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A space-time Caputo fractional order and modified homotopy perturbation method for evaluating the pathological response of tumor-immune cells 用于评估肿瘤免疫细胞病理反应的时空卡普托分数阶和修正同调扰动法
Pub Date : 2024-04-06 DOI: 10.1016/j.health.2024.100325
Morufu Oyedunsi Olayiwola, Adedapo Ismaila Alaje

Tumors result from genetic mutations or environmental factors that prompt cells to divide uncontrollably. This study aims to examine the behavior of tumor-immune cell growth in the presence of chemotherapy drug diffusion at a Caputo fractional order. To accomplish this, we employed the modified homotopy perturbation method to solve a proposed system of nonlinear differential equations. We obtained the analytical solutions to study the spatiotemporal pathological response of tumor-immune cell growth. Our analysis also considered the impact of the Caputo-fractional order on the system's dynamics and compared the results with the classical integer-order scenario. Our findings demonstrated that the proposed method is an effective and precise technique for understanding the intricate interactions of tumor-immune cell growth. Additionally, we revealed that the Caputo-fractional order plays a significant role in the system's behavior and should not be overlooked in future analyses of such systems. In conclusion, this study holds important implications for cancer research by providing insights into the behavior of tumor-immune cell growth in the presence of time-fractional administration of chemotherapy drugs.

肿瘤是基因突变或环境因素促使细胞失控分裂的结果。本研究旨在探讨在卡普托分数阶化疗药物扩散条件下肿瘤免疫细胞的生长行为。为此,我们采用了改进的同调扰动法来求解所提出的非线性微分方程系统。我们获得了解析解,从而研究了肿瘤免疫细胞生长的时空病理反应。我们的分析还考虑了卡普托分数阶对系统动力学的影响,并将结果与经典的整数阶方案进行了比较。我们的研究结果表明,所提出的方法是一种有效而精确的技术,可用于理解肿瘤-免疫细胞生长过程中错综复杂的相互作用。此外,我们还发现卡普托分数阶在系统行为中起着重要作用,在今后分析此类系统时不应忽视。总之,这项研究为化疗药物分时给药情况下肿瘤免疫细胞的生长行为提供了见解,对癌症研究具有重要意义。
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引用次数: 0
An ensemble-based stage-prediction machine learning approach for classifying fetal disease 用于胎儿疾病分类的基于集合的阶段预测机器学习方法
Pub Date : 2024-04-04 DOI: 10.1016/j.health.2024.100322
Dipti Dash, Mukesh Kumar

Fetal diseases often lead to the death of many babies during pregnancies. Machine learning and deep learning are promising technologies providing efficient and effective detection and treatment of various fetal diseases. We contribute to the medical field by addressing the critical challenge of fetal disease classification, a concern affecting females and infants. This study utilizes 22 features associated with fetal heart rate extracted from 2126 patient records within the Cardiotocography(CTG) datasets. Our classification system offers a cost-effective, efficient, and accurate solution. It classifies fetal diseases into three categories: Normal, Suspect, and Pathological, based on preprocessed data that underwent MinMax Scaling and employed dimensionality reduction techniques, including Principal Component Analysis(PCA) and Autoencoders. By incorporating dimensionality reduction techniques, the computation time has been reduced from 9 to 26 s to just 4 and 15 s, which is less than half of the original computation time. We assessed the performance of 11 standard machine learning algorithms and various performance metrics to identify the best classification model. We have applied the K-fold Cross-Validation technique to validate our model to improve machine learning models and identify the most effective algorithm. When the results are compared, it is observed that Extreme Gradient Boosting (XGBoost) gained the highest accuracy of 0.99% also highest precision 0.93% and outperformed all the other machine learning algorithms.

