Frontiers in Applied Mathematics and Statistics

This study presents a theoretical and mathematical framework for understanding the dynamical behavior of infectious disease spread using a compartmental modeling approach. The proposed model incorporates memory effects to capture temporal dependencies that are not adequately represented by classical formulations. Qualitative analysis is employed to investigate the stability properties of the system and the role of key mechanisms in shaping long term dynamics. Publicly available surveillance information is used only to illustrate the consistency of the model behavior with observed trends. The results highlight the value of memory based modeling structures for describing complex biological processes and provide a general mathematical perspective for studying epidemic dynamics.

Infectious disease surveillance systems in tropical countries show that respiratory disease incidence generally manifests as year-round activity with weak fluctuations and irregular seasonality. Previously, using a ten-year time series of influenza-like illness (ILI) collected from outpatient clinics in Ho Chi Minh City (HCMC), Vietnam, we found a combination of nonannual and annual signals driving these dynamics, but with unknown mechanisms. In this study, we use seven stochastic dynamical models incorporating humidity, temperature, and school term to investigate plausible mechanisms behind these annual and nonannual incidence trends. We use iterated filtering to fit the models and evaluate the models by comparing how well they replicate the combination of annual and nonannual signals. We find that a model including specific humidity, temperature, and school term best fits our observed data from HCMC and partially reproduces the irregular seasonality. The estimated effects from specific humidity and temperature on transmission are nonlinearly negative but weak. School dismissal is associated with decreased transmission, but also with low magnitude. Under these weak external drivers, we hypothesize that stochasticity makes a strong sub-annual cycle more likely to be observed in ILI disease dynamics. Our study shows a possible mechanism for respiratory disease dynamics in the tropics. When the external drivers are weak, the seasonality of respiratory disease dynamics is prone to the influence of stochasticity.

BackgroundTo control leishmaniasis, chemotherapy drugs are currently under development. However, these drugs often exhibit poor efficacy and are associated with toxicity, adverse effects, and drug resistance. At present, no specific drug is available for the treatment of leishmaniasis. Meanwhile, vaccine research is ongoing. Recent studies have analysed some experimental vaccines using mathematical models. AimIn previous work, drug targeting was focused on the entire human body rather than specifically addressing infected macrophages and parasites. In our current approach, we aim to eliminate infected macrophages and parasites through nano-drug design. Specifically, we utilise two types of nanoparticles: iron oxide and citric acid-coated iron oxide. Moving forward, we plan to advance this strategy using mathematical modelling of macrophage-parasite interactions. MethodsWe design PDE-based models of macrophages and parasites, incorporating cytokine dynamics, to support nano-drug development. Drug efficacy is estimated using posterior distributions to analyse phenotypic fluctuations of macrophages and parasites during the design phase. We investigate implicit and semi-implicit treatment schemes, focusing on energy decay properties. To model drug flow during treatment, we introduce a three-phase moving boundary problem. Comparative analyses are conducted to evaluate macrophage and parasite behaviour with and without treatment. Finally, the entire framework is implemented within a virtual lab environment. ResultsThe results show that the nano-drug exhibits better efficacy compared to combined drug doses. We analysed and compared two types of nano-drug particles: iron oxide and citric acid-coated iron oxide. We discuss how the drug effectively targets and eliminates infected macrophages and parasites. ConclusionOur models results and simulations will support researchers conducting further studies in nano-drug design for leishmaniasis. These simulations are performed within a virtual lab environment.

Age related macular degeneration is known to be one of the major causes of irreversible blindness among the older generation. We present a mathematical model of partial differential equations for the therapy of this disease, which is based on the intravitreal injection of a drug into the vitreous body. For the treatment to work, the drug has to travel past the inner-limiting membrane into the retina and reduce the free vascular endothelial growth factor (VEGF) concentration by binding to at least one of the two binding sites of the VEGF molecule. Therefore, our model consists of two compartments, the vitreous and the retina. In the vitreous we employ four coupled convection-diffusion-reaction equations with an additional coupling to the underlying aqueous humor flow and four coupled diffusion-reaction equations in the retina. The resulting PDE system is solved numerically in a realistic 3D eye geometry. Temporal discretization is based on one-step theta schemes and spatial discretization is done using the Finite Element method. The numerical results are used to demonstrate the therapy concept and to analyze the drug efficacy of aflibercept and ranibizumab. The results show, among other things, that only about 20 % of the drug reaches the retina through the inner-limiting membrane and that 50 % of the VEGF concentration has been rebuilt in the retina after 38.19 days for a single ranibizumab injection.

