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 756

Primitive rank 3 groups, binary codes, and 3-designs
Rodrigues, Bernardo Gabriel; Solé, Patrick (Springer, 2025-09)
Please read abstract in the article.
Non-solvable groups with few vanishing elements
Iroanya, Ifeanyi P.; Madanha, Sesuai Yash; Rodrigues, Bernardo Gabriel (Taylor and Francis, 2025)
Please read abstract in the article.
On the improvement of the sterile insect technique by entomopathogenic fungi : impact of residual fertility and re-mating behaviour
Dumont, Yves (Springer, 2025-09-17)
This study investigates the use of the Sterile Insect Technique (SIT) combined with Entomopathogenic Fungi soil treatment (EPFS) to control two major pests: the Mediterranean fruit fly and the Oriental fruit fly. The SIT involves releasing sterile males to mate with wild females, but the challenge lies in female polyandry (re-mating) and residual fertility in sterile males. We develop a continuous release SIT model with single- and double-mated females, but with a novel approach to accounting the residual fertility parameter, we also consider scenarios where the competitiveness of sterile males may decline between the first and the second mating. A key finding is that insect elimination, at least locally, with SIT can only occur when the product of the residual fertility parameter, and the basic reproduction number of sterile mated females, is less than 1. We also prove the existence of a sterile male release threshold, above which global elimination is possible. When is greater than one, elimination is impossible regardless of the size of sterile male releases. We also extend our results to periodic releases. We illustrate our theoretical findings using numerical simulations, with parameters from the Mediterranean fruit fly (medfly), with and without ginger root oil (GRO) treatment, and the oriental fruit fly, with and without Methyl-Eugenol (ME) treatment. Both treatments are known to enhance sterile male competitiveness. We also show that combining SIT with EPFS can greatly improve SIT efficiency, and, in particular, reduce the constraint on residual fertility. We conclude that re-mating and residual fertility can have a significant impact on the effectiveness of SIT. However, this mainly depends on whether SIT is used in combination with EPFS or not, and also on the knowledge of the parameters of sterile-mated females which seem to have been superficially studied in many SIT programs so far.
An eco-epidemiological model for malaria with Microsporidia MB as bio-control agent
Mfangnia, Charlene N.T.; Tonnang, Henri E.Z.; Tsanou, Berge; Herren, Jeremy Keith (Springer, 2025-04)
Microsporidia MB is an endosymbiont which naturally infects Anopheles mosquitoes. Due to its ability to block Plasmodium transmission, it shows potential as a bio-based agent for the control of malaria. Its self-sustainability is promising, as it can spread through both vertical and horizontal transmissions. However, its low prevalence in mosquito populations remains a challenge. We develop an eco-epidemiological mathematical model describing the co-dynamics of Microsporidia MB (within mosquito population) and malaria (within human population). The model is used to assess the potential of Microsporidia MB-infected mosquitoes on the control of malaria infection. The results on the basic reproduction numbers, the stability of the equilibria, and the existence of bifurcations are obtained, providing conditions for the extinction and persistence of MB-infected mosquitoes. We highlight relevant threshold parameters for the elimination and persistence of MB-infected mosquitoes and malaria-infected individuals. Using real data from Kenya, we found that, given a horizontal transmission rate between 0 and 0.5, a minimum vertical rate of 0.55 is required to avoid extinction of MB-infected mosquitoes. The predicted prevalence of MB-infected mosquitoes using transmission rates reported from lab experiments align with the observed low prevalence of MB-infected mosquitoes in the field, thereby validating our model and results. Finally, predictions indicate that increasing MB mosquito infection could effectively control malaria, with target prevalence varying by region: 15% in Highland, 40% on the coast, and 70% in the Lake region. This study offers insights into the use of bio-based vector population replacement solutions to reduce malaria incidence in regions where Microsporidia MB is prevalent.
