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All Journal Mikailalsys Journal of Advanced Engineering International Mikailalsys Journal of Mathematics and Statistics International Journal of Humanities, Education, and Social Sciences
Hassan Muhammad
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Religion Humanities Chemical Engineering, Chemistry & Bioengineering Computer Science & IT Education Electrical & Electronics Engineering Engineering Languange, Linguistic, Communication & Media Mathematics Mechanical Engineering Social Sciences

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Mathematical Modeling of Typhoid Fever Transmission Dynamics: A Sensitivity Analysis and Implications for Public Health Strategies Hassan Muhammad; Auwal Abdullahi; Gambo Yakubu; Adamu Ishiyaku; O. O. Niyi; Alagbe S. O
Mikailalsys Journal of Advanced Engineering International Vol 3 No 2 (2026): Mikailalsys Journal of Advanced Engineering International
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjaei.v3i2.9377

Abstract

A comprehensive mathematical model of typhoid fever was developed to investigate the complex transmission dynamics of the disease and clarify the relationships among factors influencing its spread. The model assumes population replenishment through births and uses existing data to validate its accuracy, thereby supporting a reliable representation of disease behavior. This study aims to inform and strengthen strategies for the prevention, control, and possible eradication of typhoid fever in order to support improved public health policy and quality of life. Mathematical analysis revealed that the basic reproductive number, R₀, plays a central role in determining the global dynamics of the disease. When R₀ is less than 1, the disease-free equilibrium is locally stable, indicating that the disease will eventually die out. Conversely, when R₀ exceeds 1, an endemic equilibrium exists, suggesting that the disease will persist at a stable level. Sensitivity analysis of the model parameters provided valuable insights into the relative influence of different factors on typhoid fever transmission, thereby supporting informed decision-making and effective disease management. The model was solved using the fourth-order Runge–Kutta scheme over a 40-year time horizon and implemented in MATLAB. The study concludes that mathematical modeling is a powerful tool for understanding the transmission dynamics of typhoid fever and for guiding evidence-based strategies for disease control and prevention. This study contributes to infectious disease modeling by demonstrating how equilibrium analysis, reproductive number estimation, and parameter sensitivity assessment can support public health planning aimed at reducing the burden of typhoid fever.
Robust Integral Transform Methods for the Solution of Nonlinear Fractional Ordinary Differential Equations in Viscoelastic and Biological Systems Umar Mujahid Aliyu; David Opeoluwa Oyewola; Joel John Taura; Salisu Lukunti; Hassan Muhammad; Abubakar Yahya Adamu; Abdulhalim Isah Ibrahim; Mubarak Muhammad; Imafidor Hassan Ibrahim; Mohammed Abubakar Kolo; Isah Adamu; Wallen Juliet Piapna'an; Mustapha Mohammed Mansur; Ibrahim Abubakar Adamu; Mohammed Yusuf Marafa; Abdulwasiu Umar; Sulaiman Ahmad; Nura Hashim
Mikailalsys Journal of Mathematics and Statistics Vol 4 No 2 (2026): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v4i2.9237

Abstract

Nonlinear and fractional-order differential equations frequently arise in viscoelastic and biological systems; however, their solution remains challenging due to the presence of nonlocal operators, memory effects, and complex boundary conditions. Classical integral transforms, including the Laplace and Fourier transforms, often have limitations in addressing these features effectively. This study presents a robust hybrid methodology that combines the Mahgoub Transform with the Variational Iteration Method (VIM) to solve nonlinear and fractional-order ordinary differential equations (ODEs). The proposed approach was systematically applied to linear, nonlinear, and fractional-order ODEs to evaluate its convergence, accuracy, and capacity to handle memory-dependent effects. The findings demonstrate that the Mahgoub–VIM method achieves rapid convergence, high accuracy, and improved performance compared with traditional transforms such as the Sumudu Transform. These results indicate that the proposed method provides a reliable and efficient analytical framework for modeling complex viscoelastic and biological phenomena governed by nonlinear and fractional-order dynamics. This study contributes to the advancement of integral transform-based solution methods and offers practical implications for the mathematical modeling of systems characterized by memory-dependent behavior and nonlinear responses.
Assessing Differences in Student Motivation, Achievement, and Conceptual Understanding in a Gamified Mathematics Learning Environment Hassan Muhammad; Sadik Hamagam; Usman Garba; Angel Otse Ogbu
International Journal of Humanities, Education, and Social Sciences Vol 4 No 2 (2026): International Journal of Humanities, Education, and Social Sciences
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/ijhess.v4i2.9364

Abstract

Although gamified learning has received growing attention in mathematics education, empirical evidence on its simultaneous influence on students’ motivation, mathematics achievement, and conceptual understanding in developing educational contexts remains limited. This study examined differences in students’ motivation, mathematics achievement, and conceptual understanding associated with participation in a gamified mathematics learning environment. A quasi-experimental pretest–posttest control group design was employed, involving 700 secondary school students from 15 public schools in Northeast Nigeria. Using intact classes, students were assigned to an experimental group that received curriculum-aligned gamified mathematics instruction over a four-week period or to a control group that received conventional instruction covering the same content and duration. Data were collected using pretest and posttest measures of student motivation, mathematics achievement, and conceptual understanding. Motivation was assessed using an adapted questionnaire with established internal consistency, while achievement and conceptual understanding were measured using curriculum-aligned assessments validated through expert review. Data were analysed using descriptive statistics, paired-sample t-tests, and effect size estimates. The results showed statistically significant pretest–posttest gains in motivation, achievement, and conceptual understanding among students in the gamified instruction group, with moderate to large effect sizes, whereas students in the control group demonstrated minimal changes across the same measures. These findings indicate that curriculum-aligned gamified mathematics instruction is associated with enhanced student motivation, improved academic performance, and stronger conceptual understanding within the study context. The study contributes to mathematics education literature by providing large-sample quasi-experimental evidence on the concurrent affective and cognitive outcomes of gamified instruction in secondary mathematics classrooms in a developing educational setting.
Co-Authors Abdulhalim Isah Ibrahim Abdulwasiu Umar Abubakar Yahya Adamu Adamu Ishiyaku Alagbe S. O Angel Otse Ogbu Auwal Abdullahi David Opeoluwa Oyewola Gambo Yakubu Ibrahim Abubakar Adamu Imafidor Hassan Ibrahim Isah Adamu Joel John Taura Mohammed Abubakar Kolo Mohammed Yusuf Marafa Mubarak Muhammad Mustapha Mohammed Mansur Nura Hashim O. O. Niyi Sadik Hamagam Salisu Lukunti Sulaiman Ahmad Umar Mujahid Aliyu Usman Garba Wallen Juliet Piapna'an