Following the suggestion of L. F. Jaffe [1] we propose a mathematical model of fast calcium induced calcium influx waves (CICI Waves). They can propagate at relatively high speeds (up to 1300 micrometers/s). According to [1], they propagate due to a mechanochemical interaction of actomyosin network with the cell membrane. The local stretching of the membrane caused by actin filaments opens mechanically operated ion channels resulting in the influx of calcium to the cell. Moreover, stretching a cells membrane at one point opens nearby stretch activated calcium channels because the mechanical force is relayed by the actin filaments interconnected by myosin bridges. The number of bridges as well as filament density increases with calcium concentration, causing the contraction of the actomyosin network. Thus, the force acting on the membrane from tangled actin filaments is transmitted ahead of the moving front of the calcium concentration. As a result, the ion channels are opened even before the signal of calcium reaches them. This leads to much larger propagation speed of CICI waves in comparison with calcium induced calcium released (CICR) waves, where the wave is sustained by the diffusion of calcium and autocatalytic release of calcium from the internal stores (e.g. endoplasmic reticula).

Food costs are more significantly impacted by climate change as countries grow. It is well known that climate change has an impact on the productivity of most agricultural goods, but it is unclear how specifically it will affect food costs. The present research explores how the North Atlantic Oscillation (NAO) index, a widely used climate indicator, affects food prices around the world. This is achieved by applying a robust bivariate Hurst exponent (robust bHe). The research creates a color map of this coefficient using a window-sliding technique over various intervals of time, displaying an illustration that changes overtime. Additionally, the NAO index and global food prices are examined for causal connections using variable-lag transfer entropy using a window-sliding technique. The results show that notable rises in a number of international food prices for long as well as short periods are associated with significant increases in the NAO index. Furthermore, the causative function of the NAO index in influencing global food costs is confirmed by variable-lag transfer entropy. Is highly recommended as it directly connects the research to actionable outcomes for policymakers and the overarching goal of sustainability and food security. This study provides the first direct evidence of a robust, long-range cross-correlation and causal link between the North Atlantic Oscillation (NAO) index and key global food prices. It introduces a novel, robust methodological framework to visualize this time-varying relationship, offering a critical tool for policymakers and forecasting models.

Sylvatic Yellow Fever (YF) is an infectious mosquito-borne disease with significant epidemiological relevance due to its widespread distribution and high lethality for human and non-human primates, particularly in tropical regions of the planet such as in Brazil. Identifying regions and periods of high environmental suitability for the occurrence of YF is essential for preventing or mitigating its burden, as it enables the efficient allocation of surveillance efforts, prevention, and implementation of control measures. Environmental modeling of YF occurrence has proven to be an effective approach toward this goal; however, its effectiveness strongly depends on the modeling framework's capabilities as well as the spatial and temporal precision of all associated data. We propose a fine-scale geospatial modeling of YF environmental suitability that is based on a generative machine-learning ensemble method built on a large set of high-resolution environmental covariates. First, we take the spatiotemporal statistical description of the environment of each of the 545 YF cases from 2019--2024 up to 30 m/monthly resolution at three buffer scales: 100 m, 500 m, and 1000 m ratios. Then, we perform a feature selection and train hundreds of One-Class Support Vector Machine submodels to form a robust ensemble model, whose predictions are projected to a 1x1 km resolution grid of Brazil under several metrics, exceeding seven million ensemble evaluations. The predictions ranked the Southern Brazil region with the highest mean suitability for YF, with a level of 0.64; Southeast comes next with 0.46, followed closely by Central-West region (0.44), North (0.39), and finally Northeast (0.28). The model exhibited high uncertainty for the North region, indicating that data collection efforts are much needed in this region. As for the environmental covariates, a feature analysis pointed out that Land use and cover accounts for the largest influence in the model output.

