Fractional calculus plays a crucial role in the representation of various natural and physical phenomena by incorporating the inherent non-locality and long-term memory effect of fractional operators. These models offer a more precise and systematic depiction of the underlying phenomena. The focus of this research paper is on the utilization of fractional calculus in the context of the epidemic model. Specifically, the model considers a fractional order ρ, where 0<ρ≤1, and employs the Caputo fractional order derivative to describe the transmission of malware in both wireless and wired networks. The basic reproduction number, along with the fractional order ρ, is identified as the threshold parameter in this model. The stability of the system is analysed at different stages of the reproduction number, considering both local and global asymptotic stability. Additionally, sensitivity analysis is conducted on the model parameters to determine the direction of change in the reproduction number. This analysis aids in understanding whether the reproduction number will increase or decrease under different scenarios. To obtain numerical results, the Fractional Forward Euler Method is utilized for simulation purposes. This method enables the computation of the model's dynamics and offers insights into the behaviour of the system. While the Caputo fractional order derivative offers a promising framework for modelling epidemic dynamics, they often entail significant computational overhead, limiting the scalability and practical utility of fractional calculus-based epidemic models, especially in real-time simulation and forecasting scenarios.

In response surface methodology, optimality criteria is a major tools used to measure the goodness of a design. Optimal experimental designs (or optimum designs) are a class of experimental designs that are optimal with respect to some statistical criterion. E – Optimality criterion is one of the traditional alphabetical criteria used to explore the right choice of a design both in linear or quadratic response surface models. In this paper, we investigate E – optimal experimental designs for a quadratic response surface model with two factor predictors. We developed an algorithm and a flowchart in line with a program to obtain E – optimal design and compare the result with an existing method. Two designs were formulated each with six points used to illustrate the usefulness of the new method. Based on the results, it is observed that the new technique proved a better result than the existing method. The significance is that it minimizes error due to approximation and also make the computation of the aforementioned optimality easier. We, therefore recommended this method to be used at all length of points when E – optimal is to be evaluated.

Nowadays, there are many organizations and institutions have realized the significant effect of the Internet of Things (IoT). The IoT technologies can enhance the quality of processes and services that make organizations seek to integrate these technologies to their products especially their smart devices. The IoT can be considered as one of the most important requirements that influences on detecting the best supplier. Therefore, every organization should take into account the effect of IoT on detecting the best supplier. So that, there is a need to a framework to help organizations for detecting the suitable supplier based on the effect of IoT. This work aims to introduce a proposed framework using trapezoidal neutrosophic numbers to detect the suitable supplier for purchasing smart systems based on the effect of IoT. The proposed framework consists of six phases. The proposed framework integrates the values and ambiguities index method with Single Valued Trapezoidal Neutrosophic Numbers (SVTN-numbers) which generalized fuzzy set and intuitionistic fuzzy to give more accurate results. The proposed framework is applied with a case study and the results concluded that the proposed framework can handle unclear information which exists in the purchasing process for detecting the suitable supplier of smart devices based on the effect of IoT.  Also, the proposed framework can handle uncertainty in decision making and link between customers and suppliers which can improve Supply Chain Management (SCM).

With the rapid proliferation of drones and drone networks across various application domains, ensuring their security against cyber threats has become imperative. This paper presents a comprehensive analysis and comparative analysis of the state-of-the-art techniques for detecting cyber threats in drone networks. The background provides a primer on drones, networks, drone network architectures, communication mechanisms, and enabling technologies like wireless protocols, satellite navigation, onboard computers, sensors, and flight control systems. The landscape of emerging technologies including blockchain, software-defined networking, machine learning, fog computing, ad-hoc networks, and swarm intelligence is reviewed in the context of transforming drone network capabilities while also introducing potential vulnerabilities. The paper delves into common cyber threats faced by drone networks such as hacking, DoS attacks, data breaches, and GPS spoofing. A detailed literature review of proposed threat detection techniques is provided, categorized into machine learning, multi-agent systems, blockchain, intrusion detection systems, software solutions, and miscellaneous methods. A key gap identified is handling increasingly sophisticated attacks, complex environments, and resource limitations in aerial platforms. The analysis highlights accuracy, overhead and real-time trade-offs between techniques, while factors like model optimization can influence efficacy. A comparative analysis highlights the advantages and limitations of each approach considering metrics like accuracy, scalability, flexibility, and overhead. Key observations include the trade-offs between computational complexity and real-time performance, the challenges in handling evolving attack techniques, and the dependencies between detection accuracy and factors like model selection and training data quality. The analysis provides a comprehensive reference for cyber threat detection in drone networks, benefiting researchers and practitioners aiming to advance this crucial area of drone security through robust detection systems tailored for resource-constrained aerial environments.

Stroke prediction is paramount in healthcare to enable timely intervention and reduce the burden of this devastating condition. This research paper examines the prediction of strokes using machine learning methods, aiming to enhance accuracy and efficiency in risk assessment. Numerous Machine Learning (ML) techniques, such as Support Vector Machine (SVM), XGBoost, Random Forest, Linear Regression, and Gaussian Naive Bayes, are explored using a comprehensive dataset containing patient demographics, medical history, lifestyle factors, and clinical measurements. Based on different ML models, an Enhanced Stroke Prediction Model (ESPM) is proposed. Grid search, Randomized search, and Bayesian optimization are employed as hyperparameter tuning techniques, and parameters like accuracy, precision, recall, and F1 score are analyzed. It is observed that SVM with Grid Search hyperparameter tunning performs well with an accuracy of 94.129%; Positive Predictive Value (PPV), True Positive Rate(TPR), and F1 Score achieved are 89%, 94%, and 91%, respectively. The outcomes demonstrate the suitability of these models for different aspects of stroke prediction, such as handling complex patterns, capturing non-linearity, robustness to noisy data, and modeling continuous risk scores.