes alter the predicted macroscale freezing response. We incorporate both surface catalyzed nucleation (SCN) and volume catalyzed nucleation (VCN) of intracellular ice with cellular osmotic dehydration and examine a broad range of tissue dimensions, cooling rates, convective boundary conditions, membrane permeabilities, cell sizes, activation energies, intracellular water fractions, and nucleation rates. Linearization of the cellular water transport equation about osmotic equilibrium yields an osmotic relaxation timethat can be compared with the local residence time of tissue undergoing phase change. Their ratio defines a dimensionless group, that organizes the transition between regimes in which the uncoupled enthalpy formulation and the coupled micro and macroscale formulation produce similar or substantially different results. Across the one-dimensional parameter space examined here, the two models remain within a prescribed thermal-error bound for the dimensionless group below approximately 0.1, whereas the discrepancy increases systematically above this threshold. Model divergence also depends on intracellular ice nucleation, i.e., when nucleation is sufficiently slow, cellular water transport can become rate limiting for latent heat release. Conversely, sufficiently rapid intracellular ice formation reduces the macroscopic discrepancy by providing an additional pathway for latent-heat release. Multidimensional simulations further show that geometry alone can move a nominally conventional freezing protocol into the coupled regime. In particular, multidirectional cooling can reduce the local residence time sufficiently to produce substantial differences in predicted frozen volume even when the corresponding thermal histories appear similar. Finally, we formulate an inverse approach for estimating IIF parameters from tissue scale thermal histories. Synthetic simulations indicate that parameter recovery is feasible within a finite range of cooling conditions, providing a testable strategy for future experimental measurements. Together, these results provide a mechanistic criterion for deciding when microscale biophysical processes must be retained in macroscale tissue-freezing models.

We investigate the dynamics of the spread of the infection due to a phage- during the range expansion of an E coli colony. We find a rich panoply of spatio-temporal dynamics at large colony-level length scales, arising due to the interplay of mechanical forces, growth and viral infection dynamics at smaller cellular length scales. Strikingly, the phages "surf" the front of the growing bacterial colony by hitchhiking on E coli that are advected due to the growth of bacteria in the colony, resulting in an anisotropic spread of the phages. We identify microscopic processes - of the phage release during lysis (occurring on short millisecond timescales at length scales close to that of a single bacterium) and local nematic alignment of the rod-like E coli bacteria (occurring on timescales comparable to the bacterial growth rate and the length scales of a few bacterial cells) - that enhance the advective effects driving the hitchhiking behavior. Combining our experiments with a mathematical model, we explain the multiple spatio-temporal dynamical regimes - from the coexistence of uninfected bacteria, resistant (lysogenic) cells and phages, to fixed points where the entire population turns resistant or remains uninfected. Our work broaches a new frontier in the investigation of eco-evolutionary processes arising from the mechanical and ecological forces due to the interactions between viruses and their hosts.

Purpose: We introduce the Temporal Index of Divergent Evidence (TIDE), a metric that evaluates how the topic center of gravity of a corresponding corpus of literature aligns with, or shifts relative to, a recommendation's semantics over time. Methods: TIDE computes annual mean cosine similarity using MedCPT embedding vectors between a recommendation and corresponding PubMed records binned by year (2000-2024), testing for monotonic temporal trend (Kendall {tau}). Three recommendations with expected divergent, stable, and convergent trajectories were examined: two-stage exchange for periprosthetic joint infection (PJI), emergent fasciotomy for acute compartment syndrome (ACS), and non-operative management of distal radius fractures (DRF) in adults [≥] 65 years. The signal was characterized by an additive per-token attribution, an isolated vs. in-context analysis, and an adversarial minimal-pair test. Results: PJI diverged ({tau} = -0.84, year-shuffle p = 0.001), DRF converged ({tau} = +0.42, p = 0.005), and ACS showed no detectable trend ({tau} = -0.07, p = 0.66). The two significant directions (PJI, DRF) held under matched input [CLS] pooling, while ACS remained near zero. Publication volume baselines did not distinguish the three trajectories (publication count was universally positive, {tau} = +0.77 to +0.97). A reversed-meaning minimal-pair control showed little cosine sensitivity to reversal. Paper-level TF-IDF recovered the qualitative three-case pattern. Conclusion: Embedding-based drift analysis is a proof-of-concept candidate pre-triage signal that tracks topical alignment, not evidentiary direction; superiority over TF-IDF remains unproven. The present study is hypothesis-generating, showing potential use of embedding representations as an analytical unit rather than simply for retrieval.