Fraud in the health landscape is an aggravating issue, with far-reaching consequences burdening the financial stability of the health industry and threatening the quality of medical care. It results from vulnerabilities within the current healthcare framework that are exploited by the fraudsters in their favor. In spite of many developed models that aim to detect fraudulent patterns in insurance claims, the accuracy of such models frequently suffers as a result of the imbalance issue of the Medicare dataset and irrelevant features. This study ventures to improve detection performance and accuracy by employing a deep learning model along with data sampling and feature selection techniques. Comparative analysis among different combinations is conducted to determine their efficacy to enhance the accuracy of the fraud detection model. Hence, the suggested model clearly demonstrates that a combination of myriad data sampling and feature selection techniques is helping to improve accuracy and performance. The accuracy was thus 95.4%, with negligible evidence of overfitting detected using both Chi-square and Synthetic Minority Over-sampling (SMOTE) techniques. Ultimately, the study findings underscore the significance of employing combined techniques instead of using only the baseline deep learning model for better performance in detecting Medicare insurance fraud.

This retrospective study aims to explore the interactive effects of biological maturation and relative age effect (RAE) on talent identification. 56 male elite soccer players matched for chronological age (15.08{+/-}0.41 years) were studied. Test items included anthropometry (height, body mass, sitting height, leg length, BMI and Quetelet index), physiology (power, speed, agility, speed endurance and aerobic performance), soccer-specific skills (passing, shooting and dribbling), psychology (achievement motivation, orientation and resilience) and biological maturation (APHV) tests. The test results were analyzed independent sample t-test, Pearson correlation analysis, and stratified regression. Conclusion: Biological maturation significantly influences anthropometry (height, weight and Quetelet index), lower limb explosive, and speed (single-leg jump, standing triple jump, and 30-m sprint) in U16 male elite soccer players in Shanghai. The relative age effect shows no significant impact on talent selection indicators, which is attributed to the accumulated training load effect. The mechanisms of biological maturation and RAE in youth soccer talent selection are distinct and operate independently.

Mammalian spermatogenesis occurs in the seminiferous tubules, which exhibit unique spatiotemporal differentiation patterns known as cellular association patterns. In mice, these patterns can be regarded as one-dimensional wavetrains that consistently propagate inward from both ends, resulting in one or more "sites of reversal." Segmented wavetrain pattern, in which the wave propagation direction spatially switches, was observed in our previous three-species reaction-diffusion model for interspecific species difference in spermatogenic waves (Kawamura et al., 2021). However, the biological mechanisms of the formation of sites of reversal and of this directional bias, as well as the principle of pattern formation, remain unknown. Here, we refined our previous model to match the actual biological spatiotemporal scale and examined its dynamics through extensive numerical simulations. The modified model frequently generated segmented wavetrain patterns, corresponding to the sites of reversal, but without directional bias. We systematically examined possible biological mechanisms for the bias and found that tubule elongation, especially near the rete testis, most effectively accounts for the bias among the tested. Extensive simulations revealed that the segmented pattern is numerically stable, emerges more frequently in longer domains, and shows an exponential segment size distribution with a lower limit for the stably existing segment length. These explorations imply that locally emerged unidirectional wavetrains serve as building blocks to generate the stable segmented wavetrains through their interactions. HighlightsO_LISegmented wavetrains reflect sites of reversal in seminiferous tubules. C_LIO_LISegmented patterns frequently emerge but show no inherent directional bias. C_LIO_LITubule elongation may contribute to inward propagation near the rete testis. C_LIO_LISegmented wavetrains are numerically stable and more frequent in longer domains. C_LIO_LIInteractions of local unidirectional wavetrains generate stable segmented structures. C_LI

During embryogenesis, as cells proliferate and assemble into tissues, they undergo a sequence of transitions between distinct molecular states eventually giving rise to a cellular population consisting of an appropriate distribution of specific functional cell types. Recent progress on the dynamics underlying decision-making in developmental landscape makes it feasible to start analysing the amount of information involved in constructing such systems. To explore this we introduce the notion of potency of a developmental landscape and attempt to calculate it for two development systems of current interest, in-vitro differentiation of epiblast-like cells into neural and mesodermal progenitors and the worm vulva patterning system. Our approach integrates concepts from developmental biology, information theory and dynamical systems to estimate both the number and identity of signalling regimes that give rise to distinguishable temporal response patterns.

