On the analysis of the fractional model of COVID-19 under the piecewise global operators.

An expanding field of study that offers fresh and intriguing approaches to both mathematicians and biologists is the symbolic representation of mathematics. In relation to COVID-19, such a method might provide information to humanity for halting the spread of this epidemic, which has severely impacted people's quality of life. In this study, we examine a crucial COVID-19 model under a globalized piecewise fractional derivative in the context of Caputo and Atangana Baleanu fractional operators. The said model has been constructed in the format of two fractional operators, having a non-linear time-varying spreading rate, and composed of ten compartmental individuals: Susceptible, Infectious, Diagnosed, Ailing, Recognized, Infectious Real, Threatened, Recovered Diagnosed, Healed and Extinct populations. The qualitative analysis is developed for the proposed model along with the discussion of their dynamical behaviors. The stability of the approximate solution is tested by using the Ulam-Hyers stability approach. For the implementation of the given model in the sense of an approximate piecewise solution, the Newton Polynomial approximate solution technique is applied. The graphing results are with different additional fractional orders connected to COVID-19 disease, and the graphical representation is established for other piecewise fractional orders. By using comparisons of this nature between the graphed and analytical data, we are able to calculate the best-fit parameters for any arbitrary orders with a very low error rate. Additionally, many parameters' effects on the transmission of viral infections are examined and analyzed. Such a discussion will be more informative as it demonstrates the dynamics on various piecewise intervals.

Thermal mechanism in magneto radiated [(Al2O3-Fe3O4)/blood]hnf over a 3D surface: Applications in Biomedical Engineering.

Nanofluids are a new generation of fluids which help in improving the efficiency of thermal systems by improving heat transport rate and extensive applications of this class extensively fall in biomedical engineering, the electronics industry, applied thermal and mechanical engineering, etc. The core concern of this study is to examine the interaction of Al2O3-Fe3O4 hybrid nanoparticles of lamina shaped with blood over a 3D surface by impinging novel impacts of non-linear thermal radiations, stretching, velocity slippage, and magnetic field. This leads to a mathematical flow model in terms of highly non-linear differential equations via nanofluid-effective characteristics and similarity rules. To know the actual behavior of (Al2O3-Fe3O4)/blood inside the concerned region, mathematical investigation is performed via numerical technique and the results are obtained for different parameter ranges. The imposed magnetic field of high strength is a better tool to control the motion of (Al2O3-Fe3O4)/blood inside the boundary layer, whereas, stretching of the surface is in direct proportion of the fluid movement. Furthermore, thermal radiations (Rd) and γ 1 are observed to be beneficial for thermal enhancement for both (Al2O3-Fe3O4)/blood and (Al2O3)/blood.

Chaotic Enhanced Genetic Algorithm for Solving the Nonlinear System of Equations.

Many engineering and scientific models are based on the nonlinear system of equations (NSEs), and their effective solution is critical for development in these domains. NSEs can be modeled as an optimization problem. So, the goal of this paper is to propose an optimization method, to solve the NSEs, which is called a chaotic enhanced genetic algorithm (CEGA). CEGA is a chaotic noise-based genetic algorithm (GA) that improves performance. CEGA will be configured so that it uses a new definition which is chaotic noise to overcome the drawbacks of optimization methods such as lack of diversity of solutions, the imbalance between exploitation and exploration, and slow convergence of the best solution. The goal of chaotic noise is to reduce the number of repeated solutions and iterations to speed up the convergence rate. In the chaotic noise, the chaotic logistic map is utilized since it has been used by numerous researchers and has proven its efficiency in increasing the quality of solutions and providing the best performance. CEGA is tested using many well-known NSEs. The suggested algorithm's results are compared to the original GA to prove the importance of the modifications introduced in CEGA. Promising results were obtained, where CEGA's average percentage of improvement was about 75.99, indicating that it is quite effective in solving NSEs. Finally, comparing CEGA's results with previous studies, statistical analysis by Friedman and Wilcoxon's tests demonstrated its superiority and ability to solve this kind of problem.

COVID-19: Mathematical growth vs. precautionary measures in China, KSA, and the USA.

This paper aims to study the relation between precautionary measures that were taken by countries to prevent the spread of COVID-19 and its impact on its mathematical growth. In this paper, we study the development and growth of the epidemic during the first fifty days since its appearance in three countries: China, the Kingdom of Saudi Arabia (KSA), and the United States of America (USA). An optimization process is used to determine the parameters of the closest model that simulates the data during the specified period by using one of the evolutionary computation techniques, the grasshopper optimization algorithm (GOA). The study reveals that the strict precautionary measures of applying isolation and quarantine, preventing all gatherings, and a total curfew are the only way to prevent the spread of the epidemic exponentially as China did. Also, without any measures to slow its growth, COVID-19 will continue to spread steadily for months.

Green synthesis of bimetallic ZnO-CuO nanoparticles and their cytotoxicity properties.

In this study, a simple and green strategy was reported to prepare bimetallic nanoparticles (NPs) by the combination of zinc oxide (ZnO) and copper oxide (CuO) using Sambucus nigra L. extract. The physicochemical properties of these NPs such as crystal structure, size, and morphology were studied by X-ray diffraction (XRD), field emission gun scanning electron microscopy (FEG-SEM), and transmission electron microscopy (TEM). The results suggested that these NPs contained polygonal ZnO NPs with hexagonal phase and spherical CuO NPs with monoclinic phase. The anticancer activity of the prepared bimetallic NPs was evaluated against lung and human melanoma cell lines based on MTT assay. As a result, the bimetallic ZnO/CuO NPs exhibited high toxicity on melanoma cancer cells while their toxicity on lung cancer cells was low.

Effect of L-shaped heat source and magnetic field on heat transfer and irreversibilities in nanofluid-filled oblique complex enclosure.

In this paper, the natural convection heat transfer of water/alumina nanofluid is investigated in a closed square cavity. An oblique magnetic field is applied on the cavity of angle [Formula: see text]. There is also radiation heat transfer in the cavity. The cavity includes a high-temperature source of L-shape. A low-temperature source as a quadrant of a circle is placed at the corner of the cavity. All other walls are well insulated. The novelty of this work is a low-temperature obstacle embedded in the cavity. Simulations are conducted with a Fortran code based on the control volume method and simple algorithm. Entropy generation rate, Bejan number, and heat transfer are studied by changing different parameters. Results indicate that the highest rates of heat transfer and entropy generation have occurred for the perpendicular magnetic field at high values of the Rayleigh number. At these Rayleigh numbers, the minimum value of the Bejan number is obtained for 15° magnetic field. The magnetic field variation can lead to a change up to 53% in Nusselt number and up to 34% in generated entropy. In a weak magnetic field, the involvement of the radiation heat transfer mechanism leads to an increase in the heat transfer rate so that the Nusselt number can be increased by ten units considering the radiation heat transfer when there is no magnetic field. The maximum heat transfer rate occurs in the horizontal cavity and the minimum value in the cavity of 60° angle. For water, these values are 10.75 and 9.98 for 0 and 60 angles, respectively. Moreover, a weak magnetic field increases the heat transfer rate in the absence of the radiation mechanism, while it is reduced by considering a strong magnetic field.