胎儿疾病常常导致许多婴儿在怀孕期间死亡。机器学习和深度学习是一种前景广阔的技术,能有效检测和治疗各种胎儿疾病。我们通过解决影响女性和婴儿的胎儿疾病分类这一关键挑战,为医学领域做出了贡献。本研究利用了从 2126 份患者记录中提取的 22 个与胎儿心率相关的特征,这些特征来自于心脏排畸(CTG)数据集。我们的分类系统提供了一个经济、高效、准确的解决方案。它将胎儿疾病分为三类:该系统基于经过 MinMax Scaling 的预处理数据,并采用了包括主成分分析(PCA)和自动编码器在内的降维技术,将胎儿疾病分为正常、可疑和病理三类。通过采用降维技术,计算时间从 9 秒到 26 秒缩短到 4 秒和 15 秒,不到原来计算时间的一半。我们评估了 11 种标准机器学习算法的性能和各种性能指标,以确定最佳分类模型。我们采用 K 折交叉验证技术来验证我们的模型,以改进机器学习模型并找出最有效的算法。在对结果进行比较时,我们发现极端梯度提升算法(XGBoost)获得了最高的准确率 0.99%和最高的精度 0.93%,表现优于所有其他机器学习算法。
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引用次数: 0
A robust neural network for privacy-preserving heart rate estimation in remote healthcare systems 用于远程医疗系统中保护隐私的心率估计的稳健神经网络
Pub Date : 2024-04-04 DOI: 10.1016/j.health.2024.100329
Tasnim Nishat Islam , Hafiz Imtiaz

In this study, we propose a computationally-light and robust neural network for estimating heart rate in remote healthcare systems. We develop a model that can be trained on consumer-grade graphics processing units (GPUs), and can be deployed on edge devices for swift inference. We propose a hybrid model based on convolutional neural network (CNN) and bidirectional long short-term memory (BiLSTM) architectures for estimating heart rate from Electrocardiogram (ECG) and Photoplethysmography (PPG) signals. Considering the sensitive nature of the ECG signals, we ensure a formal privacy guarantee, differential privacy, for the model training. We perform a tight accounting of the overall privacy budget of our training algorithm using the Rényi Differential Privacy technique. We demonstrate that our model outperforms state-of-the-art networks on a benchmark dataset for both ECG and PPG signals despite having a much smaller number of trainable parameters and, consequently, much smaller training and inference times. Our CNN-BiLSTM architecture can also provide excellent heart rate estimation performance even under strict privacy constraints. We develop a prototype Arduino-based data collection system that is low-cost, efficient, and useful for providing access to modern healthcare services to people living in remote areas.

在本研究中,我们提出了一种计算轻便、鲁棒性强的神经网络,用于估计远程医疗系统中的心率。我们开发的模型可在消费级图形处理器(GPU)上进行训练,并可部署在边缘设备上进行快速推理。我们提出了一种基于卷积神经网络(CNN)和双向长短期记忆(BiLSTM)架构的混合模型,用于从心电图(ECG)和光电血压计(PPG)信号中估计心率。考虑到心电图信号的敏感性,我们为模型训练提供了正式的隐私保证--差分隐私。我们使用雷尼差分隐私技术对训练算法的整体隐私预算进行了严格核算。我们证明了我们的模型在 ECG 和 PPG 信号的基准数据集上优于最先进的网络,尽管可训练参数的数量要少得多,因此训练和推理时间也要短得多。即使在严格的隐私限制条件下,我们的 CNN-BiLSTM 架构也能提供出色的心率估计性能。我们开发的基于 Arduino 的数据收集系统原型成本低、效率高,可为偏远地区的人们提供现代医疗服务。
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引用次数: 0
A hybrid Grasshopper optimization algorithm for skin lesion segmentation and melanoma classification using deep learning 利用深度学习进行皮损分割和黑色素瘤分类的混合蚱蜢优化算法
Pub Date : 2024-04-02 DOI: 10.1016/j.health.2024.100326
Puneet Thapar , Manik Rakhra , Mahmood Alsaadi , Aadam Quraishi , Aniruddha Deka , Janjhyam Venkata Naga Ramesh