Sterile insect technique in a patch system : influence of migration rates on optimal single-patch releases strategies
Dumont, Yves; Duprez, Michel; Privat, Yannick (Springer, 2025-10)
The Sterile Insect Technique (SIT) is a biological control method used to reduce or eliminate pest populations or disease vectors. This technique involves releasing sterilized insects that, upon mating with the wild population, produce no offspring, leading to a decline or eventual eradication of the target species. We incorporate a spatial dimension by modeling the pest/vector population as being distributed across multiple patches, with both wild and released sterile insects migrating between these patches at predetermined rates. We mainly focus on a two-patch system. This study has two primary objectives: first, to derive sufficient conditions for achieving the elimination of the wild population through SIT, whether releases occur in one patch or in both patches. In particular, we provide an estimate of the minimal release rates to reach elimination thanks to the diffusion rates between patches. This is the first time that such a result is given in a general manner. Second, we study an optimal SIT control strategy, where we minimize the total amount of sterile insects to release, and show that, within one patch, it can successfully reduce the wild population in that patch to a desired level within a finite time frame, provided that the migration rates between patches are sufficiently low. Numerical simulations are employed to illustrate these results and further analyze the outcomes.
A multivariate stochastic approach to determine long-term success of SA living annuity portfolios
Van Niekerk, Andries Jacobus; Moutzouris, Vasili; Mare, Eben (Actuarial Society of South Africa, 2025)
Success rates of living annuities within the South African retirement landscape are examined through portfolio modelling that includes domestic equities, cash, and international exposure, via the S&P 500 index. We define success rates based on Cooley’s framework, emphasising financial sustainability throughout retirement. Our approach incorporates foreign exposure by converting S&P 500 gains to South African Rand, accounting for stochastic foreign exchange rate fluctuations. Additionally, US and South African inflation rates are integrated to assess success rates in real terms, ensuring the impact of inflation on retirees’ income is accurately captured. This study incorporates stochastic correlation and stochastic volatility modelling to capture dynamic asset relationships under varied market conditions. The S&P 500 and JSE Top 40 equities are modelled with stochastic volatility, calibrated through the Efficient Method of Moments (EMM), enhancing volatility estimation for equity assets. These techniques support the analysis of optimal portfolio compositions and withdrawal strategies to maximise annuity success rates, providing evidence-based insights for retirement planning in South Africa.
Countability conditions in locally solid convergence spaces
Bilokopytov, Eugene; Bohdanskyi, Viktor; Van der Walt, Jan Harm (Springer, 2025-09)
Please read abstract in the article.
High-order flux splitting schemes for the Euler equations of gas dynamics
Chu, Shaoshuai; Herty, Michael; Toro, Eleuterio F. (Elsevier, 2025-09)
We develop high-order flux splitting schemes for the one- and two-dimensional Euler equations of gas dynamics. The proposed schemes are high-order extensions of the existing first-order flux splitting schemes introduced in Toro and Vázquez-Cendón (2012) where the Euler equations of gas dynamics are split into two subsystems: the advection and pressure systems. In this paper, we formulate the TV splitting within the semi-discrete framework to extend it to higher orders of accuracy for the first time. The second-order extension is obtained by using piecewise linear interpolant to reconstruct the one-sided point values of the unknowns. The third- and fifth-order schemes are developed using the finite-difference alternative weighted essentially non-oscillatory (A-WENO) framework, which is particularly effective in handling multidimensional problems and provides a more straightforward approach to constructing higher-order WENO schemes. These extensions significantly improve the resolution of discontinuities and the accuracy of numerical solutions, as demonstrated by a series of numerical experiments of both the one- and two-dimensional Euler equations of gas dynamics. HIGHLIGHTS • Extended first-order TV splitting to higher orders of accuracy. • Compared the efficiency against CU, HLL, and HLLC schemes. • Demonstrated improved resolution in 1D and 2D Euler equations of gas dynamics.
Mathematical modeling of the impact of HPV vaccine uptake in reducing cervical cancer using a graph-theoretic approach via Caputo fractional-order derivatives
Oswald, Sylas; Mureithi, Eunice W.; Berge, Tsanou; Chapwanya, Michael; Kahesa, Crispin; Mashoto, Kijakazi Obed (Elsevier, 2025)
Please read abstract in the article.
