Modeling the epidemic trend of middle eastern respiratory syndrome coronavirus with optimal control.

Since the outbreak of the Middle East Respiratory Syndrome Coronavirus (MERS-CoV) in 2012 in the Middle East, we have proposed a deterministic theoretical model to understand its transmission between individuals and MERS-CoV reservoirs such as camels. We aim to calculate the basic reproduction number ($ \mathcal{R}_{0} $) of the model to examine its airborne transmission. By applying stability theory, we can analyze and visualize the local and global features of the model to determine its stability. We also study the sensitivity of $ \mathcal{R}_{0} $ to determine the impact of each parameter on the transmission of the disease. Our model is designed with optimal control in mind to minimize the number of infected individuals while keeping intervention costs low. The model includes time-dependent control variables such as supportive care, the use of surgical masks, government campaigns promoting the importance of masks, and treatment. To support our analytical work, we present numerical simulation results for the proposed model.

Dynamics of Middle East Respiratory Syndrome Coronavirus (MERS-CoV) involving fractional derivative with Mittag-Leffler kernel.

Since 2012, the Middle East has seen a steady rise in the Middle East Respiratory Syndrome Coronavirus (MERS-CoV). A fractional derivative of the non-singular Mittag-Leffler type is used in this research to conduct a mathematical analysis of the dynamics of MERS-CoV infection transmission. The dynamics of such a disease with an additional degree of freedom and non-singular behavior are discovered through the use of the aforementioned fractional operator, and this is one of the important components of our prepared paper. Using the concept of fixed point theory, the existence and uniqueness of solutions are demonstrated. The stability analysis is also tested with the help of the Ulam-Hyers approach, respectively. The numerical solution has been conducted by using the fractional Adams-Bashforth scheme. In the numerical simulation, all classes are demonstrated through the graphical presentation regarding the changing values of fractional-order at time t. The results at various fractional-order laying between (0,1] are drawn with the help of Matlab. We also provide a comparison of the proposed approach with that of the Caputo operator. The outcomes that were achieved illustrate that the considered scheme is highly methodical and very efficient compared to the Caputo fractional operator.

Ridge Regression Method and Bayesian Estimators under Composite LINEX Loss Function to Estimate the Shape Parameter in Lomax Distribution.

In this paper, the Ridge Regression method is employed to estimate the shape parameter of the Lomax distribution (LD). In addition to that, the approaches of both classical and Bayesian are considered with several loss functions as a squared error (SELF), Linear Exponential (LLF), and Composite Linear Exponential (CLLF). As far as Bayesian estimators are concerned, informative and noninformative priors are used to estimate the shape parameter. To examine the performance of the Ridge Regression method, we compared it with classical estimators which included Maximum Likelihood, Ordinary Least Squares, Uniformly Minimum Variance Unbiased Estimator, and Median Method as well as Bayesian estimators. Monte Carlo simulation compares these estimators with respect to the Mean Square Error criteria (MSE's). The result of the simulation mentioned that the Ridge Regression method is promising and can be used in a real environment. where it revealed better performance the than Ordinary Least Squares method for estimating shape parameter.

Visualization of non-Newtonian convective fluid flow with internal heat transfer across a rotating stretchable surface impact of chemical reaction.