Background. Classical macroparasite models commonly represent worm burden heterogeneity through prescribed Poisson or negative-binomial (NB) distributions, while transmission dynamics are formulated in terms of aggregate quantities such as mean worm burden and prevalence. We revisit these assumptions using a stratified worm burden (SWB) framework that explicitly tracks the distribution of parasite burdens across heterogeneous host classes and allows demographic turnover, transmission, and interventions to be analyzed within a unified model. Methods. We derive equilibrium distributions of the SWB system under homogeneous and heterogeneous infection processes and compare them with the classical Poisson and NB distributions used in macroparasite epidemiology and control policymaking. The framework is then extended to include host demography, coupled human-snail transmission dynamics, and periodic mass drug administration (MDA). Corresponding SWB and NB-type MacDonald models are calibrated to comparable endemic prevalence and mean worm burden, allowing direct comparison of potential transmission breakpoints and intervention outcomes. Results. In the absence of demographic turnover, the SWB framework naturally generates Poisson and NB equilibrium distributions as limiting cases of homogeneous and heterogeneous infection processes. Incorporating demographic recruitment and mortality alters these benchmark distributions, producing endemic burden structures that differ systematically from their classical counterparts. Analysis of coupled human-snail systems reveals that transmission breakpoints and bistable equilibria occur only within a relatively restricted region of SWB parameter space. In contrast, comparable NB-MacDonald formulations exhibit breakpoint behavior over substantially broader parameter ranges with the net effect of overestimating the likelihood of interruption of transmission. Although calibrated models can reproduce near identical endemic prevalence and mean worm burden, they often generate markedly different responses to MDA, including differences in rebound dynamics, persistence, and elimination thresholds. Conclusions. The SWB framework links classical statistical descriptions of worm aggregation to mechanistic burden-resolved population dynamics, clarifying how endemic distributions emerge and how they are modified by demography and control interventions. Our results suggest that transmission breakpoints are not a universal feature of helminth systems but depend strongly on model structure, and that predictions of elimination and post-treatment recovery may be considerably more model-dependent than implied by prevalence-based calibration alone. The SWB approach therefore provides a flexible alternative framework for evaluating parasite transmission dynamics and predicting the outcomes of control strategies.

Behavioral variability reflects differences in internal and external parameters and provides a substrate for natural selection. However, uncovering its structure is challenging because behavior evolves nonlinearly across multiple timescales. Our goal is to reconstruct phenotypic variation from finite behavioral observations without prescribing the scales at which individuals should be compared. To achieve this, we introduce a multiscale dissimilarity that compares dynamics across all statistically resolvable resolutions by constructing reduced transfer operators at progressively finer scales and weighting their differences by finite-sampling uncertainty. This dissimilarity defines a geometry of dynamical phenotypes, which we reconstruct using diffusion maps. We show that the resulting phenotypic coordinates locally follow the parameter directions to which dynamics are most sensitive. We validate our approach in a stochastic model and apply it to bacterial and larval zebrafish behavior. In bacteria, we identify run speed as a major component of inter-individual variability, associated with the chemotaxis protein CheB. In zebrafish, we find that prior prey experience reshapes behavioral dynamics and phenotypic variability, with paramecia experience concentrating fish in a prey-capture-associated region of phenotypic space. Together, these results provide a framework for identifying internal and environmental variables that structure dynamical phenotypes across scales.

