Frontiers in Applied Mathematics and Statistics

Patients suffering from sepsis need to be treated with an effective antibiotic therapy within the first hour after sepsis onset to decrease their risk of death. Microbiological data that provide information about the suitability of antibiotic therapies, however, is usually available only after 72 hours. Consequently, the treating physicians need to judge a therapy's effectiveness based on the patients' measured health records and their general health condition. This medical assessment is complex and requires years of experience. In our study, we investigate how statistical modeling can contribute to assessing the effectiveness of antibiotic therapies. To that purpose, we describe the effectiveness of antibiotic therapies by modeling sepsis patients' health conditions using a three-state continuous-time hidden Markov model (ctHMM). In literature, procalcitonin (PCT) and lactate have proven to be helpful for deriving the health condition in this context. The state probabilities obtained by the ctHMM are subsequently used to quantify the effectiveness of antibiotic therapies. To this end, we apply two different approaches, namely (i) averaging of the state probabilities and (ii) a logistic regression model. For (i), we calculate the average of the state probabilities for the state indicating a sepsis-free condition over an antibiotic administration period of 48 hours. For (ii), we use the information about antibiotic susceptibility testings as dependent variable in the logistic regression model; as independent variables, we calculate the difference between state probabilities at the start of antibiotic administration and 48 hours later. With this work, we are able to better understand the relationship between laboratory values, in particular PCT and lactate, and the patients' health condition. We further provide approaches for quantifying the effectiveness. Therefore, our work contributes to developing a clinical decision support system which helps physicians assess the effectiveness of antibiotic therapies in patients with sepsis. Supported by such a system, a physician is able to quickly adjust an ineffective therapy which avoids antibiotic resistances and increases a patient's chance to survive a sepsis.

We develop a mathematical model of Rift Valley Fever integrating mosquito vectors, ruminants, and humans, based on an SEIR-type structure with vertical transmission in vectors. Local data from the Sudanian and especially the Sahelian zones are used to capture the impact of climatic variations on mosquito population dynamics. The mathematical analysis establishes the models positivity, determines the basic reproduction number R0, and demonstrates the local and global stability of the disease-free equilibrium. Sensitivity analysis (PRCC) highlights the most influential parameters, while the stochastic approach using a continuous-time Markov chain confirms the major role of seasonal rainfall. Numerical simulations reveal a peak in animal and human infections around the 9th month, correlating with periods of heavy rainfall. This model provides a relevant tool for surveillance and prevention within a "One Health" approach in Chad.

In this paper, we propose a new model to estimate the impact of an intervention on human hosts of a vector-borne infection, such as dengue, which occurs in yearly outbreaks of different magnitudes. The model applies to these outbreaks and, in fact, is independent of their intensity, that is, it does not require the steady-state assumption. The model takes as input the officially reported age-dependent number of cases of a vector-borne infection. It is deterministic and does not account for stochasticity. Our objective is to estimate the impact of the intervention (the efficacy), and we rely on the observed fact that the age distribution of the proportion of cases of the infections transmitted by the same vector is independent of both the intensity of transmission and the geographic area studied, at least for Brazilian regions. This finding is highlighted in the main text and forms the basis of our calculations. A hypothetical intervention is simulated using a dengue vaccine, which allows the determination of the optimal strategy for a vaccination campaign.

The aim of this paper is to model homeless accommodation settings to investigate how vaccination mitigates the outbreaks, highlighting the importance of vaccination in vulnerable settings. We estimate the daily per capita contact rate with wider community, the internal transmission rate, and the achieved vaccine coverage. We present stochastic simulation of the final size of disease outbreaks given choices of internal and external transmission. We conclude that vaccine that has effect in reducing transmission will mitigate the outbreak in homeless hostels but it will have better results when the household population has large vaccination coverage, which may lead to more cost from the health economic perspective.

