Department of Mathematics and Computer Science

Detection and classification of cervical cancer disease among women using machine learning technique Model in Western Kenya.

2026-03-26T13:36:46Z

Detection and classification of cervical cancer disease among women using machine learning technique Model in Western Kenya. Murere, JF; Wangila, S.; Koech, J. Cervical cancer is the leading cause of cancer related deaths among Kenyan women, claiming approximately the lives of 3,200 women annually. This is primarily due to the low screening uptake (16%) and late diagnosis. The aim of this study was to develop a machine leaning based model to enhance early detection of cervical cancer in Western Kenya, a region in Kenya with limited healthcare resources. Demographic, reproductive, and clinical characteristics data were collected from 968 women across health facilities in western Kenya (MTRH and Kakamega Referral hospital) utilizing a cross sectional study design. The dataset was divided into training set (70%) and testing set (30%). The training set was used to develop the five machine learning model: Logistic Regression, Random Forest, Decision Tree, Support Vector Machine (SVM), and Artificial Neural Network (ANN). The testing set was used to evaluate the models. The machine learning model were trained to classify the cervical cancer cases, addressing the class imbalances using class weighting method for SVM, decision tree, random forest and logit model and synthetic minority oversampling class technique (SMOTE) for ANN. The random forest model demonstrated the superior performance compared to the other four models as it achieved the highest accuracy (94.33%) and specificity (98.37%) making it to be highly effective at ruling out negative cases. It however had a sensitivity of 20% which indicated that it had challenges in detecting positive cases. The logistic regression model excelled in sensitivity (70%) making it suitable for initial screening. ANN model showed the lowest precision (10%). The findings from this study suggested that a two-step approach which combine both Logistic Regression for screening and Random Forest for confirmation of cervical cancer cases which will go a long way in improving early detection and reduce cervical cancer mortality in resource-constrained settings like Western Kenya.

PREDICTIVE MODELING OF CHILD MORTALITY IN MIGORI AND NYAMIRA COUNTIES USING INDIRECT METHODS

2026-03-24T08:13:49Z

PREDICTIVE MODELING OF CHILD MORTALITY IN MIGORI AND NYAMIRA COUNTIES USING INDIRECT METHODS OMARE, BRIAN Child mortality remains a critical public health challenge, particularly in developing countries like Kenya, where disparities in healthcare are stark across different regions. In counties such as Nyamira and Migori, persistent high rates of under-five child mortality demonstrate the need for more precise statistical predictions for and targeted interventions. Traditional methods for estimating child mortality, such as those derived from household surveys, are often hampered by issues like missing data and survivor bias, leading to inaccurate mortality estimates. This study sought to develop a comprehensive predictive model for under-five child mortality in Migori and Nyamira counties, Kenya, by incorporating temporal patterns and social determinants of health. Utilizing a retrospective cohort design, the study analyzed historical data from health records, census reports, and household surveys spanning 34 years (1989-2022). The analysis incorporated indirect estimation techniques to address data gaps and employed multiple linear regression, gradient boosting regressor, and spatio-temporal modeling to capture temporal and seasonal trends in child mortality. The multiple linear regression model was significant, explaining 89.9% of the change in neonatal mortality in Migori County and 80.6% of the variation in Nyamira County. Gradient boosting regressor performed optimally, accounting for 80.9% of the change in child mortality, indicating good predictive capability and suggesting that the chosen independent variables effectively capture the complexity of the response variable. Spatio-temporal modeling log-likelihood value of -111.87 indicated a relatively good fit, capturing the observed data well (pseudo-R-squared = 0.9415). Results indicated that infant mortality rates in both counties have fluctuated historically, with distinct seasonal trends influenced by factors such as disease prevalence and access to healthcare services. The temporal and seasonal analysis revealed that periods of increased respiratory complications and malaria prevalence corresponded with higher mortality rates. The study provides a methodological framework that can be adapted to other regions with comparable challenges. By addressing the limitations of traditional mortality estimation methods and leveraging advanced predictive modeling techniques, the study contributes to the ongoing efforts to improve child health outcomes in Kenya and beyond.

