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All Journal Journal of Multidisciplinary Science: MIKAILALSYS International Journal of Education, Culture, and Society Mikailalsys Journal of Advanced Engineering International Mikailalsys Journal of Mathematics and Statistics International Journal of Education, Management, and Technology International Journal of Humanities, Education, and Social Sciences
Hassan Muhammad
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Religion Agriculture, Biological Sciences & Forestry Humanities Chemical Engineering, Chemistry & Bioengineering Computer Science & IT Education Electrical & Electronics Engineering Engineering Environmental Science Languange, Linguistic, Communication & Media Materials Science & Nanotechnology Mathematics Mechanical Engineering Physics Social Sciences Other

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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; Nura AY Musa; Danladi Biong'ahu; Usman Garba
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.
Ability Performance Misalignment in WAEC Mathematics Examination Outcomes: A Quantitative Explanatory Study in North-East Nigeria Hassan Muhammad; Philip Issa Tsado; Ahmed Rufai Tete; Momozuku Umaru Salihu; Nura AY Musa
International Journal of Education, Culture, and Society Vol 4 No 3 (2026): International Journal of Education, Culture, and Society
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/ijecs.v4i3.9374

Abstract

This study investigates ability–performance misalignment in West African Examinations Council (WAEC) Mathematics examination outcomes in northeastern Nigeria. A quantitative explanatory cross-sectional design was employed using archival data from public senior secondary schools to examine discrepancies between classroom-based achievement and performance in a high-stakes external examination. The findings revealed that a substantial proportion of students exhibited ability–performance misalignment: some students with high classroom performance obtained low scores in the WAEC Mathematics examination, whereas some students with low classroom performance achieved comparatively high examination scores. Test anxiety, self-efficacy, and inconsistent assessment practices significantly contributed to this misalignment. These findings suggest that WAEC Mathematics examination results may not always accurately represent students’ mathematical achievement and highlight the need to reconsider how high-stakes assessment outcomes are interpreted and used in educational decision-making. The study contributes to the assessment literature by emphasizing the importance of integrating affective, instructional, and contextual factors when evaluating student performance and formulating assessment policies.
Comparing Mathematics Achievement across High-Stakes Examinations: Evidence from WAEC/NECO and JAMB in Nigeria Hassan Muhammad
International Journal of Education, Culture, and Society Vol 4 No 3 (2026): International Journal of Education, Culture, and Society
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/ijecs.v4i3.9375

Abstract

This study compares mathematics performance across essay-based secondary school examinations administered by the West African Examinations Council (WAEC) and the National Examinations Council (NECO) and the multiple-choice university entrance examination administered by the Joint Admissions and Matriculation Board (JAMB) in Nigeria. Using an ex post facto comparative design, archival mathematics examination records from 600 secondary school graduates were analyzed to determine the comparability of performance across the three examination systems. Mathematics performance in WAEC and NECO was operationalized using official grade classifications, whereas JAMB performance was assessed using subject-level aggregate score ranges. Data were analyzed through descriptive statistics, score standardization, and paired-samples t tests. The findings showed that a substantial proportion of candidates who attained credit-level grades in WAEC and NECO Mathematics obtained relatively low aggregate scores in JAMB Mathematics. Standardized mean comparisons further indicated that the same candidates performed better in WAEC and NECO than in JAMB, while the paired-samples analysis confirmed that the differences were statistically significant and associated with a large effect size. These results demonstrate systematic variation in mathematics performance between essay-based and multiple-choice high-stakes examinations. The study contributes empirical evidence to the mathematics education literature on assessment comparability in multi-examination contexts and underscores the need for cautious interpretation of examination outcomes generated by assessment systems with different formats and purposes, particularly when such results inform high-stakes educational decisions.
Hybrid Integral Transform Techniques for the Solution of Third-Order Nonlinear Ordinary Differential Equations 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 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.v3i2.9236

Abstract

Third-order nonlinear ordinary differential equations frequently arise in the mathematical modeling of complex engineering and physical phenomena; however, exact analytical solutions remain difficult to obtain because of strong nonlinearities and higher-order derivative effects. Classical integral transform techniques, including the Laplace and Fourier transforms, are widely used for solving differential equations but often have limitations when extended to nonlinear systems. Although modern integral transforms such as the Sumudu, Mahgoub, and Elzaki transforms offer computational advantages, their applicability is generally restricted to linear models. This study introduces a hybrid analytical approach that integrates the Mahgoub transform with the Variational Iteration Method (VIM) to solve third-order nonlinear ordinary differential equations more effectively. The proposed method converts the governing equation into the transform domain and applies an iterative correction functional to address nonlinear terms without linearization or discretization. The resulting solutions are expressed in rapidly convergent series form. Numerical validation demonstrates strong agreement with exact solutions, confirming the efficiency, accuracy, and stability of the hybrid Mahgoub–VIM approach. The study concludes that this hybrid semi-analytical method provides a reliable framework for solving higher-order nonlinear differential equations in applied mathematics and engineering analysis. These findings contribute to the development of transform-based analytical methods by extending the applicability of the Mahgoub transform to nonlinear differential equation models through variational iteration.
The Role of Augmented Reality (AR) in Enhancing Conceptual Understanding of Geometry in Mathematics Education: Systematic Review Hassan Muhammad; Nura Ay Musa; Auwal Ahmad; Nurudeen Adamu
International Journal of Education, Management, and Technology Vol 4 No 1 (2026): International Journal of Education, Management, and Technology
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/ijemt.v4i1.8073