Despite lacking a dedicated structural function, brain tissue is exposed to severe mechanical loading during accidents and trauma, with potentially permanent or lethal consequences. Therefore, characterizing its mechanical behavior assumes particular importance for designing protective equipment, planning surgeries, and training neurosurgeons, tasks that often rely on physical brain replicas made from phantom materials. Although the mechanics of brain tissue has been extensively studied, the selection of suitable phantom materials still relies on simplified metrics that fail to capture the highly nonlinear and rate-dependent behavior of the brain. In this work, we characterize the mechanical response at low-to-medium strain rates of common synthetic brain phantom materials, including Sylgard 527, Ecoflex Gel, and a composite hydrogel, and establish rigorous comparisons with porcine brain tissue as a benchmark. To this end, we employ a multi-step stress relaxation protocol under both uniaxial extension and compression across two different strain rates, introduce thermodynamic metrics, and perform comparisons based on rigorous statistical analysis. In particular, we isolate the thermodynamic equilibrium stress-strain curves, representing the baseline material's response, from rate-dependent dissipative inelastic effects, relatable to viscoelastic and poroelastic mechanisms. Our results provide a thorough comparison, revealing critical limitations in existing simulant materials and highlighting significant space for developing improved brain surrogates. The comprehensive dataset collected can also support the calibration of constitutive models, enhancing the predictive accuracy of numerical simulations involving brain tissue and its surrogates. More broadly, this study highlights the need to move beyond simplistic, scalar-metric-based comparisons of mechanical responses across materials.

Allergic conjunctivitis is an inflammation of the conjunctiva caused by allergen; it is common disorder affecting up to 40% of the population. In this work, we study seasonal allergic conjunctivitis (SAC), also called "hay fever eyes", which is caused by exposure to airborne pollens. We develop a mathematical model quantifying the ocular immune system response to the allergens. First, we present a simplified qualitative description of the immunopathogenesis of SAC. Then, we express each chosen immunopathological mechanism mathematically to construct a system of thirty-one ordinary differential equations. We compare summary statistics of the predicted observable immune signals to experimental measurements and find our model captures key qualitative features of SAC progression. We then compare our predicted time series of histamine concentration to symptom scores and find a strong correlation suggesting the model predicts relevant clinically trends. Next, we calibrate the model through multi-step process. We find the most influential parameters are the production and depletion rates of IL-4, and the production rates of IL-5 and IL-8. These cytokines are targeted in treatments for asthma, atopic dermatitis, and severe eosinophilic associated disorder and suggest potential therapeutic targets for SAC. Our calibrated model mimics most of the summary statistics of the experimentally observable immune signals with discrepancies for IL-5 and IL-13 indicating that additional immunopathological mechanisms could be important.

Clathrin-mediated endocytosis (CME) is the primary pathway for internalization of extracellular and membrane cargo in eukaryotic cells. It is characterized by a patch of the plasma membrane invaginating and pinching off to generate a cytoplasmic vesicle. Recently, experimental evidence has begun to accumulate in support of proteins assembling into liquid-like condensates at nascent CME sites, but potential functional consequences are not understood. Given that condensate capillary forces can influence membrane bending, we constructed complementary analytical and numerical model systems to probe the mechanical influence of a protein droplet on endocytosis. Model evaluations and analysis reveal that a droplet can regulate the progression of endocytosis by stalling invagination until the droplet grows past a threshold size. After the droplet-mediated brake is released, the droplet provides a force that can drive the membrane bud toward scission. Thus, we propose a ``mechanical timer'' mechanism as a function for protein phase separation in cellular membrane trafficking.

Phase separating biopolymers are often described by the sticker-spacer model, which accounts for non-attractive linkers that connect discrete attractive moieties. "Associative polymer" theories describe these systems as two coexisting fluids of stickers and spacers, respectively. In such theories the stickers and spacers are decoupled in the sense that sticker binding does not affect spacer conformations or vice versa. Informed by coarse-grained simulations, we develop a phenomenological mean-field theory to determine the microscopic coupling between the sticker and spacer degrees of freedom. Accounting for linkers connecting adjacent spacers introduces free energy contributions due to conformational entropy of the spacer and the binding combinatorics of the stickers. These contributions have opposite dependencies on spacer length because longer spacers allow a greater volume to search for binding partners but incur a greater entropy cost upon bond formation. The length dependent terms from these contributions cancel leaving a length-independent elastic term arising from the fact that a small amount of spacer stretching lowers the free energy by increasing the number of possible binding partners. The cancellation of spacer length from the theory justifies the decoupling approximation and supports mean-field treatments of heterogeneous spacers.

