International Journal of Mathematical Analysis and Modelling

Mathematical modeling of alcoholism as a social contagion: dynamics, bifurcation, and control

2026-08-09T06:26:07+00:00

Alcoholism remains a critical social and public health problem worldwide, characterized by behavioral transmission through peer influence and social reinforcement. In this study, we develop and analyze a deterministic compartmental model describing alcoholism dynamics as a social contagion process. We derive the basic reproduction number, examine local and global stability, and investigate bifurcation behavior. Sensitivity analysis identifies key parameters driving the persistence of alcohol abuse. Finally, we introduce optimal control interventions to guide public health policies. Numerical simulations reveal that combined interventions—awareness, rehabilitation, and relapse prevention—are the most effective in reducing alcohol dependence. The study provides qualitative insights into alcoholism dynamics rather than quantitative prediction.

Sustainability reporting and financial performance of manufacturing companies in Nigeria: A mixed-methods analysis

2026-08-09T07:40:31+00:00

This study examines the impact of sustainability reporting on the financial performance of manufacturing companies in Nigeria, employing a mixed-methods approach that combines quantitative regression analysis with qualitative thematic review. The research is grounded in Stakeholder Theory, Legitimacy Theory, and the Resource-Based View (RBV), providing a comprehensive framework for understanding the relationship between Environmental, Social, and Governance (ESG) practices and financial outcomes. Quantitative analysis of 15 listed manufacturing firms over the period 2019-2023 reveals a statistically significant positive correlation between sustainability reporting and key financial performance indicators, including Return on Assets (ROA) and Return on Equity (ROE). The regression model explains 33.3% of financial performance variability, with a p-value of 0.031 indicating the significance of sustainability practices. Qualitative thematic analysis identifies three categories of barriers to sustainability reporting: individual factors (lack of expertise, time constraints, limited awareness), institutional factors (regulatory uncertainty, standardization challenges, lack of incentives), and organizational factors (cultural resistance, poor communication,
financial constraints). The findings demonstrate that robust ESG frameworks contribute to enhanced operational efficiency, improved stakeholder trust, and sustainable competitive advantage. The study offers actionable recommendations for manufacturing companies and policymakers, emphasizing the need for comprehensive reporting frameworks, capacity building, and regulatory incentives. This research contributes to the growing body of literature on sustainability accounting in emerging economies and provides practical insights for advancing sustainable business practices in Nigeria’s manufacturing sector.

A class of one-stage two-derivative diagonally implicit Runge-Kutta methods for sine-Gordon equation

2026-04-27T15:02:36+00:00

The sine-Gordon equation is a nonlinear hyperbolic partial differential equation with important applications in physics, biology, and engineering. Its dispersive and oscillatory nature makes accurate numerical simulation challenging, especially when using traditional time integration methods. This research develops and analyzes a class of phase-fitted one-stage two-derivative diagonally implicit Runge-Kutta (TDDIRK) methods for solving the sine-Gordon equation efficiently. In this paper, we use the method of lines to obtain a semi-discrete continuous system. A class of one-stage two-derivative DIRK methods are derived by optimizing their coefficients to reduce phase-lag and amplification errors. The stability and phase analyses are performed to examine their properties. Numerical experiments on kink and antikink soliton problems show that the proposed phase-fitted methods achieve higher accuracy and improved efficiency compared to non-optimized schemes. The results demonstrate that these methods are effective for solving oscillatory nonlinear partial differential equations like the sine-Gordon equation.

Modeling Malaria transmission dynamics incorporating insecticide resistance in mosquito vectors

2026-08-09T07:24:19+00:00

Malaria remains a major public health challenge in sub-Saharan Africa, with Nigeria bearing the highest global burden. Emerging insecticide resistance threatens core vector-control interventions such as long-lasting insecticidal nets (LLINs) and indoor residual spraying (IRS). This study develops a deterministic compartmental SLIR-SLI model that explicitly incorporates insecticide resistance in mosquito populations by stratifying parameters via a dynamic resistance metric ρ.Model variables were informed by the Global Burden of Disease repository to provide realistic approximations of malaria transmission. Numerical simulations demonstrate that high prevalence of resistance leads to non-linear increases in infectious bites, reduces the efficacy of insecticide-induced vector mortality, and prolongs epidemic peaks. The model highlights the critical need for integrated approaches to mitigate vector resistance.

