This study presents a mathematical investigation into the phenomena of radiative heat with an unsteady MHD electrically conducting boundary layer of chemically reactive Casson nanofluid flow due to a pored stretchable sheet immersed in a porous medium in the presence of heat generation, thermophoretic force, and Brownian motion. The surface is assumed to be not flat, and has variable thickness. The magnetic field is time-dependent, and the chemical reaction coefficient is inversely varied with the distance. The nanofluid’s velocity, heat, and concentration at the surface are nonlinearly varied. A similarity transformation is introduced, and the controlling equations are converted into nondimensional forms involving many significant physical factors. The transformed forms are analyzed numerically using a computational method based on the finite difference scheme and Newton’s linearization procedure. The impact of the involved physical parameters is performed in graphical and tabular forms. Some special cases of the current work are compared with published studies, and an excellent agreement is obtained. The main results of the present work indicate that the higher values of the Casson parameter cause an increase in both the shear stress and heat flux, but a decrease in the mass flux. Also, it is noted that the chemical reaction, the nanoparticles’ volume, and the permeability factor enhance the effect the of Casson parameter on both the shear stress and heat flux, while the variable thickness and thermal radiation field reduce it; on the other hand, the variable thickness and nanoparticles’ volume enforce the influence of the Casson parameter on mass flux, but thermal radiation, the permeability factor, and chemical reaction decrease it. The present study has important applications in mechanical engineering and natural sciences. In addition, it has significant applications in devices used for blood transfusion, dialysis and cancer therapy.

This work explores the complicated realm of fullerene structures by utilizing an innovative algebraic lens to unravel their chemical intricacies. We reveal a more profound comprehension of the structural subtleties of fullerenes by the computation of modified polynomials that are customized to their distinct geometric and electrical characteristics. In addition to enhancing the theoretical underpinnings, the interaction between algebraic characteristics and fullerene structures creates opportunities for real‐world applications in materials science and nanotechnology. Our results provide a novel viewpoint that bridges the gap between algebraic abstraction and chemical reality. They also open up new avenues for the manipulation and construction of materials based on fullerenes with customized features. Topological or numerical descriptors are used to associate important physicomolecular restrictions with important molecular structural features such as periodicity, melting and boiling points, and heat content for various 2 and 3D molecular preparation graphs or networking. The degree of an atom in a molecular network or molecular structure is utilized in this study to calculate the degree of atom‐based numerics. The modified polynomial technique is a more recent way of assessing molecular systems and geometries in chemoinformatics. It emphasizes the polynomial nature of molecular features and gives numerics in algebraic expression. Particularly in this context, we describe multiple cages topologically based on the fullerene molecular form as polynomials, and several algebraic properties, including the Randić number and the modified polynomials of the first and second Zagreb numbers, are measured. By applying algebraic methods, we computed topological descriptors such as the Randić number and Zagreb indices. Our qualitative analysis shows that these descriptors significantly improve the prediction of molecular behavior. For instance, the Randić index provided insights into the stability and reactivity of fullerene structures, while the Zagreb indices helped us understand their potential in electronic applications. Our results suggest that modified polynomials not only offer a refined perspective on fullerene structures but also enable the design of materials with tailored properties. This study highlights the potential for these algebraic tools to bridge the gap between theoretical models and practical applications in nanotechnology and materials science, paving the way for innovations in drug delivery, electronic devices, and catalysis.

Marburg virus disease is a severe hemorrhagic illness caused by filoviruses that kills roughly half of those it infects, yet no licensed vaccine or specific antiviral treatment currently exists. When an outbreak strikes a resource‐poor region, health officials face an agonizing question: which interventions offer the most protection for the least cost? This study confronts that dilemma by developing a deterministic compartmental model that tracks disease transmission through symptomatic, hospitalized, and deceased individuals, the last crucial pathway often neglected in filovirus models. We combine optimal control theory with rigorous cost‐effectiveness analysis to evaluate three interventions: screening and isolation, contact reduction with infectious fluids, and enhanced clinical management. Solving the resulting two‐point boundary value problem using forward–backward sweep methods with fourth‐order Runge–Kutta integration, we compare dual and triple control strategies against a baseline of no intervention. Our sensitivity analyses, both local and global, identify community and hospital transmission rates as the dominant outbreak drivers, while burial practices emerge as the strongest leverage point for control. The findings reveal a counterintuitive truth: the epidemiologically most powerful strategy, deploying all three interventions simultaneously, is not the most economical. Instead, pairing screening with contact reduction prevents over 5500 infections at an incremental cost of just 12 cents per case averted, offering far better value than chasing marginal gains with costlier packages. We conclude that maximum disease suppression and optimal resource allocation seldom align and that mathematical modeling must integrate economic reality to guide evidence‐based response.