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

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Now showing 1 - 20 of 806

A Bayesian approach to feedback control for hyperbolic balance laws
Bambach, Markus; Chu, Shaoshuai; Herty, Michael; Lin, Yunong (Informa UK Limited (trading as Taylor and Francis Group), 2026)
We propose a Bayesian framework for feedback boundary control of hyperbolic balance laws. The method propagates a probability distribution over feedback parameters using Lyapunov decay estimates as a likelihood. For linear models, it recovers available analytical stability results and extends to nonlinear regimes where theory is limited. Using first-order local Lax–Friedrichs (LLF) discretisations, we validate the approach on the decoupled wave system and the linearised Saint-Venant equations, reproducing known stability intervals and mixed boundary couplings. We then treat nonlinear and stochastic problems, including the nonlinear Saint-Venant system, one- and two-dimensional Burgers equations, Burgers equation with random initial data, and nonconservative perturbations with source terms, and show that the inferred stability domains are robust with respect to the indicator and the prior. Finally, we demonstrate transfer to a second-order semi-discrete LLF scheme and to a two-parameter feedback model for laser powder bed fusion with power regulation.
An Archimedean vector lattice functional calculus for semicontinuous positively homogeneous functions
Schwanke, Christopher Michael (Elsevier, 2026-07)
Please read abstract in the article.
A numerical method for solving the generalized tangent vector of hyperbolic systems
Herty, Michael; Zhou, Yizhou (International Press, 2026-07-14)
This work is concerned with the computation of the first-order variation for one-dimensional hyperbolic partial differential equations. In the case of shock waves the main challenge is addressed by developing a numerical method to compute the evolution of the generalized tangent vector introduced by [A. Bressan and A. Marson, Comm. Part. Diff. Eqs., 20(9-10):1491-1552, 1995]. Our basic strategy is to combine the conservative numerical schemes and a novel expression of the interface conditions for the tangent vectors along the discontinuity. Based on this, we propose a simple numerical method to compute the tangent vectors for general hyperbolic systems. Numerical results are presented for Burgers' equation and a 2 X 2 hyperbolic system with two genuinely nonlinear fields.
Analytical and numerical methods for spillover effects in prioritized PrEP for HIV prevention
Piazzola, Chiara; Viguerie, Alex; Safdar, Salman; Gumel, Abba B. (Elsevier, 2027-01)
Pre-exposure prophylaxis (PrEP) is a highly effective intervention for preventing HIV transmission, but its high cost and uneven uptake raise key challenges for allocating resources efficiently. While spillover effects - wherein PrEP use in one group reduces infections in others - are known to occur, they remain poorly quantified and rarely guide policy. We provide a comprehensive modeling study, backed by data, for PrEP spillover effects in HIV risk populations, and develop both analytic and numerical tools for its quantification. Specifically, we first develop a novel compartmental model for HIV transmission that stratifies the total population into four interacting subpopulations: heterosexual males (HETM), high-risk heterosexual females (HETF-hi), low-risk heterosexual females (HETF-lo) and men who have sex with men (MSM). The asymptotic stability of the disease-free equilibrium of the model is analyzed. The spillover effect is directly quantified for this model by deriving an expression for the spillover-adjusted number needed to treat (NNT), a measure of the population-level impact of PrEP uptake in one group on disease incidence in others. Simulations show that PrEP delivery to MSM yields substantial indirect benefits, particularly for HETF-lo, where the spillover effect exceeds the direct effect by a factor of five. Furthermore, we show that targeting HETF-hi outperforms direct PrEP delivery to HETM, emphasizing the importance of intra-group heterogeneity. To evaluate whether these results hold under more detailed assumptions, we embed our framework into the national HOPE model maintained by the Centers for Disease Control and Prevention (CDC) and conduct global sensitivity analysis using Sobol indices with Polynomial Chaos Expansion. This approach extends our analytical insights and quantifies how uncertainty in PrEP allocation strategies propagates through complex epidemic dynamics. Further, this framework provides a numerical procedure for quantifying spillover effects in settings where direct mathematical analysis is impractical (or impossible). Our results demonstrate that spillover effects are a central driver of PrEP dynamics and that failing to account for them risks mis-allocating of control resources. This study provide both analytic and numerical methods for realistically quantifying PrEP spillover effects across models of differing complexity, bridging the gap between interpretable theoretical insights and high-dimensional national-scale simulations. HIGHLIGHTS • We introduce a method to measure spillover e5ects in PrEP use. • A risk-structured HIV transmission model is introduced and analyzed. • Spillover is linked mathematically to the number needed to treat (NNT). • Incidence in low-risk groups is best reduced by increasing PrEP in hi-risk groups. • For large models, we use Sobol sensitivity analysis to estimate spillover.