In multicellular organisms, various cellular structures exhibit cytoplasmic sharing, where cells remain interconnected. While essential for development and function in contexts such as germ cell formation and insect early embryos, the physical basis of cell volume regulation in these systems remains poorly defined. Germline cysts are formed by interconnected sister cells via intercellular bridges. In mice, germline cysts form during gametogenesis in fetal ovaries and testes. In mouse fetal female cysts, cells with numerous bridges preferentially differentiate into oocytes by selectively increasing their volume, a process that may be mediated through cytoplasmic flow. This volume bias may be influenced by hydrostatic pressure within the cytoplasm. Here, we theoretically investigate how the mechanical properties of cells affect cytoplasmic pressure and volume distribution within interconnected cells. Our soap-bubble model revealed that cells with more bridges exhibit increased volume when they have large cell-cell contact areas, as observed in fetal cysts. We found that incorporating cell cycle (including cell growth and cell division) significantly enhances the likelihood of volume bias in favor of cells with more bridges. These theoretical findings suggest that intrinsic mechanical properties, coupled with cell cycle, establish robust cyst development in fetal female germline cysts. Our findings also provide insights into the volume dynamics observed in adult male germline cysts, which are characterized by smaller cell-cell contact areas. Impact statementA theoretical model demonstrates how mechanical properties and cell cycle dynamics regulate volume distribution in germline cysts, providing a physical basis for oocyte differentiation.

The opioid crisis has severely impacted Ohio, with overdose death rates surpassing national averages and disproportionately affecting rural and Appalachian regions. Accurately predicting county-level opioid overdose deaths (OD) is critical for timely intervention but remains challenging due to the wide differences in opioid OD between large and small counties. We propose a Spatial-Temporal Graph Neural Network (ST-GNN) framework that integrates graph neural networks (GNNs) to capture spatial relationships between counties and Long Short-Term Memory (LSTM) networks to model temporal dynamics. Using quarterly OD data from Q1 2017 to Q2 2023 for 88 Ohio counties, we incorporate a nine-dimensional dynamic feature set, including naloxone administration events and high-risk opioid prescribing, along with a static Social Determinants of Health (SDoH) index. Compared to traditional statistical models and temporal deep learning baselines, our ST-GNN demonstrates superior performance, particularly in larger counties, while classification-based strategy improve predictions for small counties, leading to more stable and reliable results. Our findings emphasize the need for spatial-temporal modeling and customized training to enhance public health decision-making in addressing the opioid crisis.

BackgroundPacific saury Cololabis saira is one of the important food resources drawing attention for its recent rapid decline of catch. Their life cycle and embryonic development have been largely unknown. It is important to clarify how the habitat and reproduction of this species have been affected by the global changes of aquatic environment. ResultsWe obtained fertilized eggs of C. saira, by spontaneous spawning and artificial fertilization, and observed the embryonic development up to larval stages. Embryonic stages are documented with major periods of developmental events; cleavage, gastrulation (epiboly) and somitogenesis and organogenesis. Remarkably, segmentation of somites starts in the middle of epiboly, unlike other well-documented teleost species such as zebrafish and medaka. Morphological changes in larval stage up to feeding juvenile is also described. Growth speed of larval Pacific saury is dramatically rapid, in comparison to closely related beloniform fish such as medaka. ConclusionsIn comparison to medaka, early embryogenesis of saury proceeds slowly, although being followed by early onset of somitogenesis. This might be partly responsible for the rapid growth into adult (larger than 20 cm in body length) in only half a year. Further studies on embryonic development will uncover the molecular mechanisms underlying the characteristics of Pacific saury as an excellent source of nutrition and as an indicator of major environmental changes such as global warming.

Infrared (IR) imaging systems are used on vessels, platforms, and drones to detect cetaceans several kilometers away, helping to mitigate harm from maritime activities like vessel strikes and pile driving. To ensure operational effectiveness, the reliable detection range (RDR) --the distance at which 100% detection probability is achieved--is a critical metric. This study presents a radiometric model for calculating RDR across a wide range of environmental conditions and system parameters, which enables the evaluation of IR system performance without extensive at-sea data collection.

IntroductionWe investigated the direct effect of transverse maxillary constriction on nasal septal deviation (NSD) and nasal floor slanting. Methods and Materials60 growing Wistar rats (21days old) were divided into four groups (n=15): 1) Experimental Group 1 received active constriction force (100cN), 2) Experimental Group 2 received active expansion force (100cN), 3) Sham received the same spring as Experimental Groups without receiving any active force, and 4) Control group did not receive any appliance. Samples were collected after 28 days for microcomputed tomography (CT) analysis. ResultsExperimental Group 1 demonstrated maxillary constriction (both skeletal and dental), accompanied by mandibular shift on closure, clockwise mandibular rotation, and increased mandibular plane angle and facial height. Constriction also produced severe nasal floor slanting in the molar area that extended posteriorly. Nasal floor canting was accompanied by a slanted vomer and a C-shaped NSD. The direction of nasal floor canting and mandibular shift was always similar. Experimental Group 2, on the other hand, was not associated with nasal deviation, and a slight slanting of the nasal floor was observed only when there was a mandibular shift. ConclusionOur study suggests that the constricting transverse forces applied to the maxilla can induce slanting of the nasal floor and, consequently, the vomer, which in turn can lead to nasal septal deviation. Slanting of the nasal floor is caused mainly by rotation of the hemimaxilla in response to transverse forces and changes in occlusal forces due to a mandibular shift.

The COVID-19 pandemic has presented severe challenges in understanding and predicting the spread of infectious diseases, necessitating innovative approaches beyond traditional epidemiological models. This study introduces an advanced method for automated model discovery using the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm, leveraging a dataset from the COVID-19 outbreak in Thuringia, Germany, encompassing over 400,000 patient records and vaccination data. By analysing this dataset, we develop a flexible, data-driven model that captures many aspects of the complex dynamics of the pandemics spread. Our approach incorporates external factors and interventions into the mathematical framework, leading to more accurate modelling of the pandemics behaviour. The fixed coefficient values of the differential equation as globally determined by the SINDy were not found to be accurate for locally modelling the measured data. We therefore refined our technique based on the differential equations as found by SINDy, by investigating three modifications that account for recent local data. In a first approach, we re-optimized the coefficient values using seven days of past data, without changing the globally determined differential equation. In a second approach, we allowed a temporal dependence of the coefficient values fitted using all previous data in combination with regularization. As a last method, we kept the coefficients fixed to the original values but augmented the differential equation with a small neural network, locally optimized to the data of the past week. Our findings reveal the critical role of vaccination and public health measures in the pandemics trajectory. The proposed model offers a robust tool for policymakers and health professionals to mitigate future outbreaks, providing insights into the efficacy of intervention strategies and vaccination campaigns. This study advances the understanding of COVID-19 dynamics and lays the groundwork for future research in epidemic modelling, emphasising the importance of adaptive, data-informed approaches in public health planning.

Artificial ovarian scaffolds represent a promising therapeutic strategy for preserving reproductive health in patients. However, current in vitro approaches are limited by inadequate biomimicry of the native tissue microenvironment, leading to poor development of in vitro ovarian models. In this study, we developed region-specific hydrogel scaffolds incorporating solubilized decellularized ovarian extracellular matrix (dECM) with mechanically tuned properties to enhance the functionality of engineered 3D ovarian models. Ovine ovarian dECM was isolated by mechanical and chemical decellularization methods and subsequently solubilized and incorporated in varying concentrations in homogenous alginate (0.5%) and a composite mixture of 1% gelatin with 0.5% alginate (1:1). The synthesized hydrogels were characterized for rheological properties, including Youngs modulus, pore size, and viscosity, and cytocompatibility assays were conducted using Chinese hamster ovary (CHO) cells. The study demonstrated that both 0.5% alginate and the composite gelatin-alginate hydrogels successfully replicated the mechanical properties of native human ovarian cortical and medullary tissue, with Youngs modulus of 0.84 {+/-} 0.16 kPa, pore size (60-150 nm), and toughness of 0.4Pa, respectively. Zonal hydrogel scaffolds incorporating ovarian dECM demonstrated significantly enhanced cell viability compared to hydrogels supplemented with dECM. The study emphasises the critical role of integrating both mechanical and biochemical attributes while developing functional artificial ovarian constructs for transplantation and regenerative medicine applications. This work contributes to advancing strategies for creating physiologically relevant in vitro models of ovarian tissue.

