Mathematical Biosciences and Engineering最新文献

The effectiveness of isolation strategies against emerging infectious diseases (EIDs) is critically undermined by two interacting factors: Limited resource capacity and imperfect public compliance, yet their combined impact remains poorly quantified. We develop an ordinary differential equation (ODE) model incorporating a saturation function for resource limits and a compliance parameter ($ epsilon $) to quantify their nonlinear interaction. Theoretical analysis reveals a resource-driven backward bifurcation, indicating that reducing a basic reproduction number $ R_0 $ below 1 is necessary but may be insufficient for disease elimination when isolation capacity is critically low. Numerically, we identify a counterintuitive paradox: High compliance amplifies the infection risk when isolation resources are severely constrained. The simulation results classify the dynamic regimes under various parameter settings and reveal the qualitative impact of different isolation strategies. The study finds that increasing isolation resources, combined with a certain level of compliance, significantly reduces the infection risk and aids in disease control. Notably, specific transmission patterns emerge when isolation resources are inadequate, resulting in elevated infection risks even when compliance is high. Our results underscore the imperative of synchronizing resource allocation with behavioral interventions, particularly during early outbreak stages, providing a framework for precision public health strategies.

Clostridioides difficile, also known as C. difficile, is a prevalent cause of infectious diarrhea in United States healthcare facilities. Spread through the fecal-oral route and often through contact with spores on contaminated surfaces, C. difficile can cause severe diarrhea, stomach pain, and colitis. Most individuals can mount an effective immune response, but older populations, immunocompromised individuals, and those taking antibiotics have a higher risk of being colonized by C. difficile. While extensive research has been conducted in hospital-based settings to improve understanding of the transmission of this bacteria, few studies apply mathematical models in the context of long-term care facilities. This work introduced a mathematical model using a system of ordinary differential equations to represent C. difficile transmission dynamics in assisted living facilities, with their interactive nature and high risk factors. The equations included four resident classes (susceptible, colonized, diseased, and isolated) and three pathogen-carrying classes (high-traffic areas, low-traffic areas, and healthcare workers' hands) to simultaneously capture the movement between classes and track spore density on environmental reservoirs and healthcare workers' hands, including their contributions to disease spread. Parameter estimation using data from the Emerging Infections Program at the Centers for Disease Control and Prevention was completed and was followed by sensitivity analyses to quantify the impact of varying these parameters and their impact on incidence. Mitigation strategies, including frequent disinfection, increased healthcare worker hand hygiene compliance, a lower ratio between residents and healthcare workers, and increased resident screening had the greatest impact on reducing the incidence of C. difficile.

Accurately predicting the discharge coefficient (C_d) is fundamental to the hydraulic design and performance of side weirs. In this study, we introduced a novel artificial intelligence (AI) framework to enhance the prediction accuracy of C_d for two-cycle trapezoidal labyrinth side weirs. Using a comprehensive laboratory dataset, three distinct machine learning models (MLMs), Support Vector Machine (SVM), Artificial Neural Network (ANN), and Gene Expression Programming (GEP), were developed and rigorously compared with application of the Γ-test technique for sensitivity analysis, systematically identifying the five most influential geometric and hydraulic parameters (Fr, $ frac{text{L}}{text{B}} $, $ frac{{text{L}}_{text{e}}}{text{L}} $, $ frac{{text{Y}}_{text{1}}text{-P}}{text{P}} $, α) to serve as model inputs. The model's efficacy was evaluated across training, testing, and validation phases using multiple statistical metrics: Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Coefficient of Determination (R²), and the Maximum Developed Discrepancy Ratio (C_d(DDRmax)). The results demonstrated that the three MLMs are effective predictive tools. However, the ANN model, specifically an MLP5-7-1 architecture utilizing Atan and Identity activation functions optimized with the BFGS 385 algorithm, significantly outperformed the others. It achieved superior results (e.g., validation phase: RMSE = 0.0061, MAE = 0.0003, R² = 0.9301, C_d(DDRmax) = 5.22), confirming its highest predictive accuracy and robustness. This research conclusively shows that MLMs, particularly ANN, offer a highly precise and efficient method for predicting Cd in complex hydraulic structures.

We investigate the spatiotemporal dynamics of a tri-trophic food chain model incorporating a strong Allee effect on the prey and a fear effect on the middle predator. The model's well-posedness is established through the positivity and boundedness of solutions. We derive all equilibria and examine their local stability, revealing saddle-node and transcritical bifurcations under varying parameter conditions. The analysis demonstrates how shifts in the Allee threshold and fear intensity induce bistability, coexistence, or extinction. Numerical simulations highlight diffusion-driven instabilities and complex Turing patterns, including labyrinthine formations and unexpected "leaser slime" structures-resembling those observed in fungi and algae in aquatic systems. These findings reveal the crucial role of behavioral and ecological feedbacks in shaping pattern formation and species persistence.

Density estimation neural networks (DENNs) represent a form of artificial neural network designed to provide an efficient approach to the Bayesian estimation of a probability density on a model parameter space, conditioned on an empirical observation of the underlying system. Despite their efficiency and potential, DENNs remain underutilized for parameter estimation in mathematical modeling. In this work, we aim to boost the accessibility of the DENN approach by providing a user-friendly introduction and code that makes it easy for users to harness existing, cutting-edge DENN software. Furthermore, we insert an easily-implemented preliminary data simulation step that reduces the computational demands of the approach and empirically demonstrates that it maintains the accuracy of parameter estimation for a stochastic oscillator model.

