Journal of Advances in Mathematics and Computer Science

Forecasting HIV Case Dynamics in Enugu State, Nigeria: An Empirical Study of Growth Models and Ensemble Learning Algorithms

2026-06-10T05:39:11+00:00

The accurate prediction of HIV cases in Enugu State is critical for effective public health planning. Early intervention remains very limited due to inconsistent fluctuations in daily reported cases and the inability of a single model to capture the structural changes in the epidemic. The study aims to develop a framework for forecasting HIV case dynamics in Enugu State, Nigeria, integrating growth curve models and Ensemble algorithms. Using 17 years of cumulative HIV dataset from 2007–2023, smoothed using 7-day rolling mean, four nonlinear growth models: Exponential, Gompertz, Logistic, and Richards were fitted. Structural breaks were detected using the PELT algorithm and validated using the Chow test. The models were all fitted within each segment of the data, and the best performing model was used for that segment. The predictions from each segment were combined using three ensemble techniques: weighted average, Random Forest, and Gradient Boosting. The weighted ensemble showed the highest accuracy with R2 of 0.9996 and RMSE of 104.62 as well as strong uncertainty performance (IFMS = 662.56; ICP = 0.92). The study concludes that segmented growth modeling with ensemble learning significantly enhances the accuracy, stability, and interpretability of HIV forecasts, informing public health policy with reliable data in Enugu State. The use of routine surveillance data that sometimes contain reporting inconsistencies and omission of external determinants of HIV transmission such as as socioeconomic conditions, behavioural factors, and healthcare policy changes are the limitations of the study. The integration of these covariates and evaluation of the framework across multiple regions to enhance generalizability can be pursued in the future studies.

Sensitivity Analysis, Parameter Estimation, and Disease Prediction for a Generalized Fractional-Order Disease Model with Adaptive Immune Response

2026-06-11T07:52:05+00:00

Aims/Objectives: Predicting how infectious diseases spread is challenging because biological systems carry memory—today’s infection rate depends on the entire history of past exposure, not just the current moment. This paper presents a disease prediction framework using Caputo fractional calculus to capture memory effects, with explicit humoral and cellular immune responses (the SEIR-HCI model).

Methodology: Sensitivity analysis identifies two parameters that drive epidemic risk most strongly: the transmission rate β (sensitivity index +1) and the recovery rate \(\gamma\) (index ≈ −0.95). The model is fitted to real SARS-CoV-2 daily case data from India and South Africa using weighted least squares, with uncertainty quantification via parametric bootstrap.

Results: The proposed model reduces prediction error (RMSE) by roughly 40–41% over a standard integer-order model, with R² values of 0.957 and 0.946 for India and South Africa, respectively. The estimated memory index \(\hat{α}\) ≈ 0.887–0.912, significantly below one, confirms that real epidemic data carry substantial memory. All computations use the Adams–Bashforth–Moulton predictor-corrector scheme, convergent at order min(2, 1+α).

Conclusion: Intervention strategies targeting β (e.g., non-pharmaceutical interventions) and γ (e.g., clinical management) yield the highest returns for epidemic control. The immune compartments H (humoral) and C (cellular) are population-level phenomenological proxies; direct validation against immunological time-series data constitutes a stated limitation of the study.

Mathematical Modelling and Numerical Analysis of Hepatitis B Virus Transmission Dynamics with Vaccination and Treatment Control Strategies

2026-06-11T11:50:07+00:00

In this paper presents a mathematical model for studying the transmission dynamics of the Hepatitis B Virus (HBV), incorporating vaccination and treatment strategies. The proposed model is analyzed to establish important mathematical properties, including positivity, boundedness, and the feasible region, ensuring the biological validity of the system. The disease-free equilibrium (DFE) and endemic equilibrium (EE) points are derived, and their local as well as global stability. conditions are investigated through the basic reproduction number R₀. The analysis indicates that the disease can be effectively controlled when R₀ < 1, whereas HBV persists within the population when R₀ > 1. Furthermore, the findings highlight the crucial impact of vaccination and treatment interventions in reducing HBV transmission. The study provides valuable theoretical insights that may support the development of effective public health policies and disease management strategies for controlling Hepatitis B infection.

