Journal of Mathematical Analysis and Modeling

D-precompact Sets in D-Metric Spaces

Hussain Wahish — 2022-10-17

The aim of this paper is to define and emphasize a strong form of D-compact sets in generalized metric
spaces, namely D-precompact sets. Also with other sets, we shall study the relationships. Furthermore, we
give the notions of sequentially D-precompact sets.

Thermo-diffusion effect on magnetohydrodynamics flow of fractional Casson fluid with heat generation and first order chemical reaction over a vertical plate

Muhammad Ramzan — 2022-10-17

Analytical solution of thermo diffusion effect on magnetohydrodynamics flow of fractionalized Casson
fluid over a vertical plate immersed in a porous media is obtained. Moreover, in the model of the problem, additional effects, like a chemical reaction, heat source/sink, and thermal radiation are also considered.
The model is solved by three approaches, namely, Atangana-Baleanu, Caputo-Fabrizio, and Caputo fractional
derivative of non-integer order γ. The governing dimensionless equations for temperatures, concentrations,
and velocities are solved using Laplace transform method and compared graphically. The effects of different parameters like fractional parameter γ, Thermo diffusion Sr, and magnetic parameter M are discussed
through numerous graphs. Furthermore, comparisons among ordinary and fractionalized velocity fields are
also drawn. It is found that the velocity obtained with Atangana-Baleanu fractional derivative is less than that
obtained by Caputo, Caputo-Fabrizio, or ordinary derivatives.

Endemic Equilibrium and Forward Bifurcation in the Mathematical Model for Using Wolbachia to Control Spread of Zika Virus Disease

Michael Anyanwu — 2022-11-19

This paper focuses on the use of wolbachia to control the spread of zika virus disease. Zika virus disease is an arboviral disease that spreads through bites of female mosquitoes in the aedes family especially, aedes aegypti. Experimental studies have indicated that wolbachia could be used to prevent the spread of zika virus disease by infecting aedes aegypti with wolbachia in a laboratory and releasing them in the wild to mate with the wild aedes aegypti.

A system of nonlinear ordinary differential equations is used to model the use of wolbachia to stop the spread of zika virus disease in the human and mosquito populations. as well as the population of wolbachia-infected aedes aegypti used as control. It is shown through bifurcation analysis that the model exhibits forward bifurcation, which confirms that a unique endemic equilibrium exists in the model when the control reproduction number, $ \mathcal{R}_c>1$. The existence of forward bifurcation in the model means that $ \mathcal{R}_c<1$ is enough to guarantee eradication of zika virus disease using wolbachia as a biocontrol. Hence, the spread of zika virus disease can be controlled irrespective of the initial sizes of infected human and mosquito populations

Maclaurin’s inequalities for functions whose first derivatives are preinvex

Badreddine Meftah — 2022-11-26

In this paper, using a new identity, we study one of the famous Newton-Cotes three-point quadrature
rules. More precisely Maclaurin’s quadrature rule, for which we establish the error estimate of this method
under the constraint that the first derivatives belong to the class of preinvex functions. We also give some
applications to special means as applications. We believe that this new studied inequality and the results
obtained in this article will further inspire intrigued researchers.