Multiscale analysis of a mathematical model of human papillomavirus with combined therapy and progression to cervical cancer
Dongmo, Donzap; Tsanou, Berge; Woukeng, Jean Louis (Elsevier, 2027-02)
Cervical intraepithelial neoplasia (CIN) is the development of abnormal cells on the surface of the cervix, caused by an infection with human papillomavirus. Although in most cases it is resolved by the immune system, a small percentage of people may develop to more severe CIN, which, if left untreated, can progress to cervical cancer. Cervical cancer is the fourth most common cancer among women worldwide. This work intends to develop a nonlinear mathematical model that describes the dynamics at the microscopic level of the epithelial cells (healthy, dysplastic, cancer and immune), and the viral particles, while accounting for a dual immunotherapy. Using the two-scale convergence method, we derive the effective macroscopic model, thus highlighting the influence of the microscopic properties of the tumor on the overall dynamics of CIN. The resulting model is new in the literature and is simpler to handle as far as the computational aspects are concerned.
On some minimal linear codes invariant under the Chevalley group F4 (2)
Rodrigues, Bernardo Gabriel; Saeidi, Amin (Springer, 2026)
Please read abstract in the article.
The Riesz-Kantorovich formulas for L-vector lattices
Chamberlain, Tomas; Wortel, Marten (Springer, 2026-04-03)
Please read abstract in the article.
Classical theorems from analysis for locally band preserving functions on Dedekind complete Φ-algebras
Kikianty, Eder; Naude, Luan; Roelands, Mark; Schwanke, Christopher Michael (Springer, 2026-04-14)
In this paper we explore the concept of locally band preserving functions, introduced by Ercan and Wickstead, on Dedekind complete Φ-algebras. Specifically, we show that all super order differentiable functions are locally band preserving. Furthermore, some foundational results from classical analysis are proved in this setting, such as the Intermediate Value Theorem, the Extreme Value Theorem, and the Mean Value Theorem. Moreover, we show that these generalisations can fail for functions that are not locally band preserving. With the goal in mind to further develop the theory of complex differentiation in Dedekind complete complex Φ-algebras, a complex version of the Mean Value Theorem is also provided.
Sterile insect technique for suppression of endemic Aedes albopictus in urban Reunion Island : a pilot trial of technical feasibility and entomological impact
Brengues, Cécile; Marquereau, Lucie; Le Goff, Gilbert; Dumont, Yves; Remoue, Franck; Raude, Jocelyn; Tostain, Graziella; Taconet, Paul; Roiz, David; Fontenille, Didier; Gouagna, Louis Clément (Elsevier, 2026-05)
BACKGROUND : The sterile insect technique (SIT) has progressed from theory to a validated vector control strategy for Aedes-borne diseases, including dengue and chikungunya. We assessed the feasibility and effectiveness of SIT for suppressing Aedes albopictus in small-scale urban environments on Reunion Island. METHODS : From July 2021 to September 2022, over 10 million Ae. albopictus males sterilized as pupae with 40 Gy X-rays were released at a 20-hectare pilot site. Weekly releases ranged from 60,000 to 275,000 males (3000-13,750 per hectare). Outcomes were monitored using ovitrap surveillance and periodic adult sampling during a 6-month baseline and a 13-month intervention. RESULTS : Sterile-to-wild male ratios ranged from 6:1 to 18:1. Compared with the control site, the treated site showed a 33.5% reduction in egg abundance and a 61.5% reduction in egg viability (range 40.0-81.9). Reductions in egg fertility were temporally aligned with a 60.4% decline in female abundance relative to baseline. CONCLUSION : This study demonstrates that SIT was technically and logistically feasible and achieved measurable suppression of Ae. albopictus. Despite scale and operational constraints, the intervention achieved significant reductions in egg fertility and female abundance, providing strong proof of concept for SIT-based mosquito control on Reunion Island. HIGHLIGHTS • This pilot study confirmed the SIT technical and logistical feasibility in real world conditions. • Field data confirmed sterile male releases effectively reduced of urban mosquito populations. • A marked and sustained decline was evident in egg production, fertility and adult female abundance. • Cross-stakeholder collaboration, community support and source reduction improved SIT success. • Larger-scale trials required in order to assess the long-term epidemiological impact.
