Research Articles (Mathematics and Applied Mathematics)

Permanent URI for this collectionhttp://hdl.handle.net/2263/1978

A collection containing some of the full text peer-reviewed/ refereed articles published by researchers from the Department of Mathematics and Applied Mathematics

Browse

Now showing 1 - 20 of 777

Radicals in flip subalgebras of Matsuo algebras
Rodrigues, Bernardo Gabriel; Shpectorov, S. (Springer, 2026-04)
We develop methods for determining key properties (simplicity and the dimension of radical) of flip subalgebras in Matsuo algebras. These are interesting classes of commutative non-associative algebras that were introduced within the broader paradigm of axial algebras.
An optimized block hybrid spectral simple iteration methods for solving nonlinear evolution equations
Ahmedai, Salma; Sibanda, Precious; Motsa, Sandile; Goqo, Sicelo; Noreldin, Osman A.I. (Wiley, 2025-12)
This study presents a new optimized block hybrid method and spectral simple iteration method (OBHM-SSIM) for solving nonlinear evolution equations. In this method, we employed a combination of the spectral collocation method in space and the optimized block hybrid method in time, along with a simple iteration scheme to linearize the equations. The performance of OBHM-SSIM is compared with other established numerical methods for various nonlinear evolution equations, including the Stokes' second problem equation, Burgers─Fisher equation, Burgers─Huxley equation, the FitzHugh─Nagumo equation with time-dependent coefficients, and coupled Burgers' equations. Furthermore, the proposed OBHM-SSIM is implemented to solve -dimensional problems, specifically the nonlinear Burgers' equation and the cubic Klein─Gordon equation, demonstrating its capability to solve nonlinear systems efficiently. The extension to two-dimensional cases further validates the flexibility and accuracy of the OBHM-SSIM method, achieved with a notably reduced computational cost. Unlike conventional spectral methods, the proposed OBHM-SSIM achieves high-order accuracy with fewer grid points by optimizing intra-step points and maintaining A-stability for large time domains. We demonstrate that the OBHM-SSIM method gives highly accurate solutions with fewer grid points. This results in enhanced computational efficiency and reduced complexity, particularly for large time domains of nonlinear evolution equations. The findings of this study offer a new approach for the application of the spectral block hybrid method, ultimately improving the accuracy and efficiency of computational solutions for nonlinear evolution equations.
Pattern formation of bulk-surface reaction-diffusion systems in a ball
Villar-Sepulveda, Edgardo; Champneys, Alan R.; Cusseddu, Davide; Madzvamuse, Anotida (Society for Industrial and Applied Mathematics, 2026)
Weakly nonlinear amplitude equations are derived for the onset of spatially extended patterns on a general class of 𝑛-component bulk-surface reaction-diffusion systems in a ball, under the assumption of linear kinetics in the bulk and coupling Robin-type boundary conditions. Linear analysis shows conditions under which various pattern modes can become unstable to either generalized pitchfork or transcritical bifurcations, depending on the parity of the spatial wavenumber. Weakly nonlinear analysis is used to derive general expressions for the multicomponent amplitude equations of different patterned states. These reduced-order systems are found to agree with prior normal forms for pattern formation bifurcations with 𝑂⁡(3) symmetry, and they provide information on the stability of bifurcating patterns of different symmetry types. The analysis is complemented with numerical results using a dedicated bulk-surface finite element method. The theory is illustrated in two examples: a bulk-surface version of the Brusselator and a four-component bulk-surface cell-polarity model.