Skin cancer can be detected through visual examination and confirmed through dermoscopic analysis and various diagnostic tests. This is because visual observation enables early detection of unique skin images by artificial intelligence. Promising outcomes are shown by several Convolution Neural Network (CNN)–based skin lesion classification systems that employ tagged skin images. This study suggests a practical approach for identifying skin cancers using dermoscopy pictures, improving specialists' ability to distinguish benign from malignant tumors. The Swarm Intelligence (SI) approach used dermoscopy photographs to locate lesions on the skin areas Region of interest (ROI). The Grasshopper Optimization technique produced the best segmentation outcomes. The Speed-Up Robust Features (SURF) approach is applied to extract features based on these findings. Two groups were created using the ISIC-2017, ISIC-2018, and PH-2 databases to categorize skin tumors. With an estimated accuracy in classification of 98.52%, preciseness of 96.73%, and Matthews Correlation Coefficient (MCC) of 97.04%, the suggested classification and segmentation methodologies have been evaluated for classification efficacy, specificity, sensitivity, F-measure, preciseness, the MCC, the dice coefficient, and Jaccard's index. In every performance indicator, the method we suggest outperformed state-of-the-art methods.

皮肤癌可以通过肉眼检查发现,并通过皮肤镜分析和各种诊断测试加以确认。这是因为视觉观察可以通过人工智能对独特的皮肤图像进行早期检测。一些基于卷积神经网络(CNN)的皮肤病变分类系统采用了标记皮肤图像,取得了可喜的成果。这项研究提出了一种利用皮肤镜图片识别皮肤癌的实用方法,提高了专家区分良性和恶性肿瘤的能力。蜂群智能(SI)方法使用皮肤镜照片来定位皮肤区域感兴趣区(ROI)上的病变。草蜢优化技术产生了最佳的分割效果。根据这些结果,采用加速鲁棒特征(SURF)方法提取特征。利用 ISIC-2017、ISIC-2018 和 PH-2 数据库创建了两组皮肤肿瘤分类。所建议的分类和分割方法的估计分类准确率为 98.52%,精确度为 96.73%,马修斯相关系数(MCC)为 97.04%,并对分类效果、特异性、灵敏度、F 值、精确度、MCC、骰子系数和 Jaccard 指数进行了评估。在每个性能指标上,我们建议的方法都优于最先进的方法。
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引用次数: 0
An ensemble classification approach for cervical cancer prediction using behavioral risk factors 利用行为风险因素预测宫颈癌的集合分类法
Pub Date : 2024-03-28 DOI: 10.1016/j.health.2024.100324
Md Shahin Ali, Md Maruf Hossain, Moutushi Akter Kona, Kazi Rubaya Nowrin, Md Khairul Islam

Cervical cancer is a significant public health concern among females worldwide. Despite being preventable, it remains a leading cause of mortality. Early detection is crucial for successful treatment and improved survival rates. This study proposes an ensemble Machine Learning (ML) classifier for efficient and accurate identification of cervical cancer using medical data. The proposed methodology involves preparing two datasets using effective preprocessing techniques, extracting essential features using the scikit-learn package, and developing an ensemble classifier based on Random Forest, Support Vector Machine, Gaussian Naïve Bayes, and Decision Tree classifier traits. Comparison with other state-of-the-art algorithms using several ML techniques, including support vector machine, decision tree, random forest, Naïve Bayes, logistic regression, CatBoost, and AdaBoost, demonstrates that the proposed ensemble classifier outperforms them significantly, achieving accuracies of 98.06% and 95.45% for Dataset 1 and Dataset 2, respectively. The proposed ensemble classifier outperforms current state-of-the-art algorithms by 1.50% and 6.67% for Dataset 1 and Dataset 2, respectively, highlighting its superior performance compared to existing methods. The study also utilizes a five-fold cross-validation technique to analyze the benefits and drawbacks of the proposed methodology for predicting cervical cancer using medical data. The Receiver Operating Characteristic (ROC) curves with corresponding Area Under the Curve (AUC) values are 0.95 for Dataset 1 and 0.97 for Dataset 2, indicating the overall performance of the classifiers in distinguishing between the classes. Additionally, we employed SHapley Additive exPlanations (SHAP) as an Explainable Artificial Intelligence (XAI) technique to visualize the classifier’s performance, providing insights into the important features contributing to cervical cancer identification. The results demonstrate that the proposed ensemble classifier can efficiently and accurately identify cervical cancer and potentially improve cervical cancer diagnosis and treatment.