VECTOR AUTOREGRESSION MODELING OF MALARIA INCIDENCE AND MORTALITY RATES IN MIGORI COUNTY, KENYA

2026-03-13T07:05:59Z

VECTOR AUTOREGRESSION MODELING OF MALARIA INCIDENCE AND MORTALITY RATES IN MIGORI COUNTY, KENYA CHACHA, PAUL JACKSON Malaria prevalence in poorer countries has been a persistent public health concern, disproportionately affecting vulnerable populations such as children and pregnant women. Despite notable progress in scaling up malaria control interventions in Kenya, malaria incidence rates continue to vary widely across counties, with endemic regions like Migori County experiencing persistent challenges. This study aimed to identify key factors associated with malaria incidence and mortality in Migori County using secondary data from the Kenya National Health Management System. Multiple statistical models, including regression, Vector Autoregression (VAR), and Vector Autoregression with Exogenous Variables (VARX), were applied to examine the temporal dynamics of malaria. While malaria incidence rates declined over time, mortality rates remained relatively stable. Regression results indicated that insecticide-treated net usage and effective treatment significantly influenced both incidence and mortality rates. However, model residuals showed substantial variability and signs of poor fit, highlighting the need for improved model specifications. The VAR model revealed issues of residual autocorrelation, while the VARX model, which incorporated exogenous variables, showed improved but still imperfect performance. Bayesian VAR (BVAR) models provided consistent findings across methodologies but also underscored ongoing challenges in modeling temporal malaria data accurately. Therefore, this study concludes that while current models offer valuable insights, they remain limited in capturing the full complexity of malaria dynamics. It recommends methodological enhancements, such as using advanced techniques like Generalized Method of Moments (GMM) or machine learning, conducting rigorous residual diagnostics, and incorporating environmental, socioeconomic, and behavioral variables. Expanding the dataset across regions and timeframes could also improve the robustness and generalizability of future research aimed at informing more effective malaria control strategies.

Traffic Flow Modelling Around Roundabouts Using Navier–Stokes and Advection–Diffusion Equations

2026-02-20T06:55:08Z

Traffic Flow Modelling Around Roundabouts Using Navier–Stokes and Advection–Diffusion Equations Krifix, Momanyi Mogire; Maremwa, Shichikha; Kandie, Joseph; Ngetich, Lucy Jerop Urban roundabouts are safer than signalised junctions yet remain prone to congestion under unbalanced demand and operational incidents. Existing microscopic and macroscopic approaches rarely capture, within a single framework, the tightly coupled evolution of traffic velocity and density needed for robust design and control. We address this gap with a coupled Navier–Stokes and Advection–Diffusion (NS–AD) model on an annular domain, adopting a barotropic closure 𝒑 = 𝒂𝝆 and a conservative incident force 𝒌𝐨𝐛𝐬𝐫/∥ 𝐫 ∥. Convection is discretised with a QUICK/TVD flux (MUSCL with a van–Leer limiter), while diffusion, sources and viscosity are advanced by a semi-implicit Crank–Nicolson step, enabling high-resolution fronts without spurious oscillations over long horizons. Simulations reproduce two robust signatures: a persistent annular congestion ridge in density coincident with the circulating ring, and a co-located speed amplification that exhibits an upstream/downstream braking/acceleration asymmetry governed by −𝒂𝛁𝐥𝐧𝝆. Probe histories display a negative (|𝒗|, 𝝆) phase slope during the transient, and a quasi-1D azimuthal reduction explains the observed structures and yields a falsifiable ridge-thickness law 𝜹 ∼ 𝑫/𝒖. Difference maps between incident and baseline scenarios isolate the causal footprint of the incident as outward mass migration to the ring and momentum gain along preferred circumferential paths. We conclude that a composite potential 𝒂𝐥𝐧𝝆+ 𝚽 succinctly explains outward push, pressure support and viscous/diffusive regulation, while the numerical pairing QUICK + TVD with Crank–Nicolson provides a stable, accurate basis for design studies. For policy and practice, the results support rapid incident clearance near the central island, targeted entry metering on feeder approaches, and low-cost geometric/control provisions, such as short bypasses and advisory speeds, that reduce the effective barrier 𝒂𝐥𝐧𝝆 and add diffusion pathways. Future work should calibrate (𝒂, 𝑫, 𝝂, 𝑺(𝜽), 𝒌𝐨𝐛𝐬) against field data using ridge width, phase slope, relaxation time and entry/exit counts, extend to multi-lane and multi-class settings, assimilate real-time data for model-predictive control, and couple to emissions and safety surrogates to assess broader impacts.