Abstract Purpose This study introduces a novel approach to address unmeasured confounding in terminal event studies using the prior event rate ratio (PERR) method. The proposed approach PERR_{proxy} used a proxy event to replace the original terminal event in the pre-exposure period, enabling the application of PERR in terminal event settings. Additionally, we also applied difference in difference (DID) regression, which is conceptually analogous to PERR to estimate the standard errors and confidence intervals of PERR_{proxy}. Methods We conducted numeric simulations to evaluate the validity of PERR_{proxy} approach and assessed its performance under varying levels of unmeasured confounding effects, baseline hazard ratios, and the correlation between the proxy and terminal events. To demonstrate its practical applicability, we also performed an empirical analysis to investigate the impact of severe hospitalized COVID-19 on circulatory system disease mortality using the PERR_{proxy}. Results In simulation studies, PERR_{proxy} effectively reduced the unmeasured confounding effects compared to the conventional methods. The performance of PERR_{proxy} was influenced by the strength of unmeasured confounding, baseline hazard ratios, and the correlation between the proxy and terminal outcomes. In addition, difference in difference (DID) regression had much faster computational speed for estimating standard errors and confidence intervals compared to bootstrap. In the empirical analysis, PERR_{proxy} identified that severe hospitalized COVID-19 as a significant risk factor for the circulatory system disease mortality and reduced the unmeasured confounding effects. Conclusions The PERR_{proxy} approach extends the applicability of the original PERR method to terminal event studies, offering a promising solution for addressing unmeasured confounding. Additionally, the DID regression framework provides a computationally efficient alternative for parameter estimation in PERR-based studies. However, careful consideration is still required in PERR_{proxy} for proxy events selection and other underlying assumptions of the PERR method to ensure valid results. Keywords: prior event rate ratio, unmeasured confounding, proxy event, terminal event study, observational study, electronic health records

The impact of weather on the health of Americans and the American health system is substantial. Using available health and economic data, we developed a data-driven scenario that describes a compounded heat emergency in an archetypal community in the United States. We then characterize the potential human and economic costs of such a heat emergency to demonstrate the widespread impact on health outcomes, health systems, and society.

Diagnosed diabetes affects approximately 38.4 million Americans, but its burden is not evenly distributed across U.S. counties. Existing machine-learning studies have mainly focused on individual risk prediction using biometric, clinical, or survey variables. These approaches are less suited to explaining why diagnosed diabetes prevalence differs geographically across counties. We developed an explainable gradient-boosting framework for predicting county-level diagnosed diabetes prevalence across 2,957 U.S. counties using an ecological cross-sectional design. The analysis integrated food-environment, socioeconomic, occupational, demographic, health-behavior, and clinical indicators from five public data sources. Four regression models were compared: Elastic Net, Random Forest, XGBoost, and LightGBM. LightGBM was selected as the primary model based on validation-set RMSE and interpreted using SHAP TreeExplainer. The validation-selected LightGBM model achieved a held-out test RMSE of 0.423 percentage points, R{superscript 2} = 0.964, and MAPE = 2.76%. Although XGBoost achieved a lower test RMSE of 0.399 and R{superscript 2} = 0.968, it was retained as a secondary benchmark because primary-model selection was based only on validation performance. A sensitivity model using only structural and contextual predictors, and excluding CDC PLACES health-behavior and clinical covariates, retained substantial predictive performance (R{superscript 2} = 0.827). Poverty rate was the most frequent dominant positive structural SHAP contributor nationally (n = 772 counties, 26.1%), followed by food insecurity rate (n = 707, 23.9%), Supplemental Nutrition Assistance Program (SNAP) participation rate (n = 316, 10.7%), unemployment rate (n = 224, 7.6%), and median household income (n = 178, 6.0%). Residual Morans I decreased from 0.665 to 0.069 after model fitting. Explainable machine learning using public county-level data can characterize geographic variation in diagnosed diabetes prevalence. County-level SHAP maps may support local hypothesis generation, but should be interpreted as explanations of model predictions rather than causal effects.