宫颈癌是全世界女性关注的一个重大公共卫生问题。尽管宫颈癌是可以预防的,但它仍然是导致死亡的主要原因。早期发现对于成功治疗和提高生存率至关重要。本研究提出了一种集合式机器学习(ML)分类器,用于利用医疗数据高效、准确地识别宫颈癌。建议的方法包括使用有效的预处理技术准备两个数据集,使用 scikit-learn 软件包提取基本特征,并开发基于随机森林、支持向量机、高斯奈夫贝叶斯和决策树分类器特征的集合分类器。与使用支持向量机、决策树、随机森林、奈夫贝叶斯、逻辑回归、CatBoost和AdaBoost等多种ML技术的其他先进算法相比,所提出的集合分类器的性能明显优于它们,在数据集1和数据集2中的准确率分别达到了98.06%和95.45%。就数据集 1 和数据集 2 而言,所提出的集合分类器分别比目前最先进的算法高出 1.50% 和 6.67%,凸显了其优于现有方法的性能。研究还利用五重交叉验证技术分析了所提方法在利用医疗数据预测宫颈癌方面的优缺点。数据集 1 和数据集 2 的接收方操作特征曲线(ROC)及相应的曲线下面积(AUC)值分别为 0.95 和 0.97,表明分类器在区分类别方面的整体性能良好。此外,我们还采用了可解释人工智能(XAI)技术--SHAPLE Additive exPlanations(SHAP)来可视化分类器的性能,从而深入了解有助于宫颈癌识别的重要特征。结果表明,所提出的集合分类器可以高效、准确地识别宫颈癌,并有望改善宫颈癌的诊断和治疗。
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引用次数: 0
An in-silico game theoretic approach for health intervention efficacy assessment 健康干预效果评估的内部博弈论方法
Pub Date : 2024-03-27 DOI: 10.1016/j.health.2024.100318
Mansura Akter , Muntasir Alam , Md. Kamrujjaman

The global rise of multi-strain epidemics has raised significant concerns in the field of public health. To address this, our research introduces a game-theoretic approach to predict the evolutionary dynamics of multi-strained pathogens. Our proposed model sheds light on the pivotal role of vaccination in controlling the growth of such infectious diseases. Here, we propose a modified Susceptible-Vaccinated-Infected-Recovered (SVIR) model featuring two strains and corresponding vaccines: one is the primary vaccine that is designed to target the original strain (effectiveness: e1) and simultaneously exhibits some effectiveness against the mutant strain (e2), another is the mutant vaccine that concentrates on the mutant strain (η2) while showing significant effectiveness against the primary strain (η1). Next, we present a comprehensive time series analysis to examine the fraction of the vaccinated population who adopted these two vaccines. This work elucidates that with a slight increase effectiveness- setting e1=0.5, e2=0.3, η1=0.6, and η2=0.7- the mutant vaccine works more proficiently under both imitation dynamics known as Individual-Based Risk Assessment (IB-RA) and Strategy-Based Risk Assessment (SB-RA). Furthermore, a detailed analysis comparing these two imitation dynamics is demonstrated and also to reconcile the matter that the Strategy-Based-Risk-Assessment process should be adopted to minimize epidemic size. Finally, considering individuals’ attitudes and behaviors towards vaccination, we introduce a replicator equation. Subsequently, a thorough examination of the relationship between imitation dynamics and behavioral dynamics is presented where imitation dynamics outstripped behavioral dynamics which is confirmed by the use of heat maps.

