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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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)
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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)
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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.
A new kind of polynomials for finite groups
Asboei, A.K.; Anabanti, Chimere S. (Springer, 2025-09)
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Primitive rank 3 groups, binary codes, and 3-designs
Rodrigues, Bernardo Gabriel; Solé, Patrick (Springer, 2025-09)
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Non-solvable groups with few vanishing elements
Iroanya, Ifeanyi P.; Madanha, Sesuai Yash; Rodrigues, Bernardo Gabriel (Taylor and Francis, 2025)
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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)
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