Asian Research Journal of Mathematics

Effect of Behavioral Awareness Delay on the Dynamics of a Discrete-Time SIR Model for Mpox in Kenya: Stability and Neimark–Sacker Bifurcation Analysis

2026-09-24T03:55:52+00:00

Aims/ Objectives: To investigate how delayed behavioral awareness affects the dynamics of a discrete-time SIR model for Mpox transmission, with an emphasis on local stability and the occurrence of a Neimark–Sacker bifurcation.

Study Design: Theoretical mathematical modeling study with analytical stability analysis and numerical simulation. Place and Duration of Study: Multimedia University of Kenya, Faculty of Science and Technology; research conducted between August 2025 and August 2026.

Methodology: A normalized discrete-time SIR model incorporating a population-level behavioral awareness index Bn representing a combination of being informed about Mpox infection risk and adopting protective behavior. A discrete delay t was introduced in the behavioral-awareness response to the infection. The disease-free and endemic equilibria were derived and their local stability was analyzed using linearization and the Jury criterion. For t > 0, the system was linearized about the endemic equilibrium and the spectral radius p examined numerically in MATLAB as t varied. Time-series simulations and phase portraits were used to characterize the resulting dynamics. Time-series simulations and phase portraits were generated to illustrate the dynamics.

Results: For the selected baseline parameter configuration (R0 = 2.07), the endemic equilibrium was locally asymptotically stable for shorter delays. As the delay t increased, a complex-conjugate pair of characteristic roots crossed the unit circle at a critical delay of approximately 9–10 weeks. Numerical simulations showed sustained oscillations, consistent with a Neimark–Sacker bifurcation.

Conclusion: Delayed behavioral awareness can destabilize the endemic equilibrium and induce oscillatory Mpox dynamics through a Neimark–Sacker bifurcation. The findings support the importance of timely behavioral response and sustained risk communication. The estimated 9–10 week threshold is a model-dependent result under the selected parameter configuration and should not be interpreted as an empirical national estimate for Kenya.

A Fuzzy-Hungarian Framework for Labour Allocation under Uncertain Costs in Cocoa Processing

2026-09-15T12:36:39+00:00

Efficient allocation of labour is essential for minimising operational costs and improving productivity in cocoa processing. However, conventional assignment models, such as the Hungarian Assignment Method, assume that assignment costs are known precisely; this assumption may not adequately reflect uncertainty associated with worker performance, task difficulty, fatigue, and operational conditions. This study applies fuzzy logic and the Hungarian Assignment Method to determine the most suitable allocation of workers to cocoa-processing activities at Stevefrana Farm. The study considers six processing stages: conditioning, breaking, scalping, middling, purifying, and packaging. Labour costs were initially represented as crisp values obtained from farm records and supervisors' estimates and were subsequently modelled using triangular fuzzy numbers with a symmetric uncertainty spread of 10%. The centroid method was used to defuzzify the fuzzy costs into crisp values, after which the Hungarian Assignment Method was applied to determine the optimal worker-task allocation. In addition, the robustness of the optimal assignment was evaluated using the Robustness Index (RI), Coefficient of Variation of Fuzziness (CVF), and Robustness Degree (RD), while sensitivity analysis was conducted at uncertainty levels of 5%, 10%, 15%, and 20%. The results indicate that the optimal assignment is Worker 1 to Conditioning, Worker 2 to Middling, Worker 3 to Packaging, Worker 4 to Scalping, Worker 5 to Purifying, and Worker 6 to Breaking. This allocation yields a most likely total labour cost of GH¢555 per day, with a fuzzy cost range of GH¢499.50 to GH¢610.50. The robustness analysis produced an RI of 0.20, indicating moderate robustness; a CVF of 10%, indicating uniform relative uncertainty; and an RD of 90%, indicating high reliability. The sensitivity analysis further showed that, although robustness decreases as uncertainty increases, the optimal worker-task assignment remains unchanged across the 5%-20% uncertainty levels. The study demonstrates that integrating fuzzy logic with the Hungarian Assignment Method provides a practical decision-support framework for incorporating uncertainty into labour allocation while maintaining cost efficiency. The proposed model can assist cocoa-processing managers in improving worker-task matching, budgeting for labour-cost variability, and identifying processing stages requiring greater management attention.