BackgroundThe growing interest in applying artificial intelligence in personalized nutrition is challenged by the complex nature of dietary advice that must balance health, economic, and personal factors. Though automated solutions using either Linear Programming (LP) or Large Language Models (LLMs) already exist, they have significant drawbacks. LP often lacks personalization, whereas LLMs can be unreliable for precise calculations. ObjectivesTo develop and assess a model that integrates a Mixed Integer Linear Programming (MILP) solver with an LLM to generate personalized meal plans and compare it with standalone LLM and MILP models. MethodsThe proposed hybrid MILP+LLM model first uses an LLM (GPT-4o) to filter a unified food dataset (n=297), which combines regional Central Asian and global food items, according to the users profile. The filtered list of food items is then received by a MILP solver which identifies the set of top 10 optimal solutions. Finally, given this set of solutions, LLM chooses the most appropriate meal plan. The model was evaluated using five synthesized, clinically complex patient profiles sourced from Adilmetova et al. [4]. The performance of this hybrid model was compared against standalone MILP and LLM using 5-point Likert scale with Kruskal-Wallis and post hoc Dunns tests for Nutrient Accuracy, Personalization, Practicality, and Variety. ResultsFindings demonstrated that the proposed MILP+LLM model reached balanced performance achieving scores of more than 3.6 points in all criteria, with high scores in Nutrient Accuracy (3.96), Personalization (3.81), and Practicality (3.99). The standalone LLM model performed the weakest in all criteria, with statistically significant lower scores compared to the other two methods. The standalone MILP model performed best in Nutrient Accuracy (4.93) and in Variety (4.10) but lagged behind the MILP+LLM model in Practicality and Personalization. Kruskal-Wallis and Dunns tests showed MILP and MILP+LLM outperformed LLM across all criteria. MILP was more accurate (p<0.0001), while MILP+LLM model was more practical (p=0.021). ConclusionsThe findings suggest that integrating the LLM with the MILP solver creates a model that combines qualitative personalization with quantitative precision. This model produces comprehensive, reliable meal plans, addressing the limitations of using either model alone.

Studies of appendage regeneration in vertebrates have shown that the fundamental building block of any regenerative tissue is a blastema. The blastema is a cone-shaped accumulation that forms at the site of amputation post wound-healing and is the result of a highly coordinated process involving a cluster of cells capable of growth, migration, and differentiation. Although several key signaling pathways involved in regeneration have been identified, which cellular processes they control and how these processes are coordinated across space and time are not yet fully understood. This study introduces a computational tool to examine how the outgrowth results from the interaction of two tissue layers: the bulk (mesenchyme) and the overlying epithelium. We developed a novel hybrid agent-based modeling framework and an accompanying parameter inference pipeline to uncover the cellular properties in the epithelium and the mesenchyme driving the formation of a normal regenerative blastema with a morphology similar to that observed in experiments. Using our model, we report two conditions for blastema formation: retained local softening of the epithelial layer at the site of injury, which was confirmed experimentally with atomic force microscopy (AFM) measurements, and the involvement of the Wnt signaling pathway in the directed migration of mesenchyme cells towards the distal tip. Taken together, this combined experimental-theoretical approach provides a framework for understanding how the Wnt signaling pathway influences the formation of the early blastema at multiple levels of organization and how key cellular behaviors contribute to its formation. Author SummaryA small number of tetrapods have retained the ancestral ability to regenerate tissues and even limbs. Indifferent of species or tissue, the decisive initial stage of limb regeneration is the formation of a specialized structure called the blastema, a heterogeneous mass of mesenchymal cells, in a relatively short timescale of 2-14 days post injury or amputation. To study the mechanical and cellular conditions for limb blastema formation in the axolotl model organism, we developed a novel hybrid agent-based modeling framework and accompanying kinetic parameter inference pipeline. By recapitulating blastema morphometrics of healthy and stalled regenerative states, our model finds two conditions for blastema formation: retained local softening of the epithelial layer at the injury site post wound-healing, which we confirmed with atomic force microscopy measurements, and that the Wnt signaling pathway plays a role in the migration of mesenchyme cells to the distal tip in order to produce the blastema.