多菌株流行病在全球范围内的兴起引起了公共卫生领域的极大关注。为此,我们的研究引入了一种博弈论方法来预测多菌株病原体的进化动态。我们提出的模型揭示了疫苗接种在控制此类传染病增长中的关键作用。在这里,我们提出了一个改进的易感-接种-感染-恢复(SVIR)模型,该模型包含两种菌株和相应的疫苗:一种是主要疫苗,其设计目标是原始菌株(有效性:e1),同时对变异菌株(e2)也有一定的有效性;另一种是变异疫苗,其主要针对变异菌株(η2),同时对主要菌株(η1)也有显著的有效性。接下来,我们将进行全面的时间序列分析,研究接种这两种疫苗的人群比例。这项工作阐明,在基于个体的风险评估(IB-RA)和基于策略的风险评估(SB-RA)这两种模仿动态下,随着效力的略微提高--设定 e1=0.5、e2=0.3、η1=0.6 和 η2=0.7--突变株疫苗的效果会更好。此外,还对这两种模仿动力学进行了详细的分析比较,并说明应采用基于策略的风险评估程序,以尽量减少流行病的规模。最后,考虑到个人对疫苗接种的态度和行为,我们引入了一个复制方程。随后,我们对模仿动态和行为动态之间的关系进行了深入研究,模仿动态超过了行为动态,这一点通过热图得到了证实。
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引用次数: 0
A visual attention-based algorithm for brain tumor detection using an on-center saliency map and a superpixel-based framework 基于视觉注意力的脑肿瘤检测算法,使用中心突出图和基于超像素的框架
Pub Date : 2024-03-26 DOI: 10.1016/j.health.2024.100323
Nishtha Tomar, Sushmita Chandel, Gaurav Bhatnagar

Brain tumors are life-threatening and are typically identified by experts using imaging modalities like Magnetic Resonance Imaging (MRI), Computed Tomography (CT), and Positron Emission Tomography (PET). However, any error due to human intervention in brain anomaly detection can have devastating consequences. This study proposes a tumor detection algorithm for brain MRI images. Previous research into tumor detection has drawbacks, paving the way for further investigations. A visual attention-based technique for tumor detection is proposed to overcome these drawbacks. Brain tumors have a wide range of intensity, varying from inner matter-alike intensity to skull-alike intensity, making them difficult to threshold. Thus, a unique approach to threshold using entropy has been utilized. An on-center saliency map accurately captures the biological visual attention-focused tumorous region from the original image. Later, a superpixel-based framework has been proposed and used to capture the true structure of the tumor. Finally, it was experimentally shown that the proposed algorithm outperforms the existing algorithms for brain tumor detection.

脑肿瘤危及生命,通常由专家使用磁共振成像(MRI)、计算机断层扫描(CT)和正电子发射断层扫描(PET)等成像模式进行识别。然而,在脑部异常检测中,人为干预导致的任何错误都可能造成毁灭性后果。本研究提出了一种脑部核磁共振成像图像的肿瘤检测算法。以往的肿瘤检测研究存在缺陷,为进一步研究铺平了道路。为了克服这些缺点,本研究提出了一种基于视觉注意力的肿瘤检测技术。脑肿瘤的强度范围很广,从类似于内质的强度到类似于头骨的强度不等,因此很难对其进行阈值化处理。因此,我们采用了一种独特的熵阈方法。中心突出图可以从原始图像中准确捕捉到生物视觉注意力集中的肿瘤区域。随后,又提出了一种基于超像素的框架,用于捕捉肿瘤的真实结构。最后,实验证明,在脑肿瘤检测方面,所提出的算法优于现有算法。
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引用次数: 0
A predictive approach for myocardial infarction risk assessment using machine learning and big clinical data 利用机器学习和临床大数据进行心肌梗死风险评估的预测方法
Pub Date : 2024-03-21 DOI: 10.1016/j.health.2024.100319
Imen Boudali , Sarra Chebaane , Yassine Zitouni