A stacking model integrating GARCH and LSTM with feature interactions for time series volatility prediction
Peter, Michael; Mirau, Silas; Sinkwembe, Emmanuel; Kasumo, Christian; Guambe, Calisto (Elsevier, 2026-03)
Volatility forecasting remains a cornerstone of quantitative finance, underpinning risk management, portfolio optimization, and regulatory oversight. This study introduces a novel stacking model that integrates the generalized autoregressive conditional heteroskedasticity (GARCH) framework with long short-term memory (LSTM) networks to capture both econometric structure and nonlinear temporal dependencies in financial time series. Unlike conventional hybrid approaches that sequentially cascade outputs, the proposed framework employs GARCH and LSTM as parallel base learners, with their predictions intelligently fused through a meta-learner that exploits feature interactions and cross-model synergies. The empirical evaluation benchmarks the stacking ensemble against state-of-the-art alternatives, including DLINEAR, CKAN, N-BEATS, and individual GARCH and LSTM specifications across multiple performance metrics. Results demonstrate consistent superiority across RMSE, MAE, accuracy, RAMP, geometric mean, Hausdorff distance, and AUC metrics, validating the synergistic benefits of integrating econometric and machine learning paradigms within a theoretically grounded architecture. The model’s superior performance stems from leveraging GARCH’s parametric efficiency in modeling volatility clustering while harnessing LSTM’s capacity to capture complex nonlinear temporal patterns. Beyond methodological contributions, the framework offers practical value for enhancing systemic risk monitoring, improving stress testing frameworks, and optimizing investment strategies across diverse market conditions. The demonstrated robustness across different market regimes underscores its potential for adoption in both routine operations and crisis contexts. This research establishes stacking-based ensemble modeling as a powerful paradigm for advancing volatility prediction and provides a foundation for next-generation financial forecasting systems. HIGHLIGHTS • Stacked GARCH-LSTM captures volatility clustering and long-term dependencies. • Interaction layer models relationships of GARCH indicators with LSTM features. • Combines econometric and deep learning, boosting predictive accuracy on real data. • Stacking framework explains GARCH while utilizing LSTM learning capabilities.
Within host dynamics of HPV infection with cellular immunity and HPV-infected dormant cells reactivation
Chapwanya, Michael; Fouape, Adele Claire; Tsanou, Berge (KeAi Communications, 2026-09)
Like other viruses, human papillomavirus genotypes can remain dormant for years or decades and later reactivate due to some well-known factors. The activation of such a dormant infection years later can cause many health and behavioural problems at the individual and societal levels, respectively. From a personalised health perspective, reactivation of a dormant HPV, especially high-risk genotypes such as HPV 16 or 18 can worsen the health condition of the infected person, should they be (or happen to be newly) infected with a different HPV genotype. However, detailed mechanisms that impact the health outcome of an infected person due to rebounding dormant HPV have not been mathematically investigated. The core of this paper is to study the dynamics of an in-host high-risk HPV infection, taking into account cell-mediated immunity and the consequences of reactivation of HPV-infected dormant cells using compartmental modelling. The local and global stabilities of the equilibria are established using Lyapunov and LaSalle techniques, and the bifurcation analysis is performed. Compared to the model without the provision of virus particles due to the reactivation of infected dormant cells, our results suggest that such reactivation can exacerbate the health condition of an infected person by promoting the persistence of infection, which further weakens the active immune response and favours the progression of infection to HPV-induced cancers. In addition, we provide the sensitivity analysis of threshold parameters, state variables with respect to model parameters, and numerical simulations are used to illustrate the theoretical results.
A characterization of some finite quasisimple groups using their character codegrees
Mabena, Lehlogonolo Shaun; Madanha, Sesuai Yash; Now showing 1 - 1 of 1 Rodrigues, Bernardo Gabriel (NISC (Pty) Ltd and Informa UK Limited (trading as the Taylor & Francis Group), 2025-04)
Please read abstract in the article.