Real-time Consumer Behaviour Segmentation Using Transformer-based AI Models

2026-06-12T11:54:59+00:00

The rapid growth of digital commerce and online consumer interactions has generated vast amounts of behavioural data, creating new opportunities for organizations to understand customer preferences and improve marketing strategies. Consumer behaviour segmentation is a fundamental technique used to classify customers into distinct groups based on their characteristics and purchasing patterns. However, traditional segmentation methods such as K-Means clustering, RFM analysis, and conventional machine learning models often struggle to capture the dynamic and sequential nature of consumer behaviour in real-time environments. To address these limitations, this study proposes a Transformer-based Artificial Intelligence (AI) framework for real-time consumer behaviour segmentation.

The proposed framework utilizes self-attention mechanisms to analyse sequential consumer activities, including clicks, searches, cart additions, purchases, and reviews. By learning contextual relationships among behavioural events, the Transformer model effectively captures long-term dependencies and generates dynamic customer segments. The study employs a quantitative experimental research design using consumer behaviour datasets collected from e-commerce platforms. The performance of the Transformer model is compared with traditional machine learning and deep learning approaches, including K-Means, Random Forest, Support Vector Machine (SVM), and Long Short-Term Memory (LSTM) networks.

Experimental results demonstrate that the Transformer-based model achieves superior performance in terms of accuracy, precision, recall, and F1-score. The confusion matrix analysis further confirms the effectiveness of the proposed model in accurately classifying consumers into different behavioural segments. Additionally, real-time segmentation contributes to improved business outcomes, including higher customer retention, enhanced personalization, increased conversion rates, and better marketing effectiveness. The findings highlight the potential of Transformer-based AI models as a scalable and intelligent solution for next-generation customer analytics and real-time decision-making systems.

A Two-step Fixed Point Iteration: Stability and Data Dependence Analysis

2026-06-15T08:17:04+00:00

Fixed point iterative methods play an important role in various branches of mathematics and their applications including optimization theory, nonlinear equations, numerical analysis, differential equations, and computational sciences. The convergence behaviour of these iterative schemes is significantly influenced by variations in the data and associated parameters. This study investigates the strong convergence, stability and data dependence of a two-step fixed point iteration under suitable contractive conditions in hyperbolic spaces. The variations of the fixed point to data dependence are analysed using the established error bounds. A numerical example supported by graphical and tabular representations illustrates the effect of data dependence on the convergence behaviour. Moreover, this study provides a practical use of an iterative scheme to find the solution of an integral equation.

Magnetohydrodynamic Maxwell Nanofluid Flow Over a Stretching Surface with Multiple Slip Conditions and Soret-Dufour Effects

2026-06-20T07:51:38+00:00

Magnetohydrodynamic Maxwell nanofluid flow over a stretching permeable surface is investigated under multiple slip conditions, heat generation, activation energy, thermal radiation, and Soret-Dufour cross-diffusion effects. The study considers a steady, two-dimensional, laminar, incompressible boundary-layer flow of an electrically conducting non-Newtonian nanofluid subject to a transverse magnetic field. Velocity, thermal, and concentration slips are imposed at the boundary, while Brownian motion and thermophoresis are included through the Buongiorno nanofluid framework. The governing nonlinear partial differential equations for momentum, energy, and concentration are transformed into coupled nonlinear ordinary differential equations by employing suitable similarity transformations. The resulting boundary value problem is then solved numerically using the shooting technique together with the Runge-Kutta-Fehlberg method implemented in Maple. The numerical procedure is validated through comparison of the Nusselt number with previously published limiting results, showing close agreement. The graphical results indicate that increasing the magnetic parameter, Maxwell parameter, porosity parameter, and velocity slip parameter reduces the velocity field because of Lorentz drag, viscoelastic resistance, porous-medium resistance, and weakened wall momentum transfer. The temperature distribution increases with larger magnetic, Dufour, Soret, and thermophoresis parameters, reflecting Joule heating, diffusion-thermo coupling, thermal-diffusion interaction, and nanoparticle migration effects. The concentration field also increases with the magnetic, Dufour, and Soret numbers, demonstrating the coupling between temperature and concentration gradients within the boundary layer. These findings provide useful numerical insight into coupled momentum, heat, and mass transport in Maxwell nanofluids with slip and cross-diffusion mechanisms, with relevance to thermal engineering, polymer processing, industrial cooling, chemical processing, microfluidic devices, and related transport systems.