Could malaria mosquitoes be controlled by periodic releases of transgenic mosquitocidal Metarhizium pingshaense fungus? A mathematical modeling approach
Pant, Binod; Bilgo, Etienne; Mitra, Arnaja; Safdar, Salman; Diabate, Abdoulaye; St. Leger, Raymond; Gumel, Abba B. (Elsevier, 2026-06)
Insect pathogenic fungi present a promising alternative to chemical insecticides for controlling insecticide-resistant mosquitoes. One proposed method involves releasing male Anopheles mosquitoes contaminated with transgenic Metarhizium pingshaense (Met-Hybrid) to lethally infect females during mating. This study presents a novel deterministic mathematical model to evaluate the impact of this control approach in malaria-endemic areas. The model incorporates two fungus transmission pathways: mating-based transmission and indirect transmission through contact with fungus- colonized mosquito cadavers. We found that the fungus cannot establish in the mosquito population without transmission from infected cadavers (in this scenario, the reproduction number of the model is zero). However, if transmission from colonized cadavers is possible, the fungus can persist in the local mosquito population when the reproduction number exceeds one. Simulations of periodic releases of infected male mosquitoes, parameterized using Met-Hybrid-exposed mosquito data from Burkina Faso, show that an 86% reduction in the local female mosquito population can be achieved by releasing 10 Met-Hybrid- exposed male mosquitoes per wild mosquito every three days over six months. This matches the efficiency of some genetic mosquito control approaches. However, a 90% reduction in the wild mosquito population requires, for instance, daily releases of the fungal-treated mosquitoes in a 6:1 ratio for about 5 months, which proves less efficient than some genetic approaches. This study concludes that fungal programs with periodic releases of infected males may complement other methods or serve as an alternative to genetic-based mosquito control methods, where regulatory, ethical, or public acceptance concerns restrict genetically-modified mosquito releases.
Thermal analysis of MHD couple-stress ZnO-based blood nanofluid flow with variable thermal properties and nonlinear buoyancy effects in a vertical Forchheimer microchannel
Adeyemo, A.S.; Sibanda, P.; Goqo, S.P.; Ahmedai, Salma A.A.; Rufai, Uthman O. (Elsevier, 2026-06)
Please read abstract in the article. HIGHLIGHTS • This study models unsteady MHD ZnO-blood flow in a vertical microchannel. • The model includes variable conductivity, temperature-dependent viscosity, and nonlinear buoyancy. • We solve the governing equations using the OMDBSLLM method. • We analyze heat transfer, entropy generation, and Bejan number. • Results show potential for hyperthermia and thermal management
Kinetic simulated annealing optimization with entropy-based cooling rate
Herty, Michael; Zanella, Mattia (American Institute of Mathematical Sciences, 2026-06)
We present a modified simulated annealing method with a dynamical choice of the cooling temperature. The latter is determined via a closed-loop control and is proven to yield exponential decay of the entropy of the particle system. The analysis is carried out through kinetic equations for interacting particle systems describing the simulated annealing method in an extended phase space. Decay estimates are derived under the quasi-invariant scaling of the resulting system of Boltzmann-type equations to assess the consistency with their mean-field limit. Numerical results are provided to illustrate and support the theoretical findings.
