Modeling and Analysis of Breast Cancer with Adverse Reactions of Chemotherapy Treatment through Fractional Derivative.

The abnormal growth of cells in the breast is called malignancy or breast cancer; it is a life-threatening and dangerous cancer in women around the world. In the treatment of cancer, the doctors apply different techniques to stop cancer cell development, remove cancer cells through surgery, or kill cancer cells. In chemotherapy treatment, powerful drugs are used to kill abnormal cells; however, it has adverse reactions on the patient heart which is called cardiotoxicity. In this paper, we formulate the dynamics of cancer in the breast with adverse reactions of chemotherapy treatment on the heart of a patient in the fractional framework to visualize its dynamical behaviour. We listed the fundamental results of the fractional calculus for the analysis of our model. The model is then analyzed for the basic properties, and the existence and uniqueness of the proposed breast cancer system are investigated through fixed point theory. Furthermore, the Adams-Bashforth numerical technique is presented for the solution of fractional-order system to illustrate the time series of breast cancer model. The dynamical behaviour of different stages of breast cancer is then highlighted numerically to show the effect of fractional-order ϑ and to visualize the role of input parameter on the dynamics of breast cancer.

Magnetic Dipole Impact on the Hybrid Nanofluid Flow over an Extending Surface.

The main features of present numerical model is to explore and compare the behavior of simple and hybrid nanoparticles, which were allowed to move on a spreading sheet. The effect of magnetic dipole on hybrid nanofluid flow is considered. A magnetic dipole combined with hybrid nanofluid plays a vital role in controlling the momentum and thermal boundary layers. In view of the impacts of a magnetic dipole on the simple and hybrid nanofluids, steady, laminar and boundary layer flow of [Formula: see text] and [Formula: see text] are characterized in this analysis. The governing equations of flow problem are diminished to ordinary differential equation (ODE's) by using similarity approach. For the numerical solution of the nonlinear ODE's, Runge Kutta order 4th technique has been executed. The impact of various physical constraints, such as volume friction, viscous dissipation, Prandtl number and so on have been sketched and briefly discussed for velocity and temperature profile. In this work, some vital characteristics such as skin friction, Curie temperature and local Nusselt number are chosen for physical and numerical analysis. It has been noted that the hybrid nanofluid is more efficient in thermal conduction due to its strong thermal characteristics as compared to simple nanofluid. From results, it is also observed that the turbulence of fluid flow can be controlled through magnetic dipole.

Brownian Motion and Thermophoresis Effects on MHD Three Dimensional Nanofluid Flow with Slip Conditions and Joule Dissipation Due to Porous Rotating Disk.

This paper examines the time independent and incompressible flow of magnetohydrodynamic (MHD) nanofluid through a porous rotating disc with velocity slip conditions. The mass and heat transmission with viscous dissipation is scrutinized. The proposed partial differential equations (PDEs) are converted to ordinary differential equation (ODEs) by mean of similarity variables. Analytical and numerical approaches are applied to examine the modeled problem and compared each other, which verify the validation of both approaches. The variation in the nanofluid flow due to physical parameters is revealed through graphs. It is witnessed that the fluid velocities decrease with the escalation in magnetic, velocity slip, and porosity parameters. The fluid temperature escalates with heightening in the Prandtl number, while other parameters have opposite impacts. The fluid concentration augments with the intensification in the thermophoresis parameter. The validity of the proposed model is presented through Tables.

Epidemiologic Pattern and Types of Oral Smokeless Tobacco Usage in Saudi Arabia.

Aim: Smokeless tobacco (ST) use is a significant health risk and cause of disease. Most studies conducted in the Kingdom of Saudi Arabia (KSA) focused on cigarette smoking. Therefore, the objective was to study the epidemiologic pattern and types of oral ST usage in northern and western Saudi Arabia. Materials and methods: A total of 428 volunteers living in three cities (Hail, Mecca, and Tabuk) were investigated. All of the study subjects were currently ST users of one type or more, including toombak, shammah, pan masala (PM), Afdhal, Nashooq, and others. Results: Most of the study population were found to use toombak representing 127/428 (29.7%), followed by shammah, PM, Afdhal, Nashooq, Adani, Qat, Majun, and others, representing 67/428 (15.7%), 66/428 (15.4%), 44/428 (10.3%), 36/428 (8.4%), 32/428 (7.5%), 23/428 (5.4%), 22/428 (5.1%), 21/428 (4.9%), and 13/428 (3%) respectively. Conclusion: This survey showed a high prevalence of existing ST usage among foreign workers and Saudis, which can establish a prospective public health problem. Clinical significance: Smokeless tobacco cessation is a crucial element of tobacco control policy since it is the most important determinant of many diseases, including oral cancer. Keywords: Kingdom of Saudi Arabia, Oral cancer, Pan masala, Shammah, Smokeless tobacco, Toombak.