We propose a minimal mathematical framework to describe the go-or-grow dynamics of tumor cells comprising two phenotypically distinct populations. One population is migratory and undergoes constant diffusion, while the other proliferates in an oxygen-dependent manner. The local oxygen concentration governs transitions between these phenotypes. We then ask whether the time scale of cyclic hypoxia, where oxygen is spatially homogeneous but fluctuates between normoxic and hypoxic levels over time, alters the dynamics of the reduced generalist model in the fast phenotype-switching regime compared with the full go-or-grow model. We observe that the reduced generalist phenotype model fails to capture the go-or-grow dynamics under rapid oxygen fluctuations. Our results predict that the tumor growth rate increases in the generalist-phenotype model under rapid oxygen fluctuations compared with tumors of the proposed go-or-grow model. We then explore whether oxygen consumption, which leads to spatial heterogeneity in oxygen concentration, plays a role in distinguishing the dynamics of the reduced model from the proposed go-or-grow model. We demonstrate that the tumor in the proposed go-or-grow model exhibits a higher growth rate than the tumor in the reduced generalist-phenotype model under a slow oxygen consumption rate.

Dense, well-ordered material states of proteins form the amyloid fibers that are a hallmark of neurodegenerative disease in the brain. Beyond forming amyloid fibers, some of these proteins can also adopt other material states termed condensates which are initially liquid-like but evolve to a soft, glassy phase. Fiber growth requires a large supply of monomers and, thus, it is often speculated that fibers emerge from within a dense condensate as it ages and its microscopic dynamics slow into a glassy state. Here, we use the well-established model system Fused in Sarcoma (FUS) to directly observe, quantify and theoretically describe fiber growth and its interplay with condensates. We report the discovery that fibers grow overwhelmingly in the dilute phase surrounding the condensates while the condensates concurrently evolve to a glassy arrested solid. The resulting protein fibers and glassy condensates are both distinct solid-like phases that coexist but do not directly interconvert. Taken together, these findings reveal that there are two competitive aging pathways in FUS condensation that are linked through phase separation kinetics.

Cells use ATP-driven chaperones to extract clients from biomolecular condensates selectively, yet no closed-form criterion links molecular parameters to condensate quality control. We derive a minimal non-equilibrium sorting reactor model that reduces the reaction-diffusion dynamics to one algebraic equation. In the idealized low-load limit, a concentration-dependent partition coefficient produces a saddle-node bifurcation between functional clearance and pathological storage. The critical Damk\"ohler number is \(\mathrm{Da}_{0c}=e^{-2}\) and is independent of the feedback strength. Corrections shift the value but preserve the topology. The model predicts a Kramers-type functional lifetime and recovery costs that scale as \(R^3\). Critical slowing down near the bifurcation provides early-warning signatures for FCS and FRAP.

The emergence of treatment resistant mutants is one of the primary contributors to therapy failure in cancer. Evolution-based adaptive therapies aim to exploit the competition between sensitive and resistant cells to prolong therapeutic control. However, in the densely packed tissues of solid tumors, competition is not only determined by cell-intrinsic factors but also a result of local physical interactions between neighboring cells. The successful development of physics-informed adaptive therapies therefore hinges upon the bottom-up integration of tissue mechanics and experimentally grounded models of tumor evolution. Here, we show how population-level treatment response emerges from mechanical interactions between individual cells. Combining genetically tailored therapy-mimicry experiments in spatially structured 2D melanoma colonies with mechanistic, particle-based tissue simulations as digital twins in a real-to-sim-to-real framework, we reveal how treatment-induced changes in mechanical crowding shape a cascade of resistance expansion, spatial competitive escape, and consequent therapy failure. We then link these underlying physical mechanisms to population-level observables in an abstracted mathematical model for reinforcement-learning-based therapy optimization and a distilled treatment-decision-heuristic, which we test experimentally. Together, our results identify mechanical crowding and escape as governing principles of resistance-mediated therapy failure in solid tumours and provide a basis for mechanistically informed, evolution-based treatment strategies.