Introduction: Climate change disproportionately affects disadvantaged communities, yet construction workforce education rarely addresses interconnected pathways linking energy efficiency, nature exposure, and public health. Green-blue infrastructure delivers co-optimized benefits: reducing building energy consumption 15-30% while decreasing heat-related mortality by approximately 3.9% per degree Celsius of urban cooling (Gasparrini et al., 2017) -- epidemiological benchmarks that inform the dose-response functions embedded in the Ecosystem Justice Translator (EJT). This protocol describes, to our knowledge, the first randomized controlled trial evaluating a curriculum intervention designed to develop planetary health competencies and environmental justice awareness among high school students pursuing construction careers. Methods and analysis: This two-arm, parallel-group randomized controlled trial targets enrollment of N=200 high school students (ages 14-18) from construction career pathway programs in the San Francisco Bay Area (over-recruitment target N=250; 25% buffer for attrition). Students are individually randomized 1:1 to intervention (Community-Centered Design curriculum integrating the Ecosystem Justice Translator) or control (traditional Virtual Design and Construction curriculum), stratified by school site using block randomization. The 6-month intervention features the Ecosystem Justice Translator (EJT) -- a computational system using large language models to translate community health equity concerns into quantifiable investment priorities. The EJT's 51-theme health equity taxonomy was derived from validated public health frameworks (Centers for Disease Control and Prevention [CDC] Social Vulnerability Index, Environmental Protection Agency [EPA] EJScreen, Healthy People 2030). Primary outcome is Health-Integrated Equity Consciousness Index (HI-ECI), measured at baseline, 3, 6 (primary endpoint), and 12 months. Analysis uses intention-to-treat linear mixed-effects models with random intercepts for participants. The minimum required sample (n=26 per arm; G*Power, two-tailed a=0.05, 80% power, Hedges' g=0.80) is exceeded by enrolled N=200, which provides >99% power at Hedges' g=0.80 and supports multi-site confirmatory factor analysis. Ethics and dissemination: This protocol has been approved by Stanford University Institutional Review Board (IRB eProtocol #84369, approved February 13, 2026). Parental consent from a parent or guardian and written assent from each student participant are required prior to enrollment. All instruments, curriculum materials, and EJT source code will be released open-source under CC BY-NC-SA 4.0, permitting free use for educational, research, and non-profit purposes, concurrent with primary publication. Commercial licensing may be pursued separately through Stanford University Office of Technology Licensing (OTL docket S25-565). Trial registration: ClinicalTrials.gov NCT07315919. Pre-results. Protocol version 4.0, June 2026.

The cytoplasm is a crowded and dynamic fluid within which cellular building blocks such as mRNA, proteins, or organelles undergo transport and mixing. Although small things like proteins can eventually mix through diffusion, the high viscosity of cytoplasm means that it should be difficult to obtain significant mixing for structures in the size range of mRNA, multi-protein complexes or organelles. In large amoeboid cells, the cytoplasm undergoes active streaming coupled to cell motility, but this streaming is laminar flow which should not be effective for mixing. In this work we used a combination of live cell tracking of injected beads and computational analysis of motion and mixing in giant amoeba Chaos carolinensis with the initial goal of testing the possibility that large-scale cellular deformations during pseudopod formation might implement chaotic mixing by a Baker-transform like process. Instead, we found that Chaos carolinensis accelerates cytoplasmic mixing using a novel cytoplasmic gel state capture and release strategy. While it was previously thought that the amoeba sol to gel state transitions only occur at the trailing and leading edge of the cell body, our work indicates that these transitions occur frequently throughout the mid-cell region, driving the cytoplasmic mixing of beads and organelles. These results indicate that amoeba achieves nearly complete mixing between 1 and 2 cytoplasmic stream/flow cycle, effectively approximating the Bernoulli mixing regime and thus representing one of the theoretically fastest possible mixers.

In recent years, the use of multi-model ensemble projections in infectious disease modeling has become an established methodological approach to account for and integrate across uncertainties and structural differences present in individual models. However, the creation of long-term ensemble projections through these coordinated efforts is resource-intensive, demanding the input of multiple research teams and substantial computational power. This typically limits the ability to refine projections, update the selection of plausible epidemic trajectories, or expand the number of scenarios that can be assessed, even as new empirical data become available. To address this challenge, we define an adaptive ensemble approach that, analogously to a multi-model particle filtering method, dynamically selects individual model trajectories based on observed data throughout the epidemic projection period. We demonstrate the effectiveness of this methodology using the U.S. Flu Scenario Modeling Hub (SMH) projections for influenza hospitalizations in the United States during the 2023-2024 and 2024-2025 winter seasons. Our findings show that the adaptive ensemble yields improved predictive accuracy with respect to the original SMH ensemble projections across several scoring rules and geographical resolutions. Furthermore, the adaptive ensemble approach offers two additional applications: i) the dynamic assignment of posterior probabilities to epidemic scenarios, identifying the most plausible scenario, and representing how reality is captured by a combination of scenarios, and ii) the potential use for short-term forecasting. The adaptive ensemble approach is able to identify the most likely scenarios for the 2023-2024 and 2024-2025 U.S. influenza seasons, even in the early stages of the epidemic. It outperforms, retrospectively, a baseline model in short-term forecasting of influenza hospitalizations in the United States during the two seasons across various horizons and scoring rules, showing potential to contribute to real-time collaborative forecasting challenges such as CDC's FluSight. The proposed approach offers an efficient or low-resource strategy to increase the impact of multi-model epidemic projections by providing real-time support to modeling teams, public health authorities, and decision-makers.