Climatic factors exert a substantial influence on both biotic and abiotic components of marine ecosystems, significantly affecting the abundance and spatial distribution of fish species. In this study, we introduced a stochastic modeling framework, grounded in stochastic differential equations (SDEs), to analyze the temporal dynamics of sea surface temperature and its relationship with the abundance of Mahi Mahi (Coryphaena hippurus) in a region of the Colombian Pacific coast. Model parameters such as sea surface temperature, fish stock, and catch per unit effort for the period 2000 to 2012 were estimated using the maximum likelihood method, implemented via the Euler-Maruyama numerical scheme. The model's performance was assessed using empirical data through numerical simulation, cross-validation, and sensitivity analysis, demonstrating its applicability and robustness in capturing key ecological dynamics.

This paper develops a mathematical framework for life and health insurance premium calculation under epidemic conditions, incorporating age-structured population dynamics and disease compartments. We proposed a compartmental epidemic model with three age groups and four states (susceptible, infectious, recovered, deceased) to reflect heterogeneity in disease progression and risk exposure. The model captures differential mortality and morbidity risks across age groups and infection states, enabling dynamic adjustment of insurance premiums. By integrating actuarial principles with epidemic-driven transition probabilities, we derived explicit premium formulas and validated them through numerical simulations. Our results demonstrate that age stratification and detailed infection stages significantly impact premium pricing, particularly for older populations with higher mortality risks. Sensitivity analysis reveals that recovery and mortality rates are key drivers of premium variability. The framework provides insurers with a robust tool for pandemic risk assessment, ensuring solvency while maintaining affordability.

Despite significant advances in image processing, achieving human-like semantic understanding and explainability remains a formidable challenge. Current deep learning models excel at feature extraction but lack the ability to reason about relationships, interpret context, or provide transparent decision-making. To address these limitations, we propose the adaptive neuro-symbolic framework with dynamic contextual reasoning (ANS-DCR), a novel architecture that seamlessly integrates neural networks with symbolic reasoning. ANS-DCR introduces four key innovations: 1) A contextual embedding layer (CEL) that dynamically converts neural features into structured symbolic embeddings tailored to the scene's context; 2) hierarchical knowledge graphs (HKGs) that encode multi-level object relationships and update in real-time on the basis of neural feedback; 3) an adaptive reasoning engine (ARE) that performs scalable, context-aware logical reasoning; and 4) an explainable decision-making module (EDM) that generates human-readable explanations, including counterfactuals, enhancing interpretability. This framework bridges the gap between pattern recognition and logical reasoning, enabling deeper semantic understanding and dynamic adaptability. We demonstrate ANS-DCR's efficacy in complex scenarios such as autonomous driving, where it accurately interprets traffic scenes, predicts behaviors, and provides clear explanations for decisions. Experimental results show superior performance in semantic segmentation, contextual reasoning, and explainability compared with state-of-the-art methods. By combining the strengths of neural and symbolic paradigms, ANS-DCR sets a new benchmark for intelligent, transparent, and scalable image processing systems, offering transformative potential for applications in robotics, healthcare, and beyond. The source code of the proposed ANS-DCR is at github.com/livingjesus/ANS-DCR.

This review examines recent developments in modeling the interaction between tumor cells and the immune system, with a specific focus on the application of delay differential equations (DDEs). The models serve as crucial tools to simulate and predict the immune response to tumor proliferation, thus facilitating a more effective evaluation of clinical and therapeutic strategies before their implementation. This approach enables the hypothetical testing of various interventions, thus resulting in significant time and resource savings. The central theme is the integration of DDEs to represent biologically realistic time delays. These delays-inherent in biological processes such as the activation and migration of immune cells to the tumor site-are essential for a more accurate and dynamic representation of the system. Furthermore, this document acknowledges the inherent limitations of these mathematical models, which are simplified representations of complex biological phenomena by nature. The precision and practical utility of these models depend on the use of biologically plausible delay formulations, the validation of parameters with empirical data, and the alignment of model predictions with clinical outcomes. Ultimately, this work underscores the considerable potential and significant challenges of employing mathematical models as a bridge between theoretical understanding and applied oncology.

The classification of rare skin diseases faces significant data scarcity challenges due to the difficulty in acquiring clinical samples and the high cost of annotation, which severely hinders the training of deep neural network-based models. Few-shot learning has emerged as a cutting-edge solution, with its core capability being the identification of novel disease classes using limited annotated samples to mitigate data insufficiency. However, most existing methods fail to fully leverage the statistical information from base classes to calibrate the distribution of few-shot classes, thereby optimizing classifier inputs. Two critical research challenges remain: (1) accurately estimating the true distribution of few-shot classes with minimal samples, and (2) selecting appropriate base class information for effective distribution calibration. To address these challenges, we propose SADC (skin disease classification via adaptive distribution calibration), a new few-shot learning framework incorporating multi-scale feature extraction and adaptive sample calibration. First, our multi-scale feature extraction strategy employs feature descriptor matrices and composite metrics to optimize multi-dimensional, multi-directional feature representations, enabling precise similarity computation between base-class and few-shot samples. Second, the adaptive sample calibration strategy constructs weight matrices based on sample similarity to automatically select optimal base-class samples with adaptive weights for distribution calibration, ensuring alignment between calibrated distributions and true unbiased distributions. Experimental results demonstrated that SADC achieves state-of-the-art performance across three public dermatology datasets (ISIC2018, Derm7pt, and SD198), showing significant improvements over existing methods. The framework's innovation lies in its dual-strategy approach to distribution-aware few-shot learning, advancing the frontier of data-efficient medical image analysis.