Modelling insurance claims during financial crises : a systemic approach
Agana, Francis; Mare, Eben (MDPI, 2025-06-05)
In this paper, we introduce a generalised mutually exciting Hawkes process with random and independent jump intensities. This model provides a robust theoretical framework for modelling complex point processes and appropriately characterises the financial system, especially during periods of crisis. Based on this extended Hawkes process, we propose an insurance claim process and demonstrate that claim processes modelled as an aggregated process enable early detection of crises and inform optimal investment strategies in a financial system.
Numerical analysis of unsteady CNT-suspended Casson nanofluid flow in engine oil through a Darcy-Forchheimer porous vertical microchannel with temperature-dependent viscosity
Adeyemo, A.S.; Sibanda, Precious; Goqo, S.P.; Ahmedai, Salma A.A. (Springer, 2026-02-11)
This study investigates the impact of temperature-dependent viscosity on the unsteady magnetohydrodynamic flow of incompressible, electrically conducting Casson nanofluids containing single and multi-walled carbon nanotubes (SWCNTs and MWCNTs) dispersed in engine oil through a vertical Forchheimer porous channel. The model also accounts for the effects of the Péclet number, radiation, heat generation/absorption, and buoyancy. The governing coupled partial differential equations (PDEs) for momentum and thermal transport are numerically solved using the overlapping multidomain bivariate local linearization method. The influence of key parameters, including the Casson fluid index, variable viscosity, magnetic field, Forchheimer resistance, radiation, heat generation/absorption, Grashof number and Brinkman number are analyzed numerically. Velocity and temperature fields are enhanced by higher Casson parameter, viscosity variation, Grashof and Brinkman numbers, while they are reduced by magnetic, Forchheimer, radiation, and heat absorption effects. Overall, MWCNT nanofluids consistently demonstrate higher velocity, temperature, and Nusselt number, as well as greater entropy generation and lower Bejan number than SWCNT nanofluids.
Human-wildlife interactions in a tropical forest context : modeling, analysis, and simulations
Dumont, Yves; Hetier, Marc; Yatat-Djeumen, Valaire (Wiley, 2026)
Anthropisation and excessive hunting in tropical forests threaten biodiversity, ecosystem maintenance, and human food security. In this article, we focus on the issue of coexistence between humans and wildlife in an anthropised environment. Assuming that humans move daily between their residential area and the surrounding forest to hunt, we study a resource-consumer model with consumer migration. A comprehensive analysis of the system is carried out using classical theory and monotone systems theory. We show that the possibilities for long-term coexistence between human populations and wildlife populations are determined by hunting rate thresholds. Depending on the level of anthropisation and the hunting rate, the system may converge towards a limit cycle or a co-existence equilibrium. However, the conditions for coexistence become more difficult as anthropisation increases. Numerical simulations are provided to illustrate the theoretical results.
Constructing mathematical models from small data sets : cell-viability model of melanoma under inhibition by MAZ-51
Anguelov, Roumen; Basson, Charlise; Bipath, Priyesh; Hlophe, Yvette Nkondo; Nadasen, Carolyn Courtney; Phiri, Avulundiah Edwin; Serem, June Cheptoo (EDP Sciences, 2026-01)
The synthetic indolinone derivative MAZ-51 is a selective inhibitor of vascular endothelial growth factor receptor 3 (VEGFR-3), a tyrosine kinase receptor essential for lymphangiogenesis and tumor progression. By competing with adenosine triphosphate (ATP) for VEGFR-3 binding, MAZ-51 blocks VEGF-C activity, thereby suppressing melanoma cell proliferation and promoting apoptosis. In this study, we employ mathematical modelling to quantify the inhibitory effects of MAZ-51 on the growth of B16-F10 melanoma cells. Cell viability is modeled as a function of both treatment duration and inhibitor concentration, providing a dynamic framework for assessing therapeutic efficacy. Our approach addresses a central challenge in mathematical biology: developing models that remain interpretable and predictive despite limited and variable data. By integrating biological insight with experimental data, we derive a parsimonious model that avoids overparameterization and yields biologically meaningful parameters. The model allows straightforward computation of pharmacological measures such as the half-maximal inhibitory concentration (IC50) and provides deeper insight into the growth rate reduction of melanoma cells under VEGFR-3 inhibition. This work highlights the utility of mathematical modelling in elucidating drug action mechanisms and in quantitatively evaluating targeted cancer therapies.
