The monkeypox virus causes a respiratory illness called monkeypox, which belongs to the Poxviridae virus family and the Orthopoxvirus genus. Although initially endemic in Africa, it has recently become a global threat with cases worldwide. Using the Antangana–Baleanu fractional order approach, this study aims to propose a new monkeypox transmission model that represents the interaction between the infected human and rodent populations. An iterative method and the fixed-point theorem are used to prove the existence and uniqueness of the symmetry model’s system of solutions. It shows that the symmetry model has equilibrium points when there are epidemics and no diseases. As well as the local asymptotic stability of the disease-free equilibrium point, conditions for the endemic equilibrium point’s existence have also been demonstrated. For this purpose, the existence of optimal control is first ensured. The aim of the proposed optimal control problem is to minimize both the treatment and prevention costs, and the number of infected individuals. Optimal conditions are acquired Pontryagin’s maximum principle is used. Then, the stability of the symmetry model is discussed at monkeypox-free and endemic equilibrium points with treatment strategies to control the spread of the disease. Numerical simulations clearly show how necessary and successful the proposed combined control strategy is in preventing the disease from becoming epidemic.

The goal of this paper is to develop and present a precise theory for integer and fractional order \(\ell\)-nabla integration and its fundamental theorems. In our research work, we take two forms of higher order difference equation such as closed form and summation form. But most of the authors are focused only on the summation part only. Instead of finding the solution for the summation part, finding the solution for the closed gives the exact solution. To find the closed form solution for the integer order using the \(\ell\)-nabla operator, we used the factorial-coefficient method. For developing the theory of fractional order \(\ell\)-nabla operator and its integration, we introduce a function called \(N_{\nu}\)-type function. If the summation series is huge, this approach can help us to find the solution quickly. Suitable examples are provided for verification. Finally, we provide the application for detecting viral transmission using the nabla operator.

In this paper the authors discuss a class of differential equations known as neutral delay differential equations (NDDEs) in which the delay occurs in the derivative with the highest order. They are encountered in various fields of applied sciences and are essential for mathematically representing real-world phenomena. It was challenging to discover approximate analytical solutions for certain methods. In this study, the researchers utilized the generalized Lambert W function to derive the characteristic roots for a first-order neutral delay differential equation featuring random delays. Numerical examples were then utilized to validate the obtained results.

Queuing system modeling is one of the most important and fertile subjects in modeling domain in general and Mathematics in particular. There is a huge literature available for theoretical models but the actual difficulty is in implementation as we most often come across huge differences between what we have derived theoretically and what we witness in the actual system. This paper is an exploration towards bridging that gap between theory and reality. In this paper we consider the Able-Baker problem, a two server queuing system with Markovian parameter distributions –Inter-Arrival time and Service time distributions. We simulated such a system, obtain four measures-the number of customers in system and queue, the waiting time in system and queue-and compared those with M|M|1 and M|M|2 theoretical systems with the same parameters used for simulation and have empirically viewed the gap between theory and real system and a possible bound to expect in real systems when we start with theoretical models.

This study analyses PDA feedback, or delayed proportional derivative acceleration using a human balancing nonlinear model by applying Laplace Transform. The PDA This study analyses PDA feedback, or delayed proportional derivative acceleration using a human balancing nonlinear model by applying Laplace Transform. The PDA

The exact expectation of the financial backers with respect to the securities exchanges helps them in taking better independent directions. The financial backers utilize the measurable information accessible in the online media regarding stocks and shares, to help the investors in better planning and preparation. Metrics are an integral part of Linear Regression Model Assessment. This paper concentrates on the assessment of metrics in direct relapse contrasting the two financial exchanges in particular IBM and DELL stocks whose probabilities of building forecast of protection market costs abuse utilizing chronicled information.