Graphoidal Covering Numbers of Strong and Enhanced Power Graphs of Cyclic and Dihedral Groups

2026-09-15T12:42:02+00:00

This study investigates graphoidal coverings of power graphs, enhanced power graphs, and strong power graphs associated with selected finite cyclic and dihedral groups. The analysis focuses on determining graphoidal covering numbers and on clarifying how the underlying group structure and the relevant adjacency relation affect these parameters in a systematic manner. For cyclic groups, the graphoidal covering number of the strong power graph is obtained for the cases n = 2, n = 3, n = 4, prime n ≥ 5, and composite n ≥ 6. The study also characterises the cyclic groups for which the power graph and the strong power graph are isomorphic, showing that, for n > 2, this occurs precisely when n = 2p, with p an odd prime. In addition, the graphoidal covering number of the enhanced power graph of Zn is determined for n ≥ 4. For dihedral groups, the structures of the power, enhanced power, and strong power graphs are examined, and explicit graphoidal coveringnumbers are derived for D2p, where p is an odd prime. The resulting comparison establishes a strict ordering among the three covering numbers in this case. Overall, the results show that variations in group structure and graph adjacency produce distinct graphoidal covering behaviour across the graph classes considered.

Convex-Fair Domination under Subdivision, Duplication, Total, and Switching Operations on Paths and Cycles

2026-09-16T10:14:17+00:00

This study examines the convex-fair domination parameter under four unary graph operations and structural transformations applied to path graphs P_n and cycle graphs C_n. The operations considered are subdivision, vertex duplication, total-graph construction, and vertex switching. Convex-fair domination requires a dominating set to be geodesically convex while also ensuring that every vertex outside the set has the same number of neighbours within it. Using the baseline convexfair domination values stated for paths and cycles, the manuscript derives operation-specific expressions for the resulting transformed graphs. For paths, the analysis treats the subdivision graph S(P_n), duplication graph D(P_n), total graph T (P_n), and the graph obtained by switching a pendant vertex. Corresponding results are developed for cycles through S(C_n), D(C_n), T (C_n), and single-vertex switching. The proofs use structural isomorphisms, explicit candidate dominating sets, geodesicclosure arguments, and comparisons of neighbourhood intersections for vertices outside the selected sets. Attention is also given to how transformed graph order and the placement of boundary and internal vertices affect the proposed minimum sets. The analysis therefore describes how subdivision, duplication, total-graph construction, and switching alter the interaction between domination, convexity, and fairness in linear and cyclic graph structures. These results provide a focused basis for further study of convex-fair domination under other graph operations and in broader graph classes.

Local Stability Analysis of an Infection-Age Mathematical Model for COVID-19 Disease Dynamics

2026-09-21T12:46:46+00:00

The infectiousness of individuals with an acute respiratory infection can vary with time since entry into the infectious stage, motivating epidemic models that retain infection-age structure rather than treating all infectious individuals as epidemiologically identical. This study formulates and analyses an infection-age-structured model for COVID-19 disease dynamics with susceptible, vaccinated, exposed, infection-age-structured infectious, and recovered populations. New infectious individuals enter the structured infectious class only after progression from the exposed class, so that the boundary condition is i(0,t) = gE(t). Transmission, recovery, and disease-induced mortality may depend on infection age. An explicit basic reproduction number is obtained as;