Background German cockroach (Blattella germanica) infestation is an important urban environmental health menace associated with food contamination, allergic disease, and reduced quality of life. Long-term control depends not only on professional pest management, but also on residents knowledge and preventive behaviors. This study assessed the knowledge, Health belief model (HBM) constructs, self-efficacy, and preventive practices related to German cockroach infestation among urban residents in Tehran, Iran. Methods In this cross-sectional study, 120 adults with professionally confirmed household German cockroach infestation were recruited from licensed pest-control companies in Tehran. Data were collated using a 39-item HBM-based questionnaire assessing knowledge, perceived susceptibility, perceived severity, perceived benefits, perceived barriers, self-efficacy, and preventive practices. Descriptive statistics, Pearson correlation, and multiple linear regression were performed. Results Participants demonstrated modest knowledge regarding German cockroach biology (mean score: 0.538) and moderate preventive practices (3.157). Preventive practices were positively correlated with knowledge (r = 0.256, P = 0.005), perceived benefits (r = 0.292, P = 0.001), and self-efficacy (r = 0.244, P = 0.007). Regression analysis showed that the model explained 17.3% of the variance in preventive practices (R2 = 0.173, P = 0.001). Knowledge ({beta} = 0.191, P = 0.036), perceived benefits ({beta} = 0.231, P = 0.010), and self-efficacy ({beta} = 0.229, P = 0.012) were significant predictors. Conclusions Urban residents with confirmed German cockroach infestation showed limited knowledge and moderate preventive behaviors. Knowledge, perceived benefits, and self-efficacy were independently associated with preventive practices and demonstrated modest predictive value. Interventions targeting these behavioral factors, alongside environmental and structural improvements, may enhance sustainable household cockroach control.

The African clawed frog Xenopus laevis is a widely utilized model organism in biomedical research; however, significant challenges in experimental reproducibility and colony management remain. A major obstacle lies in the reliable identification of individual animals, since frogs are generally housed in large groups and are difficult to distinguish due to their high morphological similarity. Conventional methods, including toe clipping and microchipping, are invasive and cause distress, emphasizing the need for non-invasive methods for accurate documentation and welfare monitoring. In this study, we introduce XIBBIT (Xenopus Image-Based Biometric-pattern Identification Tool), a web-based application integrating computer vision and machine learning to identify individual Xenopus laevis based on their dorsal patterning. By exploiting these natural biometric signatures, the platform achieves reliable identification with up to 95.7% accuracy within three image captures under real life conditions. In addition to identification, XIBBIT provides a centralized colony management system. It archives individual data, including health records and experimental histories, with customizable fields. To demonstrate XIBBITs capabilities, we used the application to track egg quality across repeated egg-laying events, revealing that egg quality is a repeatable, individual-specific trait in Xenopus laevis. Furthermore, we find seasonal effects on egg laying performance with the lowest performance during late-spring and summer months. Ultimately, XIBBIT provides an effective, time-efficient, and non-invasive solution to the problem of individual Xenopus laevis identification, facilitating both experimental reproducibility and high animal welfare standards.

Feature selection is a commonly used method in biomedical artificial intelligence and machine learning to identify a subset of high-quality variables that can be used to train downstream predictive models. It has been suggested that quantum feature selection (QFS), which takes advantage of the properties of quantum computers, may better identify variables that are correlated with the outcome while simultaneously reducing redundancy between selected variables. However, there are a limited number of studies evaluating their performance, particularly in real-world data sets. Here, we assess the performance of two QFS methods compared to random forest (RF) feature selection based on feature stability and the performance of a downstream classification algorithm when used to predict urinary tract infections in the emergency department from 211 original features extracted from the electronic health record. We found that a quantum binary quadratic model (BQM) and constrained quadratic model (CQM) had similar performance to RF feature selection (median F1 score of 0.60, 0.61, and 0.61 respectively) when 10 features were selected for an XGBoost classification model. The BQM and RF also had similar feature stability (0.91 and 0.94, respectively) while the CQM had lower stability (0.72). These findings show that QFS can be used with large, clinical data sets to identify features with high stability and predictive performance. As the capacity and quality of quantum computers continue to increase, these methods may offer additional benefits to classical feature selection methods.