A POLYNOMIAL-BASED COLLOCATION METHOD FOR FRACTIONAL ORDER DIFFERENTIAL EQUATIONS USING HERMITE AND TWO-POINT TAYLOR BASES

2026-04-06T15:05:13+00:00

Complex systems with memory and hereditary properties are often modeled using fractional differential equations (FDEs), which are ubiquitous in various fields. However, the majority of FDEs lack closed-form solutions, necessitating the development of efficient numerical methods. This research presents a polynomial-based collocation framework for solving linear and nonlinear FDEs involving the Caputo fractional derivative. The proposed approach utilizes Hermite and two-point Taylor polynomials of fourth and sixth orders as basis functions to approximate the solution. The collocation technique transforms the governing equation into an algebraic system, where the solution yields the polynomial coefficients. The method's accuracy is assessed using absolute error and mean absolute error metrics, with validations against exact solutions and existing Bernstein polynomial results. Numerical and graphical evidence shows the proposed approach offers accurate, stable, and computationally efficient solutions for fractional differential equations.

Optimal control strategies for the transmission dynamics of Giardiasis

2026-08-09T07:05:03+00:00

This work develops and examines a deterministic mathematical model of giardiasis transmission, explicitly including the frequently neglected influence of asymptomatic carriers and the environmental pathogen reservoir. A thorough dynamical systems analysis of the autonomous model is performed, confirming the positivity and boundedness of solutions to ensure epidemiological well-posedness. We calculate the basic reproduction number (R0) employing the next-generation matrix approach and formally delineate the criteria for the local asymptotic stability of the disease-free equilibrium. We enhance the model by incorporating optimum control theory to meet the essential requirement for economical, time-sensitive intervention tactics. We provide three dynamic control functions that represent the medical treatment of symptomatic persons, the active
screening of asymptomatic carriers, and environmental sanitation initiatives. Utilizing Pontryagin’s Maximum Principle, we establish the requisite conditions for optimal control and simulate diverse intervention scenarios. Our findings demonstrate that single-intervention methods achieve limited efficacy, but a multifaceted, integrated strategy substantially reduces both the human disease burden and environmental pollution. Moreover, we illustrate that a focused strategy integrating immediate treatment with proactive asymptomatic screening provides a highly cost-effective option for resource-limited environments. This study offers substantial mathematical insights and a quantitative public health framework for the development of effective and sustainable giardiasis control initiatives.

Stability analysis of a Malaria epidemic model transmission dynamics

2026-08-09T06:37:04+00:00

Malaria is a vector-borne disease that has been haunting mankind and still remains a major public health issue. It is caused by the parasites, from the genus Plasmodium, which spread to people through the bite of infected adult female mosquitoes of the Anopheles species. In 2017, an estimated 219 million cases occurred worldwide with children accounting for 61% of deaths.
In this paper, we formulate a mathematical model that reduces malaria transmission dynamics and investigate the basic properties of the model; the disease Free Equilibrium and the basic reproduction number of the model were obtained. The Jacobian matrix stability technique was used to analysed the stability of the disease free equilibrium. The analysis shows that the disease free equilibrium is locally asymptotically stable that is R0 < 1.This discovery indicates that, malaria transmission can
be reduced or eliminated from the population.

Mathematical model on cascading ball dynamics with linear and quadratic aerodynamic drag as n → ∞

2026-08-09T06:18:49+00:00

Rhythmic juggling and cascading ball motion provide a natural setting for exploring how mechanical laws, temporal organization, and scalability interact in coordinated dynamical systems. In this work, we develop a theoretical framework that treats juggling as a limit process, extending discrete n-ball cascade dynamics toward an effectively infinite number of balls. Starting from classical
projectile motion, each throw is embedded within a fixed rhythmic structure that governs release and catch events. As the number of balls increases, the cascade approaches a continuous limit in which discrete throw events densely populate the rhythmic cycle. This perspective reveals how synchronization, stability, and tolerance to variability persist even as pattern complexity grows without bound. The analysis shows that key dynamical constraints such as flight-time synchronization and phase separation remain well defined in the infinite-ball limit, providing a bridge between finite juggling patterns and continuous rhythmic motion. Aerodynamic drag is incorporated to assess how dissipative effects influence this asymptotic behavior, demonstrating that while drag alters individual trajectories, the global rhythmic structure remains robust. By framing juggling as a scalable dynamical system rather than a fixed skill involving a small number of objects, this study offers new insight into the fundamental principles governing rhythmic coordination, with implications for nonlinear dynamics, human motor control, and large-scale rhythmic systems.

Sensitivity and threshold analysis of a juvenile delinquency model with multiple exposure pathways

2026-08-09T07:30:51+00:00

We analyze a compartmental model of juvenile delinquency that includes three exposure pathways (peer, social, family) and multiple infectious/delinquent compartment’s EPJ , ESJ , EFJ , IJ , AJ , CJ together with recovered and cumulative classes. Using the next-generation matrix method we derive the threshold parameter R0 (the basic reproduction number) in closed, computable form and prove that the delinquency-free equilibrium (DFE) is locally asymptotically stable if R0 < 1 and unstable if R0 > 1. We also establish global stability of the DFE under R0 < 1 by the comparison theorem. Finally, we present a rigorous sensitivity-analysis framework for R0 (normalized forward sensitivities / elasticity’s using eigenvector formulas) and discuss policy implications: which exposure pathways and parameters should be targeted for effective control. Numerical implementation steps, suggested parameter values for illustrative simulations, and policy recommendations are provided.