Vascular remodeling responds to local wall shear stress, but transport efficiency belongs to the network as a whole. We connect these scales by minimizing dissipation under a fixed maintenance budget, with vessel cost proportional to mass raised to an exponent b. At an optimum, dissipated power is proportional to vessel cost. This yields the shear set point |{tau} | {propto} r^(b-1){ell}^(b-1)/2 for radius r and length {ell}, with uniform shear recovered at b = 1. The associated local adaptation rule decreases the global functional, although the topology it reaches retains a memory of development. Simulations with 400 and 700 sinks show that staged growth improves transport mainly by allowing pruned connections to regrow. Fluctuating demand sustains loops without increasing the maintenance budget. The local condition fixes allocation on a given support, whereas growth and variable demand shape the topology that survives.

Objective A diversity of approaches and cohorts have been published in research literature for suicide risk estimation, leading to some uncertainty around which factors and conditions are most strongly contributing to risk. Methods exist for weighting estimates by propensity score, removing simplifying the interpretation of model effects. Few studies have explored the use of these tools to assess when the effect of certain factors is uncertain or inconsistent. Method A mix of 1,001,737 suicide decedents and living patients were evaluated for suicide risk, relying on a subset of commonly identified factors: demographics, psychiatric conditions, substance use disorders, and social needs. Care utilization patterns were then assessed controlling for these factors in a hospital care setting. Four methods were considered for controlling multivariate confounding of odds predicting death by suicide: multivariate logistic regression, 1-to-1 sample matching, inverse propensity weighting (IPTW), and entropy balancing (EBAL). Results Test statistics showed suicide decedents were much more likely to have various psychiatric and substance use diagnoses, social needs and more likely to heightened care utilization across sampling intervals. Greater utilization was found close to date of death. Effect sizes after IPTW and EBAL weighting were also generally greater than would have been documented by regression alone. Conclusions Propensity weighting is a useful alternative to exploring nuanced effects, especially when the direction and strength of an association differ from traditional statistics. By weighting, the overall imbalance of cases remains consistent and effect terms might reflect more nuanced associations than regression or sample matching alone.

Nitrogen dioxide (NO2) is a widespread air pollutant associated with the risk and prevalence of various respiratory infectious diseases. Epidemiological studies have reported associations between NO2 exposure and COVID-19 incidence, and biological evidence indicates that NO2 exposure increases vulnerability to infection. Motivated by these findings and by the scarcity of mechanistic epidemic models that incorporate air pollutant data, here we introduce an NO2- and mobility-informed metapopulation model and study the first COVID-19 wave in Oklahoma. County-level NO2 concentrations enter the infection rates through a first-order parameterization, alongside high-resolution mobility patterns capturing heterogeneous inter-county connectivity. Using numerical simulations, we demonstrate that higher environmental sensitivity produces earlier and more synchronized outbreaks across counties, while lower sensitivity yields delayed, asynchronous trajectories. When fitted to county-level COVID-19 incidence data, our model outperformed the classic SIR model (fitted independently in each county) in over 75% of counties in Oklahoma across all standard error metrics. The improvements were even more pronounced in forecasting tasks across epidemic stages, with county-level win rates against the SIR model of 59.74% (surge), 87.01% (peak), 80.52% (post-peak), and 88.31% (decline) by nRMSE. To isolate the contribution of NO2, we compared our model against a mobility-only model with NO2 removed and homogeneous infection rates across counties. The NO2 term improved county-level forecasts during the surge (94.81% of counties by nRMSE), post-peak (88.31%), and peak (62.34%) stages, though not during the early and decline stages, suggesting that NO2 information can generate better forecasts than mobility alone during periods of high incidence. Our results demonstrate that environmental exposure can enter the transmission structure of a mechanistic epidemic model directly and that doing so yields measurable forecasting gains.