Abstract Background: The current coverage of MCCD in India is only 22%. This is due to incomplete coverage of hospitals under MCCD and also lack of a system for non-institutional deaths in the country. The quality of MCCD in the country is also poor. One of the main reasons for this is the lack of review and feedback at the district level. This study would be the first of its kind study in the country to test the effectiveness and feasibility of involving the district level CRS/Health dept officials in review of MCCD Objectives: To assess the feasibility and effectiveness of a district level review system for MCCD in improving the coverage and quality of MCCD Methods: The study would be conducted in Chikkaballapura district for a period of 2 years. Local Registrars would do a first level of review of MCCD forms for completeness, use of abbreviations, legibility. They would also ensure that form 4/4A is written for all registered deaths in their area. A MCCD review committee would assess the quality of MCCD forms on a monthly basis and provide feedback to the certifying doctors. Comparison of the pre-test and post-test coverage and quality of MCCD will be done. Results: Constitution of the audit committee, training of local registrars, doctors and committee members and baseline assessment have been completed. Intervention has been started from Nov 2025. Expected Outcomes: Improved coverage and quality of MCCD and as a result cause of death data of the district

The human cerebral cortex folds into a stereotyped shape during gestation. Different principles govern the large and small scales of the final brain geometry. Here, I show that the fetal cerebrum can be described as a band limited spherical harmonic Fourier object which entire gyrification process collapses to a single one-dimensional curve, in which the maximum harmonic degree acts as a developmental coordinate. The closed form descriptor predicts gestational age with mean absolute error 0.13 and 0.38 weeks across fetal brain atlases, exceeding the published learning-based state of the art by a factor of three to seven. The same descriptor, applied to single subjects in the FeTA pathological dataset, can classify the per subject distance from the normative trajectory and discriminate pathological from neurotypical fetuses. The result is a single closed form, zero-training-cost descriptor that simultaneously dates the fetal brain and detects atypical development.

Wood is commonly used in the building sector, emitting volatile organic compounds (VOCs) contributing to indoor air quality. These VOC profiles can have a pleasant smell and positive effects e.g., induce relaxation. Contrarily, VOCs can have adverse health effects in higher concentrations. Therefore, some VOCs are regulated by guide values (GV). Potentially positive and negative effects of pinewood emissions, ranging from 0.2 mg/m3 (German GV I for bicyclic terpenes) to 2.0 mg/m3 (GV II) were investigated in an experimental 2 h exposure study using a within-subject design. Thirty-two healthy participants rated the perception, pleasantness, symptoms of irritation, and indicators of well-being. During a demanding working memory task (n-back) and a resting period, heart rate (HR) and HR variability (HRV) changes were measured. Before and after each session physiological markers of sensory irritation were assessed. Ratings indicated that the exposure to GV I and GV II were not perceived as more intense or pleasant. Mostly concentration-independent effects were revealed, indicating that inter-individual factors influenced the ratings rather than the VOCs. The pinewood odors during the n-back task did not cause distraction nor did it facilitate performance as previously suggested. HR/V changes indicated that pinewood odors during and after the n-back tasks did not induce relaxation. Only symptoms of nasal irritation showed some weak concentration-dependency, not supported by physiological markers or comparable ratings of sensory irritation. In conclusion, the fact that no distinct odor is detected suggests that interfering factors potentially prevent the regulation of odors at relevant indoor air concentrations.

Fascicle operating length during dynamic tasks is often compared to the isometric torque-length relationship, but there is a lack of evidence regarding the influence of joint velocity on optimal fascicle length. Moreover, there is no consensus in the literature regarding the influence of contraction initiation (pre-activation or passive start), although it could alter the interaction between fascicles and the tendon. This study aimed to investigate the effect of joint velocity and pre-activation on the torque-angle and torque-length relationships of the vastus lateralis during mono-articular isokinetic knee extensions. Twenty-one participants performed isometric, isokinetic (50{degrees}.s-1 to 450{degrees}.s-1), and isokinetic knee extensions with maximal isometric or eccentric pre-activation at 100{degrees}.s-1 and 300{degrees}.s-1. Torque, joint angle, fascicle length, and electromyographic activity of the quadriceps femoris muscles were recorded during contractions and then used to model the torque-angle and torque-length relationships. We were able to successfully fit the torque-angle and torque-length relationships (R{superscript 2}=0.93 and R{superscript 2}=0.92, respectively). A main effect of velocity was detected regarding the optimal angle (p<0.05), but no significant change was observed for the optimal fascicle length. Isometric pre-activation induced a reduction in maximal torque production compared with eccentric pre-activation and passive conditions at both isokinetic velocities (p<0.001), with no change in muscle activity. Our results suggest that muscle-tendon interactions may permit a dissimilar behavior between the torque-angle and the torque-fascicle length relationships. The reduction in torque following isometric pre-activation may be related to a contraction history-dependent phenomenon. NEW & NOTEWORTHYWe demonstrated that, at a given joint angle, increasing velocity altered fascicle operating length without shifting optimal fascicle length, likely because of muscle-tendon interactions. We also showed that maximal isometric pre-activation before a concentric contraction reduced mean and maximal torque during the isokinetic phase compared with eccentric pre-activation or no pre-activation. This effect may be linked to contraction history, since muscle activity did not differ between conditions.