A Mathematical Model to Assess the Impact of Asymptomatic Infections on Malaria Transmission Dynamics Incorporating Awareness Campaigns and Treatment

2026-04-07T09:49:34+00:00

Malaria transmission in sub-Saharan Africa is sustained in part by a large reservoir of asymptomatic infections that perpetuate transmission. While awareness-based interven- tions are widely promoted to improve prevention and treatment-seeking behaviour, their interaction with asymptomatic transmission is rarely examined. We develop a determinis- tic compartmental model that integrates awareness stratification of susceptible individuals with explicit compartments for asymptomatic, symptomatic, treated, and recovered humans, coupled with a vector population. Susceptible individuals are classified into low- and high- awareness groups, with transitions governed by awareness campaigns and waning awareness. The basic reproduction number is derived using the next-generation matrix method, and conditions for local and global stability of the malaria-free equilibrium are established. Sensi- tivity analysis identifies key parameters influencing transmission dynamics. The quantitative result of the threshold R0 reveals that asymptomatic cases contribute approximately 90.7% to the basic reproduction number, while symptomatic cases account for about 9.3%.The re- sult also shows that awareness alone is insufficient for malaria elimination in the presence of a substantial asymptomatic reservoir. However, combined strategies incorporating enhanced awareness, increased treatment coverage, reduced vector–human contact, and detection of asymptomatic infections significantly reduce transmission. The model underscores the need to integrate behavioural interventions with strategies targeting hidden infections to support malaria elimination efforts.

Estimating the fractal dimension of all share index of the Nigerian stock market (ASINSM) from 1999 to 2013

2026-08-09T07:11:51+00:00

In this study, All Share Index data of the Nigerian stock market was estimated using the fractal dimension as an estimator for a period of fifteen years (January 1999–December 2013). The Hurst parameter H ∈ [0, 1] obtained is used as a dimensionless estimate. The linear relationship between the Hurst parameter and the fractal dimension, D, is given by D = 2 − H. The study evaluates whether the Nigerian stock market exhibits persistent, random, or anti-persistent behaviour within the period under review. The result of the fractal dimension, D = 1.54, obtained showed that the market exhibited weak anti-persistent behaviour and a slight departure from a purely random walk during the particular period. Also, the yearly estimated values of D showed varying behavioural patterns: persistent, anti-persistent, and random behaviour across different economic periods. The result will help policymakers gain a better understanding of market dynamics in order to improve market transparency and stability.

Analytical Shooting Technique for Fluid Model

2026-01-11T03:55:36+00:00

Solution to boundary value problems emanated from modeling of fluid flow problems like Jeffery flow, couette flow and the likes without an exact solution has been the desire of researchers in recent years; with this a semi-analytical scheme was developed to solve some of the differential equations of nth order () emanated from modeling of fluid problems in engineering. This approach was used to solve some of the problems, and results obtained are continuous solutions that are free of discretization errors. Two shooting gradients were used to adjust the shooting angle namely Cubic Newton formula (CNF) and Modified Fourth-Order formula (MFOF), and it was observed that MFOF needs less iteration than CNF to produce an approximate solution with a very low difference from the exact solution where the exact solution is available.

Mathematical modelling and analysis of HIV/AIDS transmission with vertical and horizontal transmission incorporating treatment as control strategy

2026-08-09T06:58:26+00:00

We developed a deterministic mathematical model in this study to study the vertical and horizontal dynamics of HIV/AIDS with treatment as a critical control measure. The basic reproduction number RH0 was calculated, and the model analysis shows that the system has a forward (transcritical) bifurcation at RH0 = 1. This means that, if RH0 < 1, the disease-free equilibrium is locally
asymptotically stable and unstable if RH0 > 1; and that there is one disease endemic equilibrium when RH0 > 1, which is locally asymptotically stable when RH0 > 1. A multi-parameter sensitivity analysis was performed to identify the impacts of the various parameters on RH0 . The findings indicate that the parameters whose sensitivity indices are positive contribute to the transmission and burden of HIV/AIDS in the population, for example, the contact rates. On the other hand, those with negative sensitivity indices, especially the treatment rates σh and σA, decrease the spread of the disease and diminish the infection pressure. In addition, numerical simulations were conducted by changing the key parameters, such as the treatment rates σh and σA, the vertical transmission rate βh, and the contact rate ω1. Results from the simulation suggest that the higher the treatment rates, the lower the HIV/AIDS prevalence rates and cumulative numbers of new infections, respectively, and the higher the contact and vertical transmission rates, the more the spread of the disease is intensified. Overall, the results indicate that combining treatment with prevention is critical to the control of the dynamics of HIV/AIDS transmission.