where Λ = (1-b)p, α = θ+μ, y = μ+g, and π(a) is the probability of remaining infectious to infection age a . The disease-free equilibrium is locally asymptotically stable when R₀<1 and unstable when R₀>1; a positive endemic equilibrium exists when R₀>1. For the illustrative parameter set used in the numerical analysis, the baseline value is R₀=0.4694. Multiplying the transmission kernel by three gives R₀=1.4081 and produces persistent infection in the corresponding numerical trajectory. The normalised functional sensitivity density, \(β(a)π(a)/∫_0^Tβ (s)π(s) ds,\) attains its maximum at approximately 2.49 days for the specified kernels, indicating that early infection ages make the largest model-specific contribution to . This peak is a property of the assumed mathematical functions and should not be interpreted as a direct empirical estimate of the biological peak of SARS-CoV-2 infectiousness. The results illustrate how infection-age structure can identify temporal contributions to epidemic transmission while retaining a transparent threshold criterion for local disease invasion.

A Linear Hybrid Multi-Step Approach for Efficient Numerical Integration of Third-Order Ordinary Differential Equations (IVPs)

2026-09-21T12:58:50+00:00

This study develops a fifth-order fully hybrid block method for the direct numerical solution of third-order initial value problems. A continuous approximation is constructed using interpolation and collocation, and three intra-step hybrid points are incorporated into the block formulation. The resulting discrete schemes approximate the solution together with its first and second derivatives without reducing the governing third-order equation to an equivalent system of first-order equations. The principal numerical properties of the method are examined through local truncation-error analysis, consistency, zerostability, convergence, and absolute-stability considerations. The local truncation-error analysis establishes a uniform order of five for the developed block method. The corresponding difference formulation satisfies the root condition required for zero-stability; together with consistency, this establishes convergence. The stability behaviour is further investigated through a standard third-order test equation. Four numerical initial value problems are then used to assess computational performance at a fixed step size. Across the reported test problems, the proposed method produces absolute errors smaller than those of the comparator methods presented in the manuscript, including comparisons with methods of equal or higher formal order. These results indicate that the proposed fully hybrid formulation provides accurate numerical approximations for the class of third-order initial value problems considered in this study.

Mathematical Modelling and Optimal Control of Malaria Transmission in Children under Five Years: A Scenario-based Framework for Bungoma County, Kenya

2026-09-22T13:25:05+00:00

Malaria remains an important cause of morbidity in young children in western Kenya, where intervention effectiveness depends not only on nominal coverage but also on biological efficacy, adherence, vector behaviour, insecticide susceptibility, and local transmission intensity. This study develops a deterministic human–mosquito model for children under five years of age and formulates a five-control optimal-control problem representing effective vaccine protection, long-lasting insecticidal-net protection, treatment effort, larval-source management, and adult-vector removal. The revised framework explicitly includes maturation out of the under-five population and assigns vector-control actions to biologically appropriate processes. The model is analysed for positivity, boundedness, the effective reproduction number, local and global stability of the disease-free equilibrium, and normalised control sensitivity. A weighted Lyapunov function establishes global asymptotic stability in the feasible region when the effective reproduction number is below unity. A 100-day forward–backward sweep simulation is then used as a structural scenario analysis rather than as an empirical calibration to Bungoma surveillance data. Under the no-control numerical scenario, the basic reproduction number is 1.551. A reference control profile reduces the effective reproduction number to 0.292. In the optimal-control simulation, cumulative modelled incident infections decline by 73.2% relative to the no-control trajectory while using substantially less integrated control effort than sustained high-intensity fixed-control scenarios. The results illustrate how intervention mechanisms, control effort, and terminal-time assumptions shape mathematical conclusions. They should not be interpreted as estimates of current Bungoma County incidence, programme coverage, or economic cost-effectiveness. The framework provides a transparent basis for future calibration with validated local surveillance, entomological, intervention-coverage, and cost data.

Gender Differences in Mathematics Achievement, Attitudes, and Learning Experiences among Junior High School Students in Ghana: Evidence from the Ejisu Municipality

2026-09-26T06:24:01+00:00

Gender disparities in mathematics participation and achievement remain an important concern because of their implications for educational equity and subsequent participation in science, technology, engineering, and mathematics (STEM). This study examined gender differences in mathematics achievement, attitudes, and learning experiences among Junior High School students in the Ejisu Municipality of Ghana. A quantitative cross-sectional survey design was employed. The study involved 241 students (108 males and 133 females) drawn from four model Junior High Schools. Data were obtained from students’ questionnaire responses and mathematics examination records. Descriptive statistics were used to summarise achievement, attitudes, learning support, and perceived challenges, while chi-square tests of independence were used to examine gender differences in categorical achievement and interest outcomes.