Abstract

Geometry, a fundamental branch of mathematics, often challenges students due to its abstract nature and the demands it places on spatial reasoning and visualization, and traditional teaching methods frequently fail to convey complex geometric concepts effectively, leading to low engagement and poor understanding. This systematic review investigates the impact of Augmented Reality (AR) on enhancing students’ conceptual understanding of geometry in mathematics education by synthesizing existing empirical studies on AR-based geometry instruction. AR technology provides interactive, immersive learning environments that enable learners to manipulate three-dimensional geometric shapes and transformations in real time, thereby supporting deeper cognitive engagement with abstract content. The reviewed studies consistently report that AR interventions enhance spatial reasoning, improve visualization abilities, and foster deeper conceptual understanding of geometric ideas, while also increasing student motivation, engagement, and retention and supporting the development of critical problem-solving skills. At the same time, the review identifies key implementation challenges, including the high cost and limited availability of AR tools, as well as the need for targeted teacher training to design and facilitate AR-enhanced lessons. The review concludes that AR holds strong potential as a pedagogical innovation for geometry education, provided that infrastructural, financial, and professional development barriers are addressed, and recommends future research focusing on longitudinal designs, more affordable AR solutions, and the integration of AR into advanced geometric topics and diverse educational contexts.
Modeling Cholera Dynamics with Vaccination and Asymptomatic Transmission: A Mathematical Framework for Outbreak Control Hassan Muhammad; Alagbe S.O. Philip Issa Tsado; Angel Otse Ogbu
Journal of Multidisciplinary Science: MIKAILALSYS Vol 4 No 2 (2026): Journal of Multidisciplinary Science: MIKAILALSYS
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mikailalsys.v4i2.9368

Abstract

Cholera remains a persistent public health challenge in regions with limited access to clean water and adequate sanitation. Although mathematical models have substantially advanced understanding of cholera dynamics, the waning effectiveness of vaccination and the contribution of asymptomatic carriers to disease transmission have received comparatively limited attention. This study develops a mathematical model that incorporates these two epidemiologically important mechanisms to evaluate cholera transmission dynamics and outbreak-control strategies. The model stratifies the population into susceptible individuals (S), vaccinated individuals (V), asymptomatically infected individuals (A), symptomatically infected individuals (I), individuals receiving treatment in health centers (C), recovered individuals (R), and the concentration of bacteria in the aquatic environment (B). The basic reproduction number (R₀) was derived, indicating that cholera can be eliminated when R₀ < 1. Using data from cholera outbreaks reported between 2022 and 2025, numerical simulations were conducted to assess alternative intervention strategies. Sanitation measures alone reduced total cases by 43.1%, vaccination by 37.3%, and treatment by 28.0%, whereas the combined implementation of vaccination and sanitation produced a 69% reduction. Sensitivity analysis identified the human-to-human transmission rate (β₁), environment-to-human transmission rate (β₂), and vaccine effectiveness (σ) as the most influential parameters governing disease control. The findings demonstrate that integrated interventions are substantially more effective than single-control strategies and highlight the importance of combining vaccination campaigns with water, sanitation, and hygiene programs. This model contributes to cholera epidemiology by simultaneously accounting for asymptomatic transmission and waning vaccine effectiveness, thereby providing a quantitative framework for designing more effective outbreak-control policies.
Co-Authors Abdulhalim Isah Ibrahim Abdulwasiu Umar Abubakar Yahya Adamu Adamu Ishiyaku Ahmed Rufai Tete Alagbe S. O Alagbe S.O. Philip Issa Tsado Angel Otse Ogbu Auwal Abdullahi Auwal Ahmad Danladi Biong&#039;ahu David Opeoluwa Oyewola Gambo Yakubu Ibrahim Abubakar Adamu Imafidor Hassan Ibrahim Isah Adamu Joel John Taura Mohammed Abubakar Kolo Mohammed Yusuf Marafa Momozuku Umaru Salihu Mubarak Muhammad Mustapha Mohammed Mansur Nura AY Musa Nura Hashim Nurudeen Adamu O. O. Niyi Philip Issa Tsado Salisu Lukunti Sulaiman Ahmad Umar Mujahid Aliyu Usman Garba Wallen Juliet Piapna&#039;an