Studying of COVID-19 fractional model: Stability analysis Khalaf, Sanaa L.; Kadhim, Mohammed S.; Khudair, Ayad R.
Partial differential equations in applied mathematics : a spin-off of Applied Mathematics Letters,
06/2023, Letnik:
7
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This article focuses on the recent epidemic caused by COVID-19 and takes into account several measures that have been taken by governments, including complete closure, media coverage, and attention ...to public hygiene. It is well known that mathematical models in epidemiology have helped determine the best strategies for disease control. This motivates us to construct a fractional mathematical model that includes quarantine categories as well as government sanctions. In this article, we prove the existence and uniqueness of positive bounded solutions for the suggested model. Also, we investigate the stability of the disease-free and endemic equilibriums by using the basic reproduction number (BRN). Moreover, we investigate the stability of the considering model in the sense of Ulam–Hyers criteria. To underpin and demonstrate this study, we provide a numerical simulation, whose results are consistent with the analysis presented in this article.
Moisture absorption and durability in water environment are major concerns for natural fibres as reinforcement in composites. This paper presents a study on the influence of water ageing on ...mechanical properties and damage events of flax–fibre composites, compared with glass–fibre composites. The effects of the immersion treatment on the tensile characteristics, water absorption and acoustic emission (AE) recording were investigated. The water absorption results for the flax–fibre composites show that the evolution appears to be Fickian and the saturated weight gain is 12 times as high that the glass–fibre composites. Decreasing continuously with increasing water immersion time, the tensile modulus and the failure strain of flax–fibre composites are hardly affected by water ageing whereas only the tensile stress is reduced regarding the glass–fibre composites. AE indicate that matrix–fibres interface weakening is the main damage mechanism induced by water ageing for both composites.
Abstract
The material characteristics of foreign Object Debris (FOD) are the essential criteria in determining the extent of an aircraft’s damage. Foreign object debris (FOD) can cause significant ...accidents and financial losses on airport runways. A new FOD material recognition strategy is proposed in this paper using an ensemble learning algorithm, namely KNN, Adaboost, and Random Forest Tree, to classify FOD images. In addition, this study uses different feature extraction methods like Linear Discriminant Analysis (LDA) and Gray-level co-occurrence matrix(GLCM) to extract FOD features. The KNN, Adaboost, and Random Forest Tree precision are 94.20%, 98.9%, and 99.7%, respectively. The dataset that was used has been collected by researchers from several datasets. As a result, the experiment results reveal that the proposed framework is effective and accurate. The results showed that the best classification machine algorithm is Random Forest Tree.
This paper adopts a new terminology, “delta q-Mittag-Leffler stability”, for studying the stability of nonlinear q-fractional dynamical systems on the time scale. In fact, the idea of delta ...q-Mittag-Leffler stability is inspired by the idea of Mittag-Leffler stability, which is designed to investigate the stability of fractional dynamical systems. The sufficient conditions for delta q-Mittag-Leffler stability of considered dynamical systems with Caputo delta q-derivatives have been introduced.
This article aims to present a new approach based on the operational matrix method for solving integro-differential equations using numerical techniques. In this method, we employ fourth-degree hat ...functions (FDHFs) to construct operational matrices. The approach involves two main steps. First, we utilize FDHFs to create operational matrices, which allows us to transform the given problem into a system of algebraic equations. The second step involves solving these algebraic equations numerically. Additionally, we provide an analysis of the errors involved and compare the proposed method with existing techniques. The results demonstrate that the proposed method outperforms its counterparts, highlighting its superiority.