Myocardial infarction is one of the most common cardiovascular diseases in emergency departments. Early prevention of this dangerous condition significantly impacts public health and considerable socioeconomic outcomes. The emergence of electronic health records (EHR) and the availability of real-world clinical data have provided opportunities to improve the quality and efficiency of healthcare by using artificial intelligence tools. In this study, we focus on the early recognition of risk factors, which can provide valuable information for early prediction of myocardial infarction and promoting a healthy life. Based on a big clinical dataset, we develop a predictive analytics approach for myocardial infarction. A vital step in efficient prediction is assessing the significance of input features, their relationships and their contributions to the disease. Therefore, we adopted statistical techniques, principal component analysis (PCA) and feature engineering. To reveal patterns and insights on our dataset, we implemented machine learning (ML) models varying from classical to more sophisticated: decision trees (DT), random forests (RF), gradient boosting algorithms (GBoost, LightGBM, CatBoost, and XGBoost) and deep neural networks (DNN). The imbalance-data issue is tackled by employing random under-sampling technique. The light gradient boosting model (LightGBM) with feature engineering on the balanced dataset is the best prediction performance achieved in this study.

心肌梗塞是急诊科最常见的心血管疾病之一。及早预防这种危险的疾病对公众健康和可观的社会经济成果都有重大影响。电子健康记录(EHR)的出现和真实世界临床数据的可用性为利用人工智能工具提高医疗质量和效率提供了机会。在本研究中,我们重点关注风险因素的早期识别,这可以为早期预测心肌梗死和促进健康生活提供有价值的信息。基于大型临床数据集,我们开发了一种心肌梗塞预测分析方法。高效预测的一个重要步骤是评估输入特征的重要性、它们之间的关系及其对疾病的贡献。因此,我们采用了统计技术、主成分分析(PCA)和特征工程。为了揭示数据集的模式和见解,我们采用了从经典到更复杂的机器学习(ML)模型:决策树(DT)、随机森林(RF)、梯度提升算法(GBoost、LightGBM、CatBoost 和 XGBoost)和深度神经网络(DNN)。不平衡数据问题通过采用随机欠采样技术来解决。在本研究中,在平衡数据集上采用特征工程的轻梯度提升模型(LightGBM)取得了最佳预测性能。
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引用次数: 0
A novel Deep Learning architecture for lung cancer detection and diagnosis from Computed Tomography image analysis 从计算机断层扫描图像分析中检测和诊断肺癌的新型深度学习架构
Pub Date : 2024-03-20 DOI: 10.1016/j.health.2024.100316
Lavina Jean Crasta, Rupal Neema, Alwyn Roshan Pais

Timely identification of lung nodules, which are precursors to lung cancer, and their evaluation can significantly reduce the incidence rate. Computed Tomography (CT) is the primary technique used for lung cancer screening due to its high resolution. Identifying white, spherical shadows as lung nodules in CT images is essential for accurately detecting lung cancer. Convolutional Neural Network (CNN)-based methods have performed better than traditional techniques in various medical image applications. However, challenges still need to be addressed due to insufficient annotated datasets, significant intra-class variations, and substantial inter-class similarities, which hinder their practical use. Manually labeling the position of nodules on CT slices is critical for distinguishing between benign and malignant cases, but it is an unreliable and time-consuming process. Insufficient data and class imbalance are the primary factors that may result in overfitting and below-par performance. The paper presents a novel Deep Learning (DL) framework to detect and classify lung cancer in input CT images. It introduces a 3D-VNet architecture for accurate segmentation of pulmonary nodules and a 3D-ResNet architecture designed for their classification. The segmentation model achieves a Dice Similarity Coefficient (DSC) of 99.34% on the LUNA16 dataset while reducing false positives to 0.4%. The classification model shows performance metrics with accuracy, sensitivity, and specificity of 99.2%, 98.8%, and 99.6%, respectively. The 3D-VNet network outperforms previous segmentation methods by accurately calibrating lung nodules of various sizes and shapes with excellent robustness. The classification model’s metrics show that the suggested method outperforms current approaches regarding accuracy, specificity, sensitivity and F1-Score.