Modeling the impact of budget limitation on the screening and treatment pathway of HPV-induced precancerous cervical lesions
Fodjo, Marius Tadjuidje; Youmbi, Aurelien Kambeu; Mayeh, Maison; Whegang, Solange; Kenfack, Bruno; Tsanou, Berge (AIMS Press, 2026-04)
Please read abstract in the article.
On the existence and uniqueness of numerical solutions for heterogeneous Duhem operators
Pokam Kakeu, Achille Landri; Banda, Mapundi Kondwani (Springer, 2026-04-10)
In this work, we propose a multiscale finite element method for solving heterogeneous nonlinear parabolic problems involving Duhem operators that model hysteresis in spatially varying media. A formulation of the method is introduced to facilitate the mathematical analysis, linking microscopic heterogeneities to macroscopic behavior. We establish the existence, uniqueness and boundedness of the numerical solution for both periodic and Dirichlet coupling scenarios, laying a strong foundation for the practical implementation of the multiscale method in computational settings.
A numerical model of coupled phloem-xylem flows for dynamic long-distance transport in trees
Sellier, D.; Mammeri, Y.; Peynaud, E.; Gomez-Gallego, M.; Leuzinger, S.; Dumont, Yves; Dickson, A.; Williams, N. (International Society for Horticultural Science, 2025-02-27)
In trees, the vascular system is dual in structure and function. Sap flows upwards in the xylem to hydrate tissues and refill reserves from transpiration loss, in the leaves, some of the water recirculates into the phloem and sap, loaded with photoassimilates, flows downwards to supply tissues with carbohydrates. Flow and counter-flow occur in physically separated but hydraulically connected pathways. Water exchanges take place all along them. Understanding the entire system and its subprocesses is essential to precisely quantify the carbon-water fluxes at the soil-atmosphere interface. That understanding is also key to predict the functional limits of vascular transport and if dysfunction occurs, how it will impact the vitality of plant communities in response to drought events and foliar pathogen outbreaks. Here we present an integrated, spatially explicit model of phloem-xylem transport. The model implements Münch’s osmo-regulated pressure flow hypothesis for phloem transport and cohesion-tension for xylem transport. The evolution of phloem pressure, carbohydrate concentration and xylem pressure are governed by three coupled nonlinear partial differential equations. Sap flow velocity, volume flow and the amount of shrinkage and swelling are calculated as derived variables. The model uses a special-purpose numerical scheme and can simulate response to dynamic forcing such as the diurnal patterns of phloem loading and transpiration. Unlike in other models, transport equations are solved for a surface and account for tangential movement of water and carbohydrates. Phloem and xylem are treated as elasto-porous media with distributed hydraulic and mechanical properties. We also present a semi-automated image processing method to calculate the theoretical hydraulic conductivity of phloem and xylem tissues based on their anatomy. Key hydraulic characteristics are given for the phloem of juvenile Pinus radiata D. Don.
Universal set of observables for forecasting physical systems through causal embedding
Manjunath, Gandhi; De Clercq, Adriaan; Steynberg, Matthys J. (Institute of Electrical and Electronics Engineers, 2026-05)
We show how a pair of points can uniquely represent a left-infinite sequence obtained from observations of an underlying dynamical system through a phenomenon called causal embedding. A driven dynamical system creates such pairs, and a function can be learned on them that can reconstruct the underlying dynamics as in Takens delay embedding. The approach assures embedding stability unlike Takens delay embedding, and learnability, which can be absent, while stability can be present in the current reservoir computing framework. This accurately models underlying systems where recent methods like the next-generation reservoir computing fail. We demonstrate results and compare with the other methods, including SINDY-PI.

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