Micro-macro decomposition of particle swarm optimization methods
Herty, Michael; Veneruso, Sara (American Institute of Mathematical Sciences, 2026-02)
Solving non-convex minimization problems using multi-particle metaheuristic derivative-free optimization methods is still an active area of research. Popular methods are Particle Swarm Optimization (PSO) methods, that iteratively update a population of particles according to dynamics inspired by social interactions between individuals. We present a modification to include constrained minimization problems using exact penalization. Additionally, we utilize the hierarchical structure of PSO to introduce a micro-macro decomposition of the algorithm. The probability density of particles is written as a convex combination of microscopic and macroscopic contributions, and both parts are propagated separately. The decomposition is dynamically updated based on heuristic considerations. Numerical examples compare the results obtained using the algorithm in the microscopic scale, in the macroscopic scale, and using the new micro-macro decomposition.
Modeling the impact of hospitalization-induced behavioral changes on the spread of COVID-19 in New York City
Oveson, Alice; Girvan, Michelle; Gumel, Abba B. (KeAi Communications, 2025-12)
The COVID-19 pandemic, caused by SARS-CoV-2, highlighted heterogeneities in human behavior and attitudes of individuals with respect to adherence or lack thereof to public health-mandated intervention and mitigation measures. This study is based on using mathematical modeling approaches, backed by data analytics and computation, to theoretically assess the impact of human behavioral changes on the trajectory, burden, and control of the COVID-19 pandemic during the first two waves in New York City. A novel behavior-epidemiology model, which considers n heterogeneous behavioral groups based on level of risk tolerance and distinguishes behavioral changes by social and disease-related motivations (such as peer-influence and fear of disease-related hospitalizations), is developed. In addition to rigorously analyzing the basic qualitative features of this model, a special case is considered where the total population is stratified into two groups: risk-averse (Group 1) and risk-tolerant (Group 2). The 2-group model was calibrated and validated using daily hospitalization data for New York City during the first wave, and the calibrated model was used to predict the data for the second wave. The 2-group model predicts the daily hospitalizations during the second wave almost perfectly, compared to the version without behavioral considerations, which fails to accurately predict the second wave. This suggests that epidemic models of the COVID-19 pandemic that do not explicitly account for heterogeneities in human behavior may fail to accurately predict the trajectory and burden of the pandemic in a population. Numerical simulations of the calibrated 2-group behavior model showed that while the dynamics of the COVID-19 pandemic during the first wave was largely influenced by the behavior of the risk-tolerant (Group 2) individuals, the dynamics during the second wave was influenced by the behavior of individuals in both groups. It was also shown that disease-motivated behavioral changes (i.e., behavior changes due to the level of COVID-19 hospitalizations in the community) had greater influence in significantly reducing COVID-19 morbidity and mortality than behavior changes due to the level of peer or social influence or pressure. Finally, it is shown that the initial proportion of members in the community that are risk-averse (i.e., the proportion of individuals in Group 1 at the beginning of the pandemic) and the early and effective implementation of non-pharmaceutical interventions have major impacts in reducing the size and burden of the pandemic (particularly the total COVID-19 mortality in New York City during the second wave).
Mating versus alternative blood sources as determinants to mosquito abundance and population resilience
Ngwa, Gideon Akumah; Ghakanyuy, Bime Markdonal; Teboh-Ewungkem, Miranda I.; Banasiak, Jacek (Elsevier, 2025-12)
A deterministic nonlinear ordinary differential equation model for mosquito dynamics in which the mosquitoes can quest for blood either within a human population or within non-human/vertebrate populations is derived and studied. The model captures both the mosquito’s aquatic and terrestrial forms and includes a mechanism to investigate the impact of mating on mosquito dynamics. The model uses a restricted form of homogeneous mixing based on the idea that the mosquito has a blood-feeding habit determined by its blood-feeding preferences and its gonotrophic cycle. This characterisation allows us to compartmentalise the total mosquito population into distinct compartments according to the spatial location of the mosquito (breeding site, resting places and questing places) as well as blood-fed status. Issues of overcrowding and intraspecific competition both within the aquatic and the terrestrial stages of the mosquito’s life forms are addressed and considered in the model. Results show that the inclusion of mating induces bistability, a phenomenon whereby locally stable trivial and non-trivial equilibria co-exist with an unstable non-zero equilibrium. The local nature of the stable equilibria is demonstrated by numerically showing that the long-term state of the system is sensitive to initial conditions. The bistability state is analogous to the phenomenon of the Allee effect that has been reported in population biology. The model’s results, including the derivation of the threshold parameter of the system, are comprehensively tested via numerical simulations. The output of our model has direct application to mosquito control strategies, for it clearly shows key points in the mosquito’s developmental pathway that can be targeted for control purposes. HIGHLIGHTS • A model for mosquito population dynamics incorporating hosts seeking and mating. • Bi-stability: Simultaneous locally stable non-zero and zero equilibria. • Allee effect: Extinction or persistence linked to size of initial densities. • Pathway to evaluate the use of the sterile insect technique for mosquito control.