The significant increase in drug abuse cases prompts developers to investigate techniques that mimic the hallucinations imagined by addicts and abusers, in addition to the increasing demand for the ...use of decorative images resulting from the use of computer technologies. This research uses Deep Dream and Neural Style Transfer technologies to solve this problem. Despite the significance researches on Deep Dream technology, there are several limitations in existing studies, including image quality and evaluation metrics. We have successfully addressed these issues by improving image quality and diversifying the types of generated images. This enhancement allows for more effective use of Deep Dream in simulating hallucinated images. Moreover, the high-quality generated images can be saved for dataset enlargement, like the augmentation process. Our proposed deepy-dream model combines features from five convolutional neural network architectures: VGG16, VGG19, Inception v3, Inception-ResNet-v2, and Xception. Additionally, we generate Deep Dream images by implementing each architecture as a separate Deep Dream model. We have employed autoencoder Deep Dream model as another method. To evaluate the performance of our models, we utilize normalized cross-correlation and structural similarity indexes as metrics. The values obtained for those two quality measures for our proposed deepy-dream model are 0.1863 and 0.0856, respectively, indicating effective performance. When considering the content image, the metrics yield values of 0.8119 and 0.3097, respectively. Whiefor the style image, the corresponding quality measure values are 0.0007 and 0.0073, respectively.
This paper focuses on solving a class of nonlinear optimal control problems by constructing novel hat functions based on fourth-order polynomials, namely, fourth-degree hat functions (FDHFs). The ...FDHFs are used in this method to approximate the state equations and cost function. In fact, the FDHFs enable us to turn the optimal control problem under consideration into a nonlinear optimal control problem with unknown coefficients that is easy to solve by any numerical method. The main advantages of the proposed method are its simplicity, ease of application, low computational expense, and avoidance of numerical integration. Several examples have been discussed to demonstrate the efficacy and applicability of the suggested method.
Background: There is no doubt that vaccination is crucial for preventing the spread of diseases; however, not every vaccine is perfect or will work for everyone. The main objective of this work is to ...predict which vaccine will be most effective for a candidate without causing severe adverse reactions and to categorize a patient as potentially at high risk of death from the COVID-19 vaccine.
Methods: A comprehensive analysis was conducted using a dataset on COVID-19 vaccine adverse reactions, exploring binary and multiclass classification scenarios. Ensemble models, including Random Forest, Decision Tree, Light Gradient Boosting, and extreme gradient boosting algorithm, were utilized to achieve accurate predictions. Class balancing techniques like SMOTE, TOMEK_LINK, and SMOTETOMEK were incorporated to enhance model performance.
Results: The study revealed that pre-existing conditions such as diabetes, hypertension, heart disease, history of allergies, prior vaccinations, other medications, age, and gender were crucial factors associated with poor outcomes. Moreover, using medical history, the ensemble learning classifiers achieved accuracy scores ranging from 75% to 87% in predicting the vaccine type and mortality possibility. The Random Forest model emerged as the best prediction model, while the implementation of the SMOTE and SMOTETOMEK methods generally improved model performance.
Conclusion: The random forest model emerges as the top recommendation for machine learning tasks that require high accuracy and resilience. Moreover, the findings highlight the critical role of medical history in optimizing vaccine outcomes and minimizing adverse reactions.
The article’s purpose is to examine ăthe Hyers–Ulam stability (HUS) for some linear fractional dynamic equations (FDEs) with the Caputo Δ−derivative on time scale. If we swap out a certain FDE for a ...fractional dynamical inequality, we want to know how close the solutions of the fractional dynamical inequality are to the solutions of the exact FDEs. Meanwhile, the generalized HUS result is obtained as a direct corollary. To achieve this goal, we solve the aforementioned equations utilizing the time scale version of the Laplace transform. Subsequently, the HUS is investigated in accordance with theseăsolutions.
In this paper, we introduce the delta q−Laplace transform on a time scale and investigate some of its properties. We discuss some important properties of fractional delta q−calculus. Then, based on ...these properties and the q−Laplace transform, we propose an analytical method for solving a class of linear Caputo delta fractional dynamic equations (q−FDEs). This method relies on transforming the corresponding equation into an integer-order linear delta q−dynamic equation (q−DE). In fact, this transformation removes certain terms from a solution of the considered linear Caputo delta q−FDE, resulting in residual terms that satisfy the linear delta q−DE. Several examples are provided to demonstrate the effectiveness and efficiency of the proposed method.