The results indicated a statistically significant association between gender and mathematics pass status, χ²(1, N = 241) = 16.62, p < .001, ϕ = .263. The pass rate was 52.8% among male students compared with 27.1% among female students. Gender was also significantly associated with reported positive interest in mathematics, χ²(1, N = 241) = 18.86, p < .001, ϕ = .280, with 72.2% of male students and 44.4% of female students reporting positive interest. Teachers were the most frequently reported source of mathematics learning support (100%), followed by parents (62%), peers (58%), and home tutors (41%). Difficulty understanding mathematical concepts (68%), lack of confidence (61%), and mathematics anxiety (57%) were the most frequently reported learning challenges.

The findings demonstrate gender-associated differences in mathematics achievement and interest within the participating schools. Because the study was cross-sectional and restricted to four schools in one municipality, the findings should not be interpreted as evidence of causal effects or generalised uncritically to all Ghanaian students. The results nevertheless highlight the importance of further investigating the educational and psychosocial conditions associated with gender differences in mathematics learning.

Adaptive Fusion of Biometric Scores by Fuzzy Weighting Based on Fuzzy C-Means

2026-09-26T06:29:42+00:00

Multimodal biometric systems can improve recognition by combining information from multiple modalities, but the reliability of individual scores may vary across comparisons. This study evaluates Adaptive Fuzzy Weighting based on Fuzzy C-Means (AFW-FCM), a score-level fusion method in which the contribution of each modality is adjusted for each comparison according to confidence derived from the distribution of its scores. For each modality, a two-cluster Fuzzy C-Means model is learned from the training scores. The degree of membership of a score in the learned regions is used to define a confidence value, which is then normalised across the available modalities to obtain adaptive fusion weights. The method is evaluated primarily on BioSecure DS2 and additionally on NIST BSSR1 and a 50-subject subsample of CASIA-IrisV4. Under nominal conditions on BioSecure DS2, AFW-FCM achieved 97.4% accuracy, a 2.5% equal error rate, and an area under the curve of 0.995. On NIST BSSR1, it achieved 97.1% accuracy and a 2.8% equal error rate. On the CASIA-IrisV4 subsample, it achieved 96.1% accuracy, a 3.0% equal error rate, and an area under the curve of 0.985. Under Gaussian score perturbation at σ = 0.20, accuracy was 91.2%, compared with 82.8% for fixed weights. These results indicate that comparison-specific fuzzy weighting can maintain comparatively stable fusion performance under the controlled evaluation conditions used in this study.

Numerical Investigation of Bright Soliton-Like Pulse Evolution in Silica- and CS_2-Core Suspended Photonic Crystal Fibres