Turing patterns across geometries : a proven DSC-ETDRK4 solver from plane to sphere
Owolabi, Kolade M.; Pindza, Edson; Mare, Eben (Elsevier, 2025-08)
This paper presents a unified and robust numerical framework that combines the Discrete Singular Convolution (DSC) method for spatial discretization with the Exponential Time Differencing Runge–Kutta (ETDRK4) scheme for temporal integration to solve reaction–diffusion systems. Specifically, we investigate the formation of Turing patterns – such as spots, stripes, and mixed structures – in classical models including the Gray–Scott, Brusselator, and Barrio–Varea–Aragón–Maini (BVAM) systems. The DSC method, employing the regularized Shannon’s delta kernel, delivers spectral-like accuracy in computing spatial derivatives on both regular and curved geometries. Coupled with the fourth-order ETDRK method, this approach enables efficient and stable time integration over long simulations. Importantly, we rigorously establish the necessary theoretical results – including convergence, stability, and consistency theorems, along with their proofs – for the combined DSC-ETDRK4 method when applied to both planar and curved surfaces. We demonstrate the capability of the proposed method to accurately reproduce and analyze complex spatiotemporal patterns on a variety of surfaces, including the plane, sphere, torus, and bumpy geometries. Numerical experiments confirm the method’s versatility, high accuracy, and computational efficiency, making it a powerful tool for the study of pattern formation in reaction–diffusion systems on diverse geometries.
Kinetic variable-sample methods for stochastic optimization problems
Bonandin, Sabrina; Herty, Michael (American Institute of Mathematical Sciences, 2025)
We discuss kinetic-based particle optimization methods and variable-sample strategies for problems where the cost function represents the expected value of a random mapping. Kinetic-based optimization methods rely on a consensus mechanism targeting the global minimizer, and they exploit tools of kinetic theory to establish a rigorous framework for proving convergence to that minimizer. Variable-sample strategies replace the expected value by an approximation at each iteration of the optimization algorithm. We combine these approaches and introduce a novel algorithm based on instantaneous collisions governed by a linear Boltzmann-type equation. After proving the convergence of the resulting kinetic method under appropriate parameter constraints, we establish a connection to a recently introduced consensus-based method for solving the random problem in a suitable scaling. Finally, we showcase its enhanced computational efficiency compared to the aforementioned algorithm and validate the consistency of the proposed modeling approaches through several numerical experiments.
Contribution of the 2021 COVID-19 vaccination regime to COVID-19 transmission and control in South Africa : a mathematical modeling perspective
Tegegn, Tesfalem Abate; Terefe, Yibeltal A. (Elsevier, 2025-10)
Please read abstract in the article.
A minimax approach to duality for linear distributional sensitivity testing
Van Zyl, Gusti (Taylor and Francis, 2025)
We consider the dual formulation of the problem of finding the maximum of 𝔼𝜈⁡[𝑓⁡(𝑋)], where ν is allowed to vary over all the probability measures on a Polish space 𝒳 for which 𝑑𝑐⁡(𝜇,𝜈)≤𝑟, with 𝑑𝑐 an optimal transport distance, f a real-valued function on 𝒳 satisfying some regularity, μ a ‘baseline’ measure and 𝑟≥ 0. Whereas some derivations of the dual rely on Fenchel duality, applied on a vector space of functions in duality with a vector space of measures, we impose compactness on 𝒳 to allow the use of the minimax theorem of Ky Fan, which does not require vector space structure.
A multiscale consensus-based algorithm for multilevel optimization
Herty, Michael; Huang, Yuyang; Kalise, Dante; Kouhkouh, Hicham (World Scientific Publishing, 2025-09)
In this paper, a novel multiscale consensus-based optimization (CBO) algorithm for solving bi- and tri-level optimization problems is introduced. Existing CBO techniques are generalized by the proposed method through the employment of multiple interacting populations of particles, each of which is used to optimize one level of the problem. These particle populations are evolved through multiscale-in-time dynamics, which are formulated as a singularly perturbed system of stochastic differential equations. Theoretical convergence analysis for the multiscale CBO model to an averaged effective dynamics as the time-scale separation parameter approaches zero is provided. The resulting algorithm is presented for both bi-level and tri-level optimization problems. The effectiveness of the approach in tackling complex multilevel optimization tasks is demonstrated through numerical experiments on various benchmark functions. Additionally, it is shown that the proposed method performs well on min–max optimization problems, comparing favorably with existing CBO algorithms for saddle point problems.
Exploring the epidemiological impact of Pneumonia-Listeriosis co-infection in the human population : a modeling and optimal control study
Chukwu, Chidozie Williams; Tchoumi, Stephane Yanick; Koutou, Ousmane; Herdicho, Faishal Farrel; Fatmawati (Springer, 2025-05)
Pneumonia and Listeriosis are significant public health concerns, both individually and as co-infections, particularly in vulnerable populations such as the elderly, immunocompromised individuals, and infants. Using a mathematical modeling approach, this study explores the epidemiological impact of Pneumonia–Listeriosis co-infection within human populations. By developing a comprehensive model incorporating the transmission dynamics of both diseases, we aim to understand the synergistic effects of co-infection on disease prevalence, morbidity, and mortality. Mathematical analysis was established, encompassing the transmission threshold calculation, calculated equilibrium points, and local stability. The model also assesses the influence of key parameters, such as transmission rates, recovery rates, and co-infection interactions, on the overall disease burden. Sensitivity analysis is performed to identify the most critical factors driving the spread of the co-infection. Furthermore, we include the optimal control interventions to minimize the spread of Pneumonia–Listeriosis co-infection and the costs associated with implementing control. Our findings provide valuable insights into the complexities of managing co-infections and highlight the importance of targeted interventions to reduce the public health impact of Pneumonia–Listeriosis co-infection. The results of this study inform public health strategies aimed at mitigating the dual burden of these infections, thereby improving patient outcomes and reducing healthcare costs.
Simpler characterizations of total orderization invariant maps
Schwanke, Christopher Michael (World Scientific Publishing, 2025)
Given a finite subset A of a distributive lattice, its total orderization to(A) is a natural transformation of A into a totally ordered set. Recently, the author showed that multivariate maps on distributive lattices which remain invariant under total orderizations generalize various maps on vector lattices, including bounded orthosymmetric multilinear maps and finite sums of bounded orthogonally additive polynomials. Therefore, a study of total orderization invariant maps on distributive lattices provides new perspectives for maps widely researched in vector lattice theory. However, the unwieldy notation of total orderizations can make calculations extremely long and difficult. In this paper we resolve this complication by providing considerably simpler characterizations of total orderization maps. Utilizing these easier representations, we then prove that a lattice multi-homomorphism on a distributive lattice is total orderization invariant if and only if it is symmetric, and we show that the diagonal of a symmetric lattice multi-homomorphism is a lattice homomorphism, extending known results for orthosymmetric vector lattice homomorphisms.
A vector Allee effect in mosquito dynamics
Banasiak, Jacek; Ghakanyuy, Bime Markdonal; Ngwa, Gideon Akumah (American Institute of Mathematical Sciences, 2025-11)
Please read abstract in the article.

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