Mathematical Analysis of Fractal-Fractional Mathematical Model of COVID-19

In this work, we modified a dynamical system that addresses COVID-19 infection under a fractal-fractional-order derivative. The model investigates the psychological effects of the disease on humans. We establish global and local stability results for the model under the aforementioned derivative. Additionally, we compute the fundamental reproduction number, which helps predict the transmission of the disease in the community. Using the Carlos Castillo-Chavez method, we derive some adequate results about the bifurcation analysis of the proposed model. We also investigate sensitivity analysis to the given model using the criteria of Chitnis and his co-authors. Furthermore, we formulate the characterization of optimal control strategies by utilizing Pontryagin's maximum principle. We simulate the model for different fractal-fractional orders subject to various parameter values using Adam Bashforth's numerical method. All numerical findings are presented graphically. © 2023 by the authors.

Ensemble Learning using Transformers and Convolutional Networks for Masked Face Recognition

Wearing a face mask is one of the adjustments we had to follow to reduce the spread of the coronavirus. Having our faces covered by masks constantly has driven the need to understand and investigate how this behavior affects the recognition capability of face recognition systems. Current face recognition systems have extremely high accuracy when dealing with unconstrained general face recognition cases but do not generalize well with occluded masked faces. In this work, we propose a system for masked face recognition. The proposed system comprises two Convolutional Neural Network (CNN) models and two Transformer models. The CNN models have been fine-tuned on FaceNet pre-trained model. We ensemble the predictions of the four models using the majority voting technique to identify the person with the mask. The proposed system has been evaluated on a synthetically masked LFW dataset created in this work. The best accuracy is obtained using the ensembled models with an accuracy of 92%. This recognition rate outperformed the accuracy of other models and it shows the correctness and robustness of the proposed model for recognizing masked faces. The code and data are available at https://github.com/Hamzah-Luqman/MFR. © 2022 IEEE.

A Detailed Study of a Fractal-Fractional Transmission Dynamical Model of Viral Infectious Disease with Vaccination

This article is devoted to investigate a mathematical model consisting on susceptible, exposed, infected, quarantined, vaccinated, and recovered compartments of COVID-19. The concerned model describes the transmission mechanism of the disease dynamics with therapeutic measures of vaccination of susceptible people along with the cure of the infected population. In the said study, we use the fractal-fractional order derivative to understand the dynamics of all compartments of the proposed model in more detail. Therefore, the first model is formulated. Then, two equilibrium points disease-free (DF) and endemic are computed. Furthermore, the basic threshold number is also derived. Some sufficient conditions for global asymptotical stability are also established. By using the next-generation matrix method, local stability analysis is developed. We also attempt the sensitivity analysis of the parameters of the proposed model. Finally, for the numerical simulations, the Adams-Bashforth method is used. Using some available data, the results are displayed graphically using various fractal-fractional orders to understand the mechanism of the dynamics. In addition, we compare our numerical simulation with real data in the case of reported infected cases. © 2022 Kamal Shah et al.