Mathematical Modelling of Traffic Flow Dynamics Around Roundabouts Using Navier– Stokes and Advection–Diffusion Equations

2026-02-20T06:51:08Z

Mathematical Modelling of Traffic Flow Dynamics Around Roundabouts Using Navier– Stokes and Advection–Diffusion Equations Krifix, Momanyi Mogire; Maremwa, Shichikha; Kandie, Joseph; Ngetich, Lucy Jerop Traffic congestion is a persistent challenge in urban transport systems, particularly around roundabouts where nonlinear merging and circulating flows create instability and delays. Traditional microscopic, mesoscopic, and macroscopic models often neglect explicit treatment of priority rules, capacity drops, and queue spillback, limiting their ability to predict roundabout-induced congestion. To address this gap, this study develops a coupled Navier–Stokes–advection–diffusion framework for simulating traffic dynamics at roundabouts. The governing equations are discretized using the finite volume method with a QUICK scheme for spatial accuracy and advanced in time with a Crank–Nicolson integration for stability. Non-dimensionalization ensures general applicability across different traffic environments. Simulation results reproduce fundamental traffic relations, identify optimal densities for maximum throughput, and reveal oscillatory stop-and-go waves consistent with empirical observations. Scenario analysis shows that increased diffusion enhances stability but reduces flow capacity, capturing real-world trade-offs between efficiency and control. The study concludes that embedding yield laws and circulating feedback into continuum equations provides a rigorous foundation for analyzing roundabout performance. Policy recommendations include adopting geometry- and flow-calibrated entry controls, while future research should incorporate stochastic demand and adaptive control strategies to refine predictive accuracy. This contribution provides both theoretical innovation and practical insights for sustainable traffic management.

A Novel Poiseuille-Based Mathematical Model for Carotid Artery Blood Flow: Modelling Geometry Interruptions and Vascular Stress during Accidents

2026-02-20T06:44:19Z

A Novel Poiseuille-Based Mathematical Model for Carotid Artery Blood Flow: Modelling Geometry Interruptions and Vascular Stress during Accidents Ngetich, Lucy Jerop; Maremwa, Shichikha; Kandie, Joseph; Krifix, Momanyi Mogire Carotid artery injuries during accidents are a significant contributor to trauma-related morbidity and mortality, necessitating accurate models for predicting vascular stress and flow disruption. Existing approaches either oversimplify flow and underestimate wall shear stress, neglect trauma-induced geometric interruptions, or require computationally intensive methods unsuitable for emergency use. To address these limitations, this study develops a hybrid Poiseuille–Womersley model that integrates distributed and localized pressure loss terms, a geometric penalty factor for lumen constriction, and pulsatile corrections to capture transient flow dynamics. Analytical derivations supported by simulation reveal that accident-induced reductions in carotid lumen diameter cause disproportionate declines in volumetric flow rate, sharp decreases in wall shear stress, and alterations in velocity fields that cannot be captured by steady-state assumptions. The model thus extends classical hemodynamic formulations to accident scenarios, providing an efficient yet physiologically consistent framework. These results confirm geometry as a primary driver of vascular stress under trauma conditions. The study concludes that lightweight analytical models can complement diagnostic and emergency care tools, offering rapid assessment capability. Policy makers and clinicians are encouraged to incorporate such trauma-informed hemodynamic tools into stroke prevention and emergency response strategies, while future work should focus on clinical validation, patient-specific adaptation, and integration with real-time Doppler imaging.