2026-09-28T10:56:26+00:00

Photonic crystal fibres (PCFs) permit substantial control of dispersion and nonlinearity through geometry and core-material selection, making suspended and liquid-core designs attractive for nonlinear pulse manipulation. This study examines bright soliton-like pulse evolution in silica-core and carbon disulfide (CS₂)-core PCFs using a generalized cubic–quintic nonlinear Schrödinger equation that retains second-, third-, and fourth-order dispersion. Fibre coefficients at 1.55 μm were taken from a previously published finite-element characterisation of suspended PCFs. Pulse propagation was solved directly with a symmetric split-step Fourier method rather than assuming a closed-form travelling-wave solution. A hyperbolic-secant input with T₀ =0.5 ps was used, with the input peak power scaled to the conventional fundamental-soliton condition of the unsuspended member of each material family. Over four baseline dispersion lengths, the unsuspended silica and CS₂ cases remained nearly invariant, whereas core suspension produced measurable temporal compression. For silica-core PCFs, the minimum intensity full width at half maximum (FWHM) decreased from 0.881 ps at the input to 0.748 ps for suspension factor (SF) 1.222 and 0.394 ps for SF 1.444, corresponding to compression factors of 1.18 and 2.24. For CS₂-core PCFs, the corresponding minimum FWHM values were 0.777 and 0.557 ps, with compression factors of 1.13 and 1.58. Grid-refinement tests changed the strongest-compression FWHM values by less than 0.01%, and relative pulse-energy drift remained below 5*10^-10. Because the dispersion and nonlinear coefficients vary simultaneously with suspension, these results should be interpreted as responses of the complete parameter sets rather than as isolated effects of individual coefficients. The calculations support suspended PCFs as tunable platforms for short-pulse reshaping while defining the numerical and physical conditions under which the comparison is reproducible.

Approximate Controllability of Road Traffic Using an Advection-diffusion Model: The Case of the RN1 in Mbanza-Ngungu

2026-10-06T13:00:52+00:00

This study develops a mathematical model of a saturated section of the RN1 in Mbanza-Ngungu, applies the Hilbert Uniqueness Method (HUM) to regulate congestion, and validates the approach numerically using finite elements in MATLAB.

Based on 15 observation sessions, traffic is modelled with the macroscopic LWR approach through a linearized advection-diffusion equation with a source term. The point source of the car park, initially modelled by a Dirac mass, is regularized into a Gaussian , S_ε∈L² (Ω), thus making the model compatible with the functional framework of the HUM. The control, constructed via the adjoint operator on ω=[400,600]×[2,6]m, is applied to the equation discretized by P1 finite elements and an implicit Euler scheme (Δt = 0.1 s).

The final adjoint datum is obtained by inverting the regularized HUM operator with a conjugate gradient scheme (64 iterations, relative residual below 10⁻⁶). The simulations show that the localized control reduces the root-mean-square deviation from the target state from 21.3 to 2.5 veh·km⁻¹ in 60 seconds, i.e. an 88% reduction of the initial deviation, the residual deviation representing only 5.3% of the target density (2.5/47.0), and lowers the density peak from 94.2 to 78.7 veh·km⁻¹ compared with the uncontrolled evolution. It removes 10.6 vehicles from the segment, i.e. a mean extraction rate of 636 veh·h⁻¹. The adjoint solution ψ reveals a strong spatial sensitivity around the car park, confirming the relevance of the chosen control zone. The result obtained is one of approximate controllability, inherent to the parabolic nature of the linearized model, and the constructed control is subject to no sign or amplitude constraint: the extraction rate it requires exceeds the observed through-traffic flow (291 veh·h⁻¹), which currently limits its operational implementation.

A Deterministic Matrix-Based Inventory-State Model for Multi-Product and Multi-Period Systems

2026-10-09T12:33:39+00:00

A deterministic matrix algebra approach for modelling inventory management in multi- product, multi-period systems has been developed, overcoming the limitations of existing inventory models which rely on conventional methods and computational software. The framework combines the initial inventory vector, replenishment matrix, demand matrix and a lower triangular accumulation matrix to calculate inventory levels with non-negativity and storage capacity constraints. The model is extended to evaluate procurement cost, sales revenue and profit in a single mathematical approach. The proposed model was tested on inventory data obtained from FAN-M Global Investment, Jalingo, Taraba State Nigeria with eighteen Fast-Moving Consumer Goods (FMCG) products observed for eighteen consecutive weeks. The results demonstrated that the matrix-based operations was able to track inventory movement across products and periods, calculate the cumulative inventory balances, identify inventory imbalances, maintain feasible stock levels, and provide a transparent assessment of financial performance using matrix operations alone. The study concludes that matrix algebra provides a simple, transparent and computationally efficient alternative for deterministic inventory management in organisations with limited computational resources and contributes a practical analytical approach for multi-product and multi-period inventory decision-making.