Efficient dynamics : reduced-order modeling of the time-dependent Schrödinger equation
Owolabi, Kolade M. (Wiley, 2026-02)
This work develops and rigorously analyzes reduced-order modeling (ROM) techniques for the time-dependent Schrödinger equation (TDSE), with the goal of efficiently capturing essential quantum dynamics at significantly reduced computational cost. Three major ROM frameworks–Proper Orthogonal Decomposition (POD), Dynamic Mode Decomposition (DMD), and Reduced Basis Methods (RBM) are explored and compared–in the context of quantum wavefunction evolution. Comprehensive mathematical formulations are presented, including projection-based Galerkin approximations, a priori and a posteriori error estimates, stability analyses, and convergence guarantees. Numerical experiments are conducted for canonical quantum systems such as the infinite square well, harmonic oscillator, and tunneling through potential barriers, as well as a time-dependent controlled two-level system. It is demonstrated that ROMs can achieve orders-of-magnitude dimensionality reduction while maintaining high fidelity with full-order model (FOM) solutions. Furthermore, the framework is extended to higher-dimensional problems, nonlinear potentials, and multi-particle systems, with applications in quantum control and entanglement dynamics. Visualization of ROM accuracy through mesh, surface, and isosurface plots, as well as convergence studies, confirms the robustness of the proposed methods. To support reproducibility and further research, all MATLAB code used to generate the numerical experiments is made publicly available via GitHub. These results establish ROM as a powerful tool for real-time simulation, control, and optimization in computational quantum mechanics.
A pre-existing fluid-driven permeable fracture with Darcy flow
Nchabeleng, Mathibele; Fareo, Adewunmi (Springer, 2025-11)
This study examines the propagation of a pre-existing fluid-driven fracture in a permeable rock. Incompressible laminar Newtonian fluid drives the fracture which experiences fluid loss through the fracture interface into the surrounding rock matrix. Because the Carter’s model derived from Darcy law has its many flaws, a new model for the fluid loss relating the leak-off depth to the net fluid pressure in the fracture is employed in this work. The elasticity of the rock is modelled using the Khristianovic-Geertsma-de Klerk (KGD) model. Starting out with lubrication equations, a system of partial integro-differential equations relating the width of the fracture to the net pressure and the leak-off depth is derived. Similarity solutions derived for the fracture half-width, net pressure, and depth of leak-off are used to reduce the system of partial integro-differential equations to a system of ordinary integro-differential equations. Numerical results are obtained for the fracture length, fracture half-width, leak-off depth and the net fluid pressure.
A meta-population model of malaria with asymptomatic cases, transmission blocking drugs, migration and screening
Tchoumi, Stephane Yanick; Banasiak, Jacek; Ouifki, R. (AIMS Press, 2025-07-10)
We consider a two-Patch malaria model, where the individuals can freely move between the patches. We assume that one site has better resources to fight the disease, such as screening facilities and the availability of transmission-blocking drugs (TBDs) that offer full, though waning, immunity and non-infectivity. Moreover, individuals moving to this site are screened at the entry points, and the authorities can either refuse entry to infected individuals or allow them in but immediately administer a TBD. However, an illegal entry into this Patch is also possible. We provide a qualitative analysis of the model, focusing on the emergence of endemic equilibria and the occurrence of backward bifurcations. Furthermore, we comprehensively analyse the model with low migration rates using recent refinements of the regular perturbation theory. We conclude the paper with numerical simulations that show, in particular, that malaria can be better controlled by allowing the entry of detected cases and treating them in the better-resourced site rather than deporting the identified infectives and risking them entering the site illegally.
Natural population dynamics of Asian citrus psyllid, Diaphorina citri, and its control based on pheromone trapping
Cardona-Salgado, Daiver; Dumont, Yves; Vasilieva, Olga (Elsevier, 2025-12)
The Asian citrus psyllid (Diaphorina citri) is a major agricultural pest and the principal vector of Huanglongbing (HLB), a devastating citrus disease. Thus, its control is of utmost importance: since D. citri mates multiple times, the use of mating disruption has the potential to reduce or eliminate populations. In this work, we develop a sex-structured, piecewise smooth dynamical system modeling the natural population dynamics of D. citri, focusing on adult stages and mating behavior. The main goal of this manuscript is to show that the population of D. citri, when near a locally asymptotically stable equilibrium, can be effectively suppressed using pheromone traps via two control strategies, mating disruption and male-targeted removal. For this reason, we focus on local stability analysis and the design of practical control interventions that are biologically meaningful and implementable. By applying a feed-forward control approach, which only requires assessing the initial size of the psyllid population, we identify the threshold as a function of the two control parameters above which a local insect elimination is reachable. We also show that a feedback control with periodic assessments of the wild population sizes is applicable, and then deduce that a mixed-type control regime, combining both studied control approaches, yields the best results. We present several simulations to illustrate our theoretical findings and to estimate the minimal amount of pheromones and time needed to reach the local elimination of existing psyllids. Finally, we discuss possible implementations of our results as a part of Integrated Pest Management programs.