The present investigation focuses on the characteristics of heat and mass transfer in the context of their applications. There has been a lot of interest in the use of non-Newtonian fluids in engineering and biological disciplines. Having such considerable attention to non-Newtonian fluids, the goal is to explore the flow of Jeffrey non-Newtonian convective fluid driven by a non-linear stretching surface considering the effect of nonlinear chemical reaction effect. The relevant set of difference equations was changed to ordinary equations by using a transformation matrix. To create numerical solutions for velocity and concentration fields, the Runge-Kutta fourth-order method along with the shooting approach is utilized. The innovative fragment of the present study is to scrutinize the magnetized viscous non-Newtonian fluid over extending sheet with internal heat transfer regarding the inspiration of nonlinear chemical reaction effect, which still not has been elaborated on in the available works to date. Consequently, in the restrictive sense, the existing work is associated with available work and originated in exceptional agreement. Graphs depict the effects of various variables on motion and concentration fields, like the Hartman number, Schmidt number, and chemical reaction parameter. The performance of chemical reaction factor, Schmidt number, Hartmann number, and Deborah numbers on velocities component, temperature, and concentration profiles are discussed through graphs. The effect of emerging parameters in the mass transfer is also investigated numerically and 3D configuration is also provided. It is observed that the Deborah numbers and Hartmann numbers have the same effect on velocity components. Also, the thickness of the boundary layer reduces as the Hartmann number increases. As the Schmit number grows, the concentration field decline. For destructive and generative chemical reactions, the concentration fields observed opposite effects. It is also noticed that the surface mas transfer reduces as the Hartmann number rises. The statistical findings of the heat-transfer rate are also documented and scrutinized.

The flow, thermal and mass properties of Soret-Dufour model of magnetized Maxwell nanofluid flow over a shrinkage inclined surface.

A mathematical model of 2D-double diffusive layer flow model of boundary in MHD Maxwell fluid created by a sloping slope surface is constructed in this paper. The numerical findings of non-Newtonian fluid are important to the chemical processing industry, mining industry, plastics processing industry, as well as lubrication and biomedical flows. The diversity of regulatory parameters like buoyancy rate, magnetic field, mixed convection, absorption, Brownian motion, thermophoretic diffusion, Deborah number, Lewis number, Prandtl number, Soret number, as well as Dufour number contributes significant impact on the current model. The steps of research methodology are as followed: a) conversion from a separate matrix (PDE) to standard divisive calculations (ODEs), b) Final ODEs are solved in bvp4c program, which developed in MATLAB software, c) The stability analysis part also being developed in bvp4c program, to select the most effective solution in the real liquid state. Lastly, the numerical findings are built on a system of tables and diagrams. As a result, the profiles of velocity, temperature, and concentration are depicted due to the regulatory parameters, as mentioned above. In addition, the characteristics of the local Nusselt, coefficient of skin-friction as well as Sherwood numbers on the Maxwell fluid are described in detail.

Mathematical modeling and analysis of the SARS-Cov-2 disease with reinfection.

The COVID-19 infection which is still infecting many individuals around the world and at the same time the recovered individuals after the recovery are infecting again. This reinfection of the individuals after the recovery may lead the disease to worse in the population with so many challenges to the health sectors. We study in the present work by formulating a mathematical model for SARS-CoV-2 with reinfection. We first briefly discuss the formulation of the model with the assumptions of reinfection, and then study the related qualitative properties of the model. We show that the reinfection model is stable locally asymptotically when R0<1. For R0≤1, we show that the model is globally asymptotically stable. Further, we consider the available data of coronavirus from Pakistan to estimate the parameters involved in the model. We show that the proposed model shows good fitting to the infected data. We compute the basic reproduction number with the estimated and fitted parameters numerical value is R0≈1.4962. Further, we simulate the model using realistic parameters and present the graphical results. We show that the infection can be minimized if the realistic parameters (that are sensitive to the basic reproduction number) are taken into account. Also, we observe the model prediction for the total infected cases in the future fifth layer of COVID-19 in Pakistan that may begin in the second week of February 2022.

Optimal Periods of Conducting Preventive Maintenance to Reduce Expected Downtime and Its Impact on Improving Reliability.

The present research mainly aims to use a mathematical formula to determine the optimal intervals for conducting preventive maintenance operations for machines to reduce the expected failure time when the malfunction data follow the Weibull distribution. The reliability function, failure rate, and the average time between machine failures were derived after performing preventive maintenance operations and before conducting preventive maintenance operations to state the amelioration that happens to machines. These rely on real data of performing preventive maintenance operations and the downtime required to repair machine or device faults that occur between preventive maintenance periods and the downtime necessary to perform preventive maintenance operations on the machine or device. Thus, the study concluded that preventive maintenance operations are working to increase the reliability of the machine and improve it, as well as to increase the average period of time for the machine to operate between faults.