A Novel Poiseuille Equation Framework for Pulsatile Flow Dynamics in Accident-Induced Carotid Artery Constrictions

2026-02-20T06:40:02Z

A Novel Poiseuille Equation Framework for Pulsatile Flow Dynamics in Accident-Induced Carotid Artery Constrictions Ngetich, Lucy Jerop; Maremwa, Shichikha; Kandie, Joseph; Krifix, Momanyi Mogire Stroke and carotid artery injury remain significant contributors to global morbidity, with accident-induced disruptions in blood flow presenting acute clinical risks. Existing modelling approaches are either overly simplistic, relying on steady Poiseuille theory, or computationally demanding, as in fluid–structure interaction simulations, which limits their use in real-time diagnostic settings. This paper proposes a novel Poiseuille-based mathematical model that incorporates accident-like geometry interruptions and pulsatility via a nine-point stencil, a geometrypenalty factor, and a Womersley-inspired correction term. Using physiologically validated parameters for viscosity, density, and pressure gradients, the model reproduces key hemodynamic markers including volumetric flow, velocity fields, and wall shear stress under both normal and obstructed conditions. The findings show that even modest reductions in lumen radius lead to sharp declines in flow and shear, while pulsatility modifies waveform oscillations without altering the magnitude of disruption. The study concludes that geometry remains the primary driver of hemodynamic collapse, while pulsatility governs temporal detail. By providing a computationally efficient and clinically interpretable surrogate, the model bridges the gap between oversimplified analytical solutions and resource-intensive CFD. It is recommended that such reduced-order frameworks be integrated into clinical risk screening and trauma diagnostics, with future work directed toward validation against patient-specific data and incorporation of non-Newtonian blood properties.

Novel Mathematical Modelling of Pulsatile Blood Flow in Carotid Arteries via Poiseuille Equation

2026-02-17T10:56:30Z

Novel Mathematical Modelling of Pulsatile Blood Flow in Carotid Arteries via Poiseuille Equation Ngetich, Lucy Jerop; Maremwa, Shichikha; Kandie, Joseph; Krifix, Momanyi Mogire Cardiovascular diseases remain the leading global cause of death, with carotid artery dysfunction contributing significantly to ischemic stroke and long-term disability. The problem addressed in this study is the limited availability of mathematical models that can capture pulsatile blood flow dynamics under accident-induced geometric interruptions, while remaining computationally efficient. To address this gap, the study developed a novel Poiseuille-based framework, incorporating finite volume methods, Gauss–Legendre quadrature, and mesh discretization to model pulsatile flow in the carotid artery. Simulation results demonstrated that flow rate 𝑸 decreases with increasing arterial radius under turbulent conditions, contrary to laminar Poiseuille predictions, due to enhanced vascular stress and backflow. Furthermore, the model confirmed that velocity positively correlates with flow rate, consistent with fluid mechanics principles. These findings emphasize the influence of arterial geometry and turbulence on flow dynamics, aligning with prior studies on stenosis and bifurcations. In conclusion, the research provides a tractable, physiologically relevant model that bridges simplified Poiseuille theory with complex hemodynamic realities. Policy recommendations include supporting the integration of mathematical modeling into stroke risk screening and accident-related diagnostics, while future studies should validate the model with patientspecific imaging and extend it to non-Newtonian blood properties

VECTOR AUTOREGRESSION MODELING OF MALARIA INCIDENCE AND MORTALITY RATES IN MIGORI COUNTY, KENYA: A TIME SERIES ANALYSIS INCORPORATING EXOGENOUS INFLUENCES

2025-12-09T06:12:52Z

VECTOR AUTOREGRESSION MODELING OF MALARIA INCIDENCE AND MORTALITY RATES IN MIGORI COUNTY, KENYA: A TIME SERIES ANALYSIS INCORPORATING EXOGENOUS INFLUENCES Chacha, Paul Jackson; Otieno, Argwings; Koech, Julius Malaria remains hyperendemic in Kenya’s Lake Victoria basin despite scalable interventions. It is a pressing public health challenge in Migori county that reported a 27% mortality rate in 2020 in children aged 6-59 months, far exceeding national levels. Reports indicate different contributing factors to malaria dynamics in Migori County, including marginal insecticide-treated net (ITN) use, ITN access, effective antimalaria treatment, and prevalence of malaria infection. The present study seeks to elucidate the temporal interaction between malaria incidence and mortality by employing a range of time series analyses, incorporating exogenous influences by applying classical vector autoregressive (VAR) model to capture lagged dependencies. Further, the study invoked a Bayesian VAR (BVAR) after incorporating exogenous variables for parameter estimating, utilizing Monte Carlo simulