Frontiers in Applied Mathematics and Statistics

Background: Tuberculosis remains a persistent infectious disease whose control is complicated by latent infection, delayed treatment, incomplete recovery, reinfection, and continuing transmission from infectious individuals. Although treatment is central to tuberculosis management, it is frequently represented only as a transition parameter in mathematical models rather than as a separate epidemiological state. In this study, treatment was therefore incorporated explicitly as an independent compartment so that its influence on transmission, recovery, disease-induced mortality, and long-term disease persistence could be evaluated. Methods: A deterministic nonlinear compartmental model was formulated by dividing the total population into susceptible, exposed, actively infected, treated, and recovered classes. Reinfection of recovered individuals, progression from latent infection to active disease, movement of infectious individuals into treatment, treatment-associated recovery, natural mortality, and disease-induced mortality were included. Positivity and boundedness of the solutions were examined to establish biological validity. The basic reproduction number, R0, was derived through the next-generation matrix approach. Disease-free and endemic equilibria were determined, and their local and conditional global stability properties were investigated using Jacobian analysis, the Routh-Hurwitz criterion, center manifold theory, Lyapunov functions, and LaSalles invariance principle. Normalized sensitivity indices, Latin hypercube sampling, partial rank correlation coefficients, and numerical simulations were also applied. Results: The disease-free equilibrium was shown to be locally asymptotically stable when ,R0<1 whereas sustained transmission and a unique endemic equilibrium were associated with R0>1. Under the stated reduced-model assumptions, stability of the endemic equilibrium was established. Transmission-related parameters were identified as the strongest positive contributors to disease persistence. In contrast, treatment and recovery parameters were found to reduce the reproduction number and infectious burden. Numerical simulations indicated that stronger treatment implementation and reduced transmission opportunities produced substantial reductions in active tuberculosis cases. Conclusion: Treatment was shown to function as both a clinical pathway and an epidemiological control mechanism. The proposed framework may support the design of treatment-centered strategies for reducing tuberculosis prevalence and preventing long-term endemic persistence.

Across metazoa, morphogen gradients differentially regulate gene expression and activate a spatially distinct program to specify body axis development. The Drosophila gap gene network, initiated by maternal morphogen Bicoid, is one of the most well-studied systems. Several regulatory interactions act synergistically to produce distinct gap gene expression patterns along the anterior-posterior (AP) axis of the blastoderm stage Drosophila embryo to ensure the proper segmentation of the larval and, eventually, adult stage fly. Several mathematical models have been proposed to summarize the interconnectivity of gap gene regulatory elements and predict expression in mutant systems. However, these models have not successfully predicted the gap gene expression profile over the entire AP axis. Here, we present an Enhancer Activity-informed Gap GEne Regulatory network (EAGER) model that incorporates enhancer activity-driven differential regulation along the AP axis, which successfully summarizes gap gene expression patterns over the entire AP axis. We validated the predictions of EAGER on Kr mutants and performed a comprehensive parametric sensitivity and identifiability analysis to evaluate the robustness of the EAGER model fits and predictions. We also propose a reduced version of the model, rEAGER, which identifies a minimal set of regulatory interactions and successfully summarizes the gap gene interactions over the entire AP axis. Our results suggest that the expression driven by individual enhancers must be accounted for in models of developmental pattern formation.

The measurement of light received at the cornea of the eye is a paramount consideration for the understanding of the relation between environmental illumination and the non-image-forming effects of light. The field of view (FOV) at the cornea is less than a full hemisphere, because it is partially occluded by human facial morphology. The International Commission on Illumination (CIE) has defined a standard model of human FOV. A suitably designed physical occluder attached to the sensor (of a light meter) has been proposed as a means of incorporating the effect of human FOV when taking measurements. Similarly, when using simulation to predict light received at the cornea, a geometrical description of the occluder at the eye point(s) can be added to the 3D model of the scene. The first occluder model proposed to represent CIE human FOV was enumerated in terms of: the CIE definition; the radius of the occluder; and, the radius of the light sensor disc. We present a simpler model based only on the CIE definition and the occluder radius. Both models were tested using a virtual goniophotometer. Various sensor response functions describing the spatial sensitivity across the sensor disc, including several we characterized through laboratory measurements, were included in the test. For all functions considered, the performance of the simpler occluder model was equivalent to or better than the model first proposed.

Employing DLA methods, this paper explores the self-assembly of collagen fibers and resulting fibrosis at three scales up to the scale of regular lobule models. This allows a mechanistic exploration of the effects of collagen on drug transport (flow and diffusion) and metabolism. In addition, this method permits an analysis of fiber growth characteristics. First, variations of the DLA method of Parkinson et al (1994) will be used to generate multiple explicit collagen microfibril self-assembly using DLA particles in one dimension using cubic grid blocks of (4 mm)3 in a 240 x 20 x 20 grid model. The second stage will be to assess the consequences of various densities of these fibers in three dimensions on flow reductions at a higher scale. Here we utilize DLA methods in cubic grid blocks of (80 nm)3 to mimic 3D collagen self-assembly of fibrils. We then apply a pressure gradient or specified flow rates across a spatially gridded version of these models to quantify flow effects. This region represents a local zone of liver tissue affected by fibrosis. Analytic models of fibrotic effects on flow are employed for comparison. A third stage explores the implications of fibrosis in a liver lobule model using multiple grid blocks of size 3200 mm to represent the lobule tissue. Here, a continuum model of fiber density is employed, based on the previous two scales. The model also includes the effects of additional grid blocks representing sinusoidal flow paths found in the lobule. We contrast and quantify drug propagation and metabolism of molecular dissolved versus nanoparticle delivery vehicles in fibrotic media, achieved by upscaling explicit collagen distributions to appropriate average values.

Malaria is still one of the most dangerous causes of morbidity and mortality in tropical and subtropical regions even though it has been actively combated for many years. In 2023, there were approximately 263 million malaria cases and 597,000 deaths from this disease on a global scale, with sub-Saharan Africa being the region most affected by it [24]. Climate factors affect mosquito biology, including their abundance, survival, and biting rates, as well as parasite development, while human awareness plays a crucial role in adopting preventive measures and effective treatments. Despite the progress in both climate- and awareness-based malaria modelings, few studies integrate these factors in one comprehensive model that involves the detailed mechanisms of transmission processes. The current study develops a deterministic climate-driven SEAIR-SEI malaria transmission model that includes the impact of temperature, rainfall, and humidity on mosquito biology and endogenous community awareness. The model was proven to be well-posed by showing the positivity and boundedness of its solution and through the demonstration of the existence and uniqueness of its solution. The malaria-free equilibrium was determined, and the basic reproduction number was calculated using the next-generation matrix method. The model underwent local and global stability analyses to characterise the diseases persistence in the population. Additionally, a normalized forward sensitivity analysis was conducted, revealing the mosquito biting rate as the key force driving malaria transmission. Four time-dependent malaria interventions, namely, long-lasting insecticidal nets, community awareness campaigns, indoor residual spraying, and prompt treatment, were included in the model through optimal control theory and analysed using Pontryagins Maximum Principle. The numerical results for the optimal control problem showed that employing all four interventions leads to the best outcome by decreasing the objective functional value by 88.17%, reducing the total number of infected humans by 92.49%, and minimizing the total number of infectious mosquitoes by 93.87%. Interestingly, combining two interventions, indoor residual spraying, and prompt treatment, also yielded nearly optimal results. Therefore, the designed control strategy can serve as an efficient and affordable framework for malaria control in sub-Saharan Africa.

Human Papillomavirus (HPV) infection among men who have sex with men (MSM) has become a significant public health concern, particularly in countries where male vaccination is unavailable. Given the high susceptibility of MSM to HPV and anal cancer, and the unavailability of HPV vaccination for males in low- and middle-income countries (LMICs), there is a need to identify alternative interventions for reducing disease transmission and burden in this population. The novel mathematical model presented in this article couples smoking behavior dynamics with HPV transmission and anal cancer progression among MSM. Smoking reduction is introduced as an intervention to assess its effects on disease transmission and burden. The basic reproduction number (R0) is derived using the next-generation matrix method, and a global sensitivity analysis is performed using partial rank correlation coefficients (PRCC) to identify the influence of model parameters on RR0. Further, the theoretical analysis of the model reveals a backward bifurcation, implying that RR0 < 1 is necessary but not sufficient to eradicate the disease. The study finds that smoking reduction among MSM reduces HPV infection and anal cancer burden relative to baseline projections without intervention. The joint effect of smoking reduction and vaccination shows that the critical vaccination coverage needed to achieve RR0 <1 decreases as the level of smoking reduction increases. A similar outcome is observed for contact reduction. These findings highlight the importance of concurrent interventions, which can significantly curtail the spread of HPV and reduce disease burden in both the high-risk group and the general population.

Neural temporal point processes (NTPPs) are powerful tools for modeling sequences of timestamped events with statistical temporal structure. Density-based NTPPs, in particular, are an interesting opportunity to merge the universal function approximation capability of neural networks with a defined statistical model in a way that has many potential applications. We demonstrate one such application to heartbeat dynamics, a physiologic point process. We specifically apply a lognormal mixture NTPP to compute instantaneous estimates of the mean and standard deviation of beat-to-beat intervals. We compare our results to the state of art (Barbieri et al.) point process model for heartbeat dynamics, which uses a more physiologically rigorous inverse Gaussian model. We find that the NTPP model maintains reasonable accuracy while improving upon robustness to noise.

Researchers must often rely on observational data to draw conclusions about the causal relationship between an exposure and an outcome. This is common in environmental epidemiology research, where the assignment to an exposure can be unethical or impossible. Consider a setting in which we seek to estimate excess mortality during heat waves, but are unable to randomize individuals to moderate or extreme heat. We propose to follow a causal framework for non-randomized time series that uses what we call historical time series matching to construct hypothetical randomized experiments, in which background covariates are balanced. We applied this framework and assessed the following causal question: Are daily mortality counts among elderly Americans higher during hot versus warm summer time periods? We addressed this causal question by drawing frequentist, Fisherian, and Bayesian inferences for five American cities. We estimated the average treatment effect of heat on three-day mortality with 95% Fisherian intervals to be 0.5 [-3.6, 4.4] deaths in Pittsburgh, 3.7 [0.7, 6.6] deaths in Seattle, 12.5 [6.1, 18.9] deaths in Chicago, 8.5 [1.4, 15.6] deaths in Los Angeles, and 20.3 [11.2, 29.5] deaths in New York.

Coronary flow waveforms have a distinct diastolic-dominant shape with periods of low or retrograde flow during systole. While the general waveform shape has been attributed to complex interactions between cardiac and vascular mechanics, there is limited research into the variability in coronary flow waveforms and what this variability may reveal about cardiac function. This work presents a shape analysis of left anterior descending artery (LAD) flow waveforms using Fourier transforms and Singular Value Decomposition (SVD) performed on baseline data collected from 32 pigs. Pigs included in the study reflect two breeds (Ossabaw and Yorkshire) and three different experimental conditions (lean-control, lean-paced, and obese-paced). Fourier transforms were used to decompose the waveforms into 15 harmonics for each pig. An SVD analysis is then used to extract temporal patterns of the waveforms. Correlations between pig-specific coefficients for the SVD modes and clinical metrics were used to investigate physiological explanations of LAD waveform variability. Temporal LAD flow patterns of the second SVD mode are significantly correlated with heart rate. The third SVD mode significantly correlates with mean blood pressure and maximum hyperemic flow. Furthermore, the fourth SVD mode is weakly correlated with left-ventricular end diastolic pressure and endocardial-epicardial flow ratios. This work demonstrates that LAD flow waveforms can be broken down into temporal patterns that correlate with physiological features. Furthermore, this shape-analysis method allows for waveform reconstruction and simplifies visualization of the temporal patterns identified using SVD, an advantage over existing methods that focus on characterizing flow waveforms by points of interest.

In many natural dynamical systems, tipping points emerge where slowly changing external factors induce shifts from one state to another, known as critical transitions or bifurcations. In epidemic systems, detecting these transitions is important for outbreak preparedness. Various statistical indicators like lag-1 autocorrelation and variance have been employed as early warning signals (EWS) of critical transitions by showing how the dynamics of the system exhibit critical slowing down (CSD) near the transition. More recently, deep learning-based algorithms have been developed that attempt to more accurately detect and classify bifurcations; however, they are limited by the systems simulated in the training dataset, the length of the time series, and have not been rigorously evaluated on real-world epidemic data spanning multiple geographic regions. In this paper, we evaluate existing deep learning-based bifurcation prediction models, on a CDC-curated dataset containing weekly influenza hospital admissions across all fifty U.S. states and the nation as a whole. We develop a pipeline for data preparation, reproduction number (Rt) estimation using the EpyEstim package (a Python implementation of the EpiEstim framework [4]), and bifurcation point identification. We systematically evaluate the models under several windowing strategies, including rolling, expanding, and fixed-length windows, and report accuracy, precision, recall, F1 score, and specificity. Our best-performing configuration (expanding window, length 100) achieves an accuracy of 90.09%, precision of 72.86%, recall of 96.23%, and F1 score of 82.93%. We additionally discuss Markov Regime Switching models as an alternative framework for detecting epidemic transitions. Our findings indicate that these models can generalize to real-world, state-level influenza data and are capable of online/real-time prediction.

Background and ObjectiveAccurately parameterizing dynamic, time-varying interactions in physiological systems is a methodological challenge, as global causal discovery methods may obscure transient, local fluctuations. This study introduces tempord, an open-source Python library designed to estimate local temporal orders and evaluate the short-term stability, directionality, and strength of causal links in non-stationary biological signals. MethodsThe algorithm estimates temporal relationships by keeping one signal stationary while iteratively shifting another one within a sliding window. To parameterize optimal inter-signal shifts (causal vector, CV), the framework utilizes linear modeling or time series distance metrics. The methodology was validated through a simulation study on synthetic bivariate signals with mathematically imposed dynamic phase delays, under both deterministic and noisy conditions. Furthermore, in-vivo capabilities were demonstrated by evaluating cardiorespiratory coupling dynamics across spontaneous and music-induced relaxation breathing states. ResultsThe simulation study demonstrated that the extracted CV trajectories precisely aligned with ground-truth temporal delays, assessed using mean absolute error and root mean square error for both noise-free and noisy synthetic data. In-vivo application demonstrated dynamic temporal stability and the detection of minor step changes during autonomic nervous system state transitions. ConclusionsThe tempord Python package bridges the gap between global causal discovery and local beat-by-beat statistical parameterization. It provides a robust "bottom-up" analytical instrument for investigating the transient mechanisms governing complex biological networks.

Background: Globally and in Bangladesh, high-risk fertility behaviour (HRFB) continues to be a significant public health issue, contributing to negative health outcomes for both mothers and children. So, this study aimed to evaluate the trends, prevalence, determinants, and socio-economic inequalities associated with HRFB among presently married women of reproductive age by utilising data from the Bangladesh Demographic and Health Survey (BDHS). Methods: We analysed data from 19,060 currently married women aged 15-49 years. HRFB was defined as the presence of any of the following: maternal age (<18 or >34 years), short birth intervals (<24 months), or high birth order ([&ge;]4). Two outcome variables were constructed: a binary indicator for any HRFB (yes/no) and a three-category variable indicating no, single, or multiple HRFBs. Bivariate analysis was conducted to determine the prevalence of HRFB, and multilevel mixed-effect logistic and multinomial regression models were applied to identify determinants, accounting for the complex survey design. Socioeconomic inequalities were examined using concentration indices and concentration curves. Results: Overall, 58% of women experienced at least one HRFB, with 33% exhibiting a single HRFB and 25% multiple HRFBs. Women who married after age 18 years, had higher education, were exposed to media, or had educated husbands were significantly less likely to experience HRFB. Higher odds of HRFB were associated with rural residence, lower household wealth, and regions such as Mymensingh, Barishal, and Chattogram. Significant inequalities were observed, with HRFB disproportionately concentrated among women with lower wealth (CIX = -0.427, p<0.001) and no education (CIX = -0.268, p<0.001). Conclusion: In Bangladesh, HRFB remains prevalent and is unevenly distributed across socio-economic and geographic groups. Targeted interventions aimed at delaying early marriage, improving educational attainment for women and their partners, expanding mass media outreach, and increasing access to reproductive healthcare- especially among disadvantaged and rural populations- are essential for reducing HRFB and improving maternal health outcomes.

Crickets are gaining attention as sustainable protein sources because of their high nutritional value and low environmental impact. Growth models are essential tools for optimising production by predicting growth characteristics. However, previous studies have not compared multiple non-linear growth models for crickets or explicitly considered environmental factors. We analysed the growth patterns of the two-spotted cricket (Gryllus bimaculatus) and the Asian cricket (Teleogryllus occipitalis) at multiple temperatures (25.0, 27.5, 30.0, 32.5 and 35.0 {degrees}C) using three non-linear models (Gompertz model, logistic model, and von Bertalanffy model) and combined the predicted body mass with observed survival rates to predict the optimal harvest time and temperature. All three models fitted the data well (R2 [&ge;] 0.97 in both species). The asymptotic body mass was highest at 30.0 {degrees}C, and the growth rate constant increased with temperature, reaching its maximum at 35.0 {degrees}C except for the logistic model in G. bimaculatus (32.5 {degrees}C). In addition, the predicted value of harvest, calculated by combining predicted body mass and observed survival probability, was highest at 30.0 {degrees}C in both species, reaching 13.82 kg/m3 at 38 days in G. bimaculatus and 7.12 kg/m3 at 62 days in T. occipitalis. These results suggest that 30.0 {degrees}C is the most suitable constant-temperature condition for maximising predicted productivity, although the optimal harvest timing differs between species.

The initial response of populations to the SARS-CoV-2 virus reduced the incidence of COVID-19 cases. However, this success was shorted lived once most populations relaxed most restrictions, resulting in an increase in infections. This feedback contributed to additional pandemic waves. The temporal unfolding of behavioural changes in populations present a challenge to mathematical models for disease dynamics. Coupled behaviour-disease models with varying levels of complexity accounting for several factors have been used to capture behavioural dynamics and SARS-CoV-2 transmission, with varying results. To study the impact of model complexity on the predictive power of models, here we formulate five coupled behaviour-disease models with varying structure and number of parameters. We fit the models to SARS-CoV-2 infection incidence and stringency of control interventions from five European countries in the first wave, and study how well these fitted models predict the second wave. We show that models with more parameters do not necessarily have a greater ability to explain and predict key features of a pandemic wave. Hence, our results show that a relatively simple coupled behaviour-disease model with important parameters can do an adequate job of providing information about the pandemic wave. Additionally, our findings show that complex models can be country-specific, working better for some countries and poorly for others. We conclude that modellers should not always opt for the most complicated possible models, if the data do not support their use.

Animals use long-range signals, such as hormones and neural signals, to coordinate the actions of distant organs. There is no precise, quantitative framework that explains the problems these control systems must solve and thus predicts their behavior under varied conditions. We consider this problem in the context of blood glucose regulation by the hormone insulin, the failure of which produces diabetes. We show that existing mathematical models of glucose regulation admit equivalent control strategies with no hormones at all, and thus cannot explain the need for hormonal regulation. We therefore introduce a minimal model of inter-organ variations in local glucose, and show that control strategies based on local glucose measurements face severe trade-offs between different control objectives. In contrast, we show that hormonal control signals from the pancreas can overcome these limitations. By exposing the benefits of hormonal control, our work paves the way to a detailed understanding of physiological design principles, with possible implications for the engineering of an artificial pancreas.

Tumors consist of heterogeneous phenotypic cells, such as normoxic cells, which are highly proliferative, and hypoxic cells, which are less proliferative. Their phenotypic switching depends on tumor microenvironmental factors, such as oxygen and nutrient concentrations supplied by local blood vessels. However, during ongoing angiogenesis, the process of sprouting new blood vessels at the tumor site from pre-existing blood vessels, and how this phenotypic switching affects and impacts tumor growth, remains poorly understood. In this article, we formulate a mathematical model to elucidate the crosstalk between vasculature and tumor cellular heterogeneity during tumor progression. The model results show a strong agreement with the experimental data. Our simulation results demonstrate that ongoing angiogenesis increases tumor growth rate. In addition, we observe that the influence of hypoxic cells on phenotypic switching from normoxic to hypoxic is more pronounced than their influence on the transition from hypoxic to normoxic. Furthermore, we perform a global sensitivity analysis using the Sobol's method to assess the importance of the model's parameters. It highlights that the volume at which blood vessels attain half-maximal rate has the maximum effect on the model.

Lassa fever is a major yet persistently neglected viral hemorrhagic disease in West Africa, with an estimated 100,000-300,000 infections and approximately 5,000 deaths reported annually across the region. Case-fatality rates are typically above 15% among hospitalized patients and may approach 50% during epidemic periods, with Nigeria accounting for the largest reported burden of confirmed cases. This study presents a pilot multi-layer GIS framework for the spatial recording, visualization, and analysis of hemorrhagic fever infections in Nigeria, focusing primarily on Lassa fever. The framework integrates epidemiological observations with environmental information to move beyond conventional static disease maps toward dynamic assessment of disease susceptibility. Confirmed Lassa fever cases recorded between 2023 and 2025 were combined with weather variables obtained from Open-Meteo, CHIRPS precipitation data, land-use information, lithological characteristics, and elevation datasets. The datasets were temporally aggregated and statistically analyzed, while multiple GIS layers were used to identify and visualize recurring spatial patterns. Ondo, Edo, Bauchi, and Taraba consistently emerged as prominent hotspot states during the study period. Weekly temporal aggregation was adopted to correspond with the reporting frequency of official epidemic surveillance, enabling short-term environmental conditions to be examined in relation to confirmed cases. The findings indicate a pronounced seasonal pattern, with increased Lassa fever activity occurring predominantly during dry periods characterized by minimal rainfall, fewer precipitation hours, and reduced humidity, particularly between December and March. Of the 28 environmental variables examined, precipitation- and humidity-related indicators demonstrated the strongest inverse associations with weekly confirmed cases, with Spearman correlation coefficients reaching {rho} =-0.75. Air temperature showed the strongest and most consistent positive association, reaching {rho} = 0.633. These findings demonstrate the potential of integrating epidemiological surveillance and environmental GIS layers to characterize spatial and temporal patterns of Lassa fever and provide a foundation for more dynamic susceptibility mapping and environmental risk assessment in Nigeria.

Background: Quantifying behavioral drivers of protective action during infectious disease outbreaks remains challenging. App-based experimental epidemic games (epigames) provide a framework for studying these decisions in naturalistic settings, but correspondence between in-game measures and real-life beliefs or behaviors requires evaluation. We examined whether an activity-based opportunity cost influenced voluntary quarantine decisions within an epigame and whether real-life health beliefs transferred into the game and predicted observed choices. Methods: We conducted a two-week randomized controlled trial from May 4 to May 17, 2026, at VinUniversity (VinUni) in Hanoi, Vietnam. Participants using the Epigames app installed in their smartphone were randomized to a low-barrier group, earning 1 point per qualifying contact with other participant when remaining active, or a high-barrier group, earning 2 points per contact. Of 439 enrolled participants, 283 were successfully randomized to one of the two groups, made at least one valid daily quarantine decision, and their data was used in the analysis. Real-life (S1) and in-game (S2) beliefs measured susceptibility, severity, quarantine self-efficacy, and perceived benefits. Belief correspondence was assessed using Holm-adjusted Spearman correlations and prospective cumulative-logit models. Quarantine choices were analyzed using participant-day binomial generalized estimating equations (GEE) and participant-level quasi-binomial models. Results: Participants made 1,823 valid daily decisions and chose quarantine on 458 participant-days (25.1%). Quarantine rates were 30.1% in the low-barrier group and 20.2% in the high-barrier group. The high barrier was associated with 41% lower population-averaged odds of quarantine (GEE odds ratio [OR] 0.59, 95% confidence interval [CI] 0.40-0.86, = 0.0059); the quasibinomial estimate was identical (OR 0.59, 95% CI 0.40-0.86, = 0.0055). Among 251 participants with matched S1-S2 data, all four corresponding beliefs were positively associated (Spearman's = 0.259-0.418; all Holm-adjusted < 0.001). Prospective ordinal models confirmed positive matched-domain associations (ORs 1.39-2.18 per one-point S1 increase). Beliefs showed little robust association with quarantine behavior, and neither S1 nor S2 beliefs jointly modified the randomized effect. Self-efficacy, network degree, and the preregistered gender main effect were also unsupported. Conclusion: A higher activity-based opportunity cost reduced voluntary quarantine within the VinUni epigame, while participants carried relative differences in stated health beliefs from real-life to in-game framing. These beliefs did not reliably predict observed quarantine choices within the game framing. Epigames can support controlled study of incentives and belief correspondence in naturalistic settings such as college campuses, but behavioral validity or real-world generalizability requires further work.

Purpose Prevention and early detection of osteoporosis remains a global challenge, more so in regions like the Philippines where screening barriers exist. Chest x-rays meanwhile are relatively inexpensive, and more frequently done, and therefore can be used for opportunistic screening. This study aimed to develop a deep learning model for osteoporosis detection from chest x-rays using DXA as the gold standard. Methods A convolutional neural network called Osteo-AI was developed using 406 pairs of chest x-rays and DXA scans of Filipino patients aged 50 and above. With data augmentation, the training set expanded to 6,300 pairs. Gradient-weighted class activation mapping technique was applied to localize and identify patterns and areas in the chest x-ray images correlating with osteoporosis. Results Training data consisted of 369 female patients and 37 males. Ages of the patients ranged from 50 to 89 with a mean age of 63 years old. Initial testing yielded promising results, with Osteo-AI achieving a diagnostic accuracy of 85.71%, easily outperforming a benchmark of 33.33% Conclusion Our findings suggest the potential of Osteo-AI to enhance osteoporosis screening accessibility, aiding in early intervention to prevent fragility fractures. Further research involving larger datasets is warranted to refine and optimize the model, potentially improving detection accuracy and expanding its utility in global healthcare settings.

In climate-health impact projection studies, projected impacts from multiple general circulation models (GCMs) are commonly aggregated by reporting the mean of GCM-specific impacts as the point estimate alongside a 95% empirical confidence interval (eCI) constructed from the 2.5th and 97.5th percentiles of the simulated pooled distribution of GCM-specific impacts. This study shows that the eCI generally does not yield the nominal coverage probability for the GCM-ensemble mean and constructs an interval aligned with the estimand. In a simulation study, the coverage of the eCI for the GCM-ensemble mean deviates from the nominal level in both directions, whereas the aligned interval yields coverage near 95% across all considered settings. The exact coverages derived analytically under a location-shift model agree with the simulation results. In a reanalysis of a heat-related mortality projection in London, the eCI is consistently wider. The eCI should be distinguished from confidence intervals for the GCM-ensemble mean; rather, the interval may be better described as a simulation-based approximate prediction interval for a GCM-specific impact under the uniformly randomly selected GCM from the considered GCM set.