Exploring the spatio–temporal dynamics in activator–inhibitor systems through a dual approach of analysis and computation
Chiteri, Vincent Nandwa; Juma, Victor Ogesa; Okwoyo, James Mariita; Moindi, Stephen Kibet; Mapfumo, Kudzanayi Zebedia; Madzvamuse, Anotida (Elsevier, 2025-07)
Real-world mathematical models often manifest as systems of non-linear differential equations, which presents challenges in obtaining closed-form analytical solutions. In this paper, we study the diffusion-driven instability of an activator-inhibitor-type reaction-diffusion (RD) system modeling the GEF-Rho-Myosin signaling pathway linked to cellular contractility. The mathematical model we study is formulated from first principles using experimental observations. The model formulation is based on the biological and mathematical assumptions. The novelty is the incorporation of Myo9b as a GAP for RhoA, leading to a new mathematical model that describes Rho activity dynamics linked to cell contraction dynamics. Assuming mass conservation of molecular species and adopting a quasi-steady state assumption based on biological observations, model reduction is undertaken and leads us to a system of two equations. We adopt a dual approach of mathematical analysis and numerical computations to study the spatiotemporal dynamics of the system. First, in absence of diffusion, we use a combination of phase-plane analysis, numerical bifurcation and simulations to characterize the temporal dynamics of the model. In the absence of spatial variations, we identified two sets of parameters where the model exhibit different transition dynamics. For some set of parameters, the model transitions from stable to oscillatory and back to stable, while for another set, the model dynamics transition from stable to bistable and back to stable dynamics. To study the effect of parameter variation on model solutions, we use partial rank correlation coefficient (PRCC) to characterize the sensitivity of the model steady states with respect to parameters. Second, we extend the analysis of the model by studying conditions under which a uniform steady state becomes unstable in the presence of spatial variations, in a process known as Turing diffusion-driven instability. By exploiting the necessary conditions for diffusion-driven instability and the sufficient conditions for pattern formation we carry out, numerically, parameter estimation through the use of mode isolation. To support theoretical and computational findings, we employ the pdepe solver in one-space dimension and the finite difference method in two-space dimension.
Mathematical modelling of the dynamics of typhoid fever and two modes of treatment in a health district in Cameroon
Tsafack, Thierry Jimy; Kwa Kum, Cletus; Tassé, Arsène Jaurès Ouemba; Tsanou, Berge (AIMS Press, 2025-02-14)
In this paper, we propose a novel mathematical model for indirectly transmitted typhoid fever disease that incorporates the use of modern and traditional medicines as modes of treatment. Theoretically, we provide two Lyapunov functions to prove the global asymptotic stability of the disease-free equilibrium (DFE) and the endemic equilibrium (EE) when the basic reproduction number is less than one and greater than one, respectively. The model is calibrated using the number of cumulative cases reported in the Penka-Michel health district in Cameroon. The parameter estimates thus obtained give a value of = 1.2058 > 1, which indicates that the disease is endemic in the region. The forecast of the outbreak up to November 2026 suggests that the number of cases will be 21,270, which calls for urgent attention on this endemic disease. A sensitivity analysis with respect to the basic reproduction number is conducted, and the main parameters that impact the widespread of the disease are determined. The analysis highlights that the environmental transmission rate and the decay rate of the bacteria in the environment are the most influential parameters for. This underscores the urgent need for potable water and adequate sanitation within this area to reduce the spread of the disease. Numerically, we illustrate the usefulness of recourse to any mode of treatment to lessen the number of infected cases and the necessity of switching from modern treatment to the traditional treatment, a useful adjuvant therapy. Conversely, we show that the relapse phenomenon increases the burden of the disease. Hence adopting a synergistic therapy approach will significantly mitigate typhoid disease cases and overcome the cycle of poverty within the afflicted communities.