Background Early outbreak detection often depends on complex, data-intensive models that have limited operational use in sparse surveillance settings. We developed a domain-mechanistic generative embedding that converts case counts and rainfall into a structured representation of dengue transmission for early epidemic-onset detection. Methods We constructed a 132-feature generative embedding from sparse dengue case and rainfall data. A tabular foundation model was evaluated using leave-one-year-out validation with paired cluster-bootstrap uncertainty intervals across 17 Philippine regions and eight dengue-endemic countries. Performance was benchmarked against raw input columns and catch22 time-series features. Findings Raw case and rainfall columns provided weak discrimination for dengue outbreak onset, with AUROC ranging from 0.56 to 0.70. The generative embedding improved prediction to AUROC 0.77 across countries and 0.89 across regions, corresponding to gains of +0.205 and +0.183 over raw columns, respectively, with paired cluster-bootstrap p[&le;]0.006. Calibration error remained low at both regional and country scales, with expected calibration error of 0.067 and 0.149, respectively. Predictability was strongest in highly seasonal settings, including Philippine Type I regions, Mexico, Brazil, and the Philippines, whereas year-round transmission or opposing coastal rainfall regimes produced weaker performance. Country estimates based on only one or two retained epidemic seasons were unstable. Interpretation Under sparse surveillance conditions, the predictive capacity of a tabular foundation model depended strongly on the representation supplied to it. A generative embedding of climate and epidemiological dynamics translated limited case and rainfall inputs into actionable early-warning signals, with accuracy scaling according to local seasonal structure. These findings support mechanism-grounded embeddings as a practical route for extending prospective dengue outbreak surveillance in data-limited settings, especially at regional scales where calibration and deployment are most appropriate.

Statistical prediction models for binary outcomes are becoming increasingly popular. One significant challenge is calibrating these models to suit the characteristics of a target population that is structurally different from the original population. Calibration is especially challenging when there is no training data available from the target population. To address this problem, we propose a novel calibration method, SimCal, which uses synthetic data generated from the model development data in conjunction with marginal statistics from the calibration cohort. We show that expert judgment modeling (EJM) may be used for calibration if cross-sectional data from the target population are available comprising expert judgments about the potential outcome and the covariates. We describe three alternative calibration approaches when calibration data are lacking: similarity-binning averaging (SBA), adaptive calibration of predictions (ACP), and Elkan calibration. In a simulation study, we compare SBA, ACP, Elkan calibration, and SimCal. R code for applying these methods is provided from the re-analysis of data on coronary artery disease. We illustrate all 5 calibration approaches with a real data set for predicting functional outcome after stroke and all approaches but EJM in the re-analysis of the Cleveland Clinic data. None of the approaches performed convincingly well in all situations. SimCal performed well when model parameters were correctly specified. EJM failed on the stroke data. Further research is urgently required for calibration in the absence of calibration data.

Predictions of skeletal muscle energy consumption under a diverse range of muscle contractile conditions are critical for improving our understanding of locomotion. Existing mathematical models, while capturing the mechanical dependence of energy consuming processes, neglect the time-dependent behaviour and recovery costs associated with regenerating ATP. This time-dependence is important for predicting the energetic response of muscles during repetitive or cyclical tasks like locomotion, where muscle undergoes many contraction cycles. This study presents a novel model to predict energetic rates based on physiological processes: Ca2+ transport costs, cross-bridge cycling costs, and ATP regeneration. Previous mathematical models include the dependence on Ca2+ transport and cross-bridge cycling, but neglect the time-dependent response and the subsequent recovery of ATP following the contraction. Model parameters were obtained from existing data on isolated muscle preparations, and predicted energetic rates were validated on separate datasets across a range of contractile conditions including dynamic, sub-maximal, and twitch contractions. The time-dependent model was able to capture the influence of contraction frequency on peak energetic rates and the time-course of energetic recovery observed experimentally. The model captures key physiological processes while maintaining a minimal number of free parameters and low computational cost. This enables generalisability across muscles and species, and implementation into larger scale musculoskeletal models.