肺结节是肺癌的前兆,及时发现和评估肺结节可大大降低肺癌的发病率。计算机断层扫描(CT)因其高分辨率而成为肺癌筛查的主要技术。将 CT 图像中的白色球形阴影识别为肺结节对于准确检测肺癌至关重要。在各种医学图像应用中,基于卷积神经网络(CNN)的方法比传统技术表现得更好。然而,由于注释数据集不足、类内差异显著、类间相似性大等原因,这些方法的实际应用仍面临挑战。手动标注 CT 切片上结节的位置对于区分良性和恶性病例至关重要,但这是一个不可靠且耗时的过程。数据不足和类不平衡是可能导致过度拟合和性能低下的主要因素。本文提出了一种新型深度学习(DL)框架,用于检测输入 CT 图像中的肺癌并对其进行分类。它引入了用于准确分割肺结节的 3D-VNet 架构和用于肺结节分类的 3D-ResNet 架构。在 LUNA16 数据集上,分割模型的骰子相似系数(DSC)达到 99.34%,同时将误报率降至 0.4%。分类模型的准确度、灵敏度和特异度分别达到 99.2%、98.8% 和 99.6%。3D-VNet 网络能准确校准各种大小和形状的肺结节,鲁棒性极佳,优于以往的分割方法。分类模型的指标显示,建议的方法在准确性、特异性、灵敏度和 F1-Score 方面均优于现有方法。
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引用次数: 0
A fractal-fractional order Susceptible-Exposed-Infected-Recovered (SEIR) model with Caputo sense 具有卡普托感的分形-分数阶易感-暴露-感染-恢复(SEIR)模型
Pub Date : 2024-03-19 DOI: 10.1016/j.health.2024.100317
Subrata Paul , Animesh Mahata , Manas Karak , Supriya Mukherjee , Santosh Biswas , Banamali Roy

This study explores the intricacies of the COVID-19 pandemic by employing a four-compartment model with a fractal-fractional derivative based on Caputo concept. The analysis hinges on Schauder fixed point theorem, used to qualitatively examine the solutions and ascertain their existence and uniqueness within the model. The fundamental reproduction number is determined through the next-generation matrix approach. This study delves into the stability of equilibrium points and conducts a sensitivity analysis of model parameters. The equilibrium without infections is locally and globally stable when the basic reproduction number is less than 1. Also, this equilibrium becomes unstable when the basic reproduction number exceeds 1. Applying Lyapunov principles and the Routh–Hurwitz criteria, it is established that the endemic equilibrium point is globally stable for the basic reproduction number values greater than 1. The proposed model incorporates Ulam-Hyers stability through nonlinear functional analysis. Lagrange interpolation method estimates solutions for the fractal-fractional order COVID-19 model. Numerical simulations are performed using MATLAB software to exemplify the model behavior in the context of the Italian case study. Furthermore, fractal-fractional calculus techniques hold significant promise for comprehending and predicting the pandemic’s global dynamics in other countries.

本研究采用基于卡普托概念的分形-分形导数四室模型,探讨了 COVID-19 大流行病的复杂性。分析以 Schauder 定点定理为基础,用于定性研究解,并确定其在模型中的存在性和唯一性。基本重现数是通过新一代矩阵方法确定的。本研究深入探讨了平衡点的稳定性,并对模型参数进行了敏感性分析。当基本繁殖数小于 1 时,无感染平衡点在局部和全局上都是稳定的。应用 Lyapunov 原理和 Routh-Hurwitz 准则,可以确定当基本繁殖数大于 1 时,流行平衡点是全局稳定的。拉格朗日插值法估计了分形-分数阶 COVID-19 模型的解。使用 MATLAB 软件进行了数值模拟,在意大利案例研究中对模型行为进行了示范。此外,分形-分数微积分技术在理解和预测其他国家的大流行病全球动态方面也大有可为。
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Healthcare analytics (New York, N.Y.)
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