Numerical boundary control of multi-dimensional hyperbolic equations
Herty, Michael; Hinzmann, Kai; Muller, Siegfried; Thein, Ferdinand (American Institute of Mathematical Sciences, 2025)
Existing theoretical stabilization results for linear, hyperbolic multi–dimensional problems are extended to discretized multi-dimensional problems. In contrast to existing theoretical and numerical analysis in the spatially one–dimensional case the effect of the numerical dissipation is analyzed and explicitly quantified. Further, using dimensional splitting, the numerical analysis is extended to the multi-dimensional case. The findings are confirmed by numerical simulations for low-order and high-order DG schemes both in the one-dimensional and two-dimensional case.
Within-host mathematical modeling of antibiotic-phage treatments on lysogenic and nonlysogenic bacteria dynamics
Ndongmo Teytsa, Hyacinthe M.; Seydi, Ousmane; Tsanou, Berge; Djidjou-Demasse, Ramses (Wiley, 2025-07)
Bacteriophages, or phages (viruses of bacteria), play significant roles in shaping the diversity of bacterial communities within the human gut. A phage-infected bacterial cell can either immediately undergo lysis (virulent/lytic infection) or enter a stable state within the host as a prophage (lysogeny) until a trigger event, called prophage induction, initiates the lysis process. We develop an approach based on a model structured in terms of time since bacterial infection. We derive important threshold parameters for the asymptotic dynamics of the system and demonstrate that the model’s qualitative behavior can range from the extinction of all bacterial strains to the persistence of a single strain (either lysogen or non-lysogen bacteria) or the coexistence of all strains at a positive steady state. We highlight the existence of critical induction rate values that lead to the coexistence of all states through periodic oscillations. We also conduct a global sensitivity analysis for an effective bacterial clearance. In scenarios where antibiotics are not sufficiently effective, we identify four key phage parameter traits: (i) the phage induction probability, describing the capacity of prophages to be induced, (ii) the probability of absorption, describing the phages’ ability to invade susceptible bacteria, (iii) the reproduction number of susceptible bacteria in the absence of antibiotics, and (iv) the latent period, describing the time since absorption. The obtained results emphasize the effective therapeutic potential of selected phages.
Multiscale analysis of Prandtl-Ishlinskii operators
Kakeu, Achille Landri Pokam (Department of Mathematics, Kyungpook National University, 2025-06)
Homogenization is a cost reducting mathematical method used to model composite materials. It replaces rapidly varying coefficients with constant ones, resulting in an idealized homogeneous material that exhibits similar macroscopic behavior, both qualitatively and quantitatively, to the actual material. The current paper focuses on the deterministic homogenization of the heat equation with hysteresis, which involves the Prandtl- Ishlinskii operator of play type. This equation serves as a model for heat conduction with phase transitions, accounting for undercooling and superheating effects. We consider a sequence of problems with spatially varying coefficients and utilize the concept of sigma-convergence to demonstrate the convergence of the corresponding solutions to the solution of the homogenized problem.
All hyperbolic cyclically presented groups with positive length three relators
Chinyere, Ihechukwu; Edjvet, Martin; Williams, Gerald (Elsevier, 2025-12)
Please read abstract in the article.
Mathematical assessment of the roles of vaccination and pap screening on the burden of HPV and related cancers in Korea
Park, Soyoung; Lim, Hyunah; Gumel, Abba B. (Springer, 2025-12-03)
This study is based on using a novel sex-structured mathematical model to assess the effectiveness of vaccination and Pap screening against HPV and related cancers in South Korea. In addition to its disease-free equilibrium (DFE) being locally-asymptotically stable when the associated control reproduction number is less than one, the model could have one or three endemic equilibria, for a special case with negligible disease-induced mortality, if the reproduction number exceeds one. It's shown, using a Krasnoselskii sublinearity argument, that this special case has a unique and locally-asymptotically stable endemic equilibrium, when the reproduction number is larger than one, if, additionally, the HPV vaccine is assumed to be perfect. The DFE of a simplified version of the model, which is calibrated using HPV-related cancer data in Korea, is globally-asymptotically stable when its reproduction number is less than one. Simulations of the full model showed that, although vaccine-derived herd immunity (needed for HPV elimination) cannot be achieved in Korea under the current vaccination coverage of females (of 88%), it can be achieved if, additionally, at least 65% of males are vaccinated at steady-state. While the current combined vaccination-screening strategy (termed Strategy A) will fail to eliminate HPV, extended strategies that include increased coverage of female vaccination (termed Strategy B) or additionally vaccinating boys (termed Strategy C) could lead to such elimination in Korea. The implementation of boys-only vaccination strategy induces a significant spillover benefit in reducing cervical cancer burden, which exceeds the corresponding spillover benefit achieved by implementing a girls-only vaccination strategy.
Spectral adventures in quantum realms : nonlinear schrödinger dynamics, quantum vortices and time-resolved wave mechanics
Owolabi, Kolade M.; Pindza, Edson; Mare, Eben (World Scientific Publishing, 2026)
In this paper, we present a comprehensive study of quantum wave phenomena using Fourier spectral numerical methods. The focus is on three interrelated topics: (1) the nonlinear Schrödinger equation (NLS) in physical systems, including optical solitons and Bose–Einstein condensates (via the Gross–Pitaevskii equation, GPE); (2) simulations of the time-dependent Schrödinger equation (TDSE) to explore quantum tunneling, wavepacket dynamics and interference; and (3) the characteristics of quantum turbulence and vortices in superfluid systems. We develop the mathematical formulations of NLS and GPE, highlighting how spectral methods efficiently capture their solutions’ high-frequency content and conserved quantities. We detail the implementation of Fourier pseudo-spectral discretization combined with split-step (operator splitting) time integration, evaluating its accuracy and stability. We also discuss numerical error analysis and comparisons with alternative discretization approaches (finite differences and finite elements). The results include simulations of soliton propagation over long distances without shape distortion, quantum tunneling of wavepackets through potential barriers, and formation of vortex lattices and turbulent energy cascades in condensates. Visualizations such as soliton amplitude profiles, probability density snapshots of tunneling wave functions, and vortex lattice images are provided to illustrate these phenomena. Our findings underscore the spectral method’s superior accuracy (exponential convergence for smooth solutions) and its ability to preserve physical invariants over long simulation times. We conclude that Fourier spectral techniques offer a robust and precise framework for graduate-level research and emerging applications in nonlinear and quantum wave systems.
The strong path partition conjecture holds for α=9
De Wet, Johan P.; Frick, Marietjie (University of Zielona Góra, 2026)
Please read abstract in the article.
Complex numbers as powers of transcendental numbers
Chalebgwa, Taboka Prince; Morris, Sidney A. (Taylor and Francis, 2025-09-18)
It is well-known that if a, b are irrational numbers, then ab need not be an irrational number. Let M be a set of real numbers. In this note it is proved that if M is any of (i) the set of all irrational real numbers, (ii) the set of all transcendental real numbers, (iii) the set of all non-computable real numbers, (iv) the set of all real normal numbers, (v) the set of all real numbers of irrationality exponent equal to 2, (vi) the set of all real Mahler S-numbers, (vii) or indeed any subset of R of full Lebesgue measure, then, for each positive real number s = 1, there exist a, b ∈ M such that s = ab. The analogous result for complex numbers is also proved. These results are proved using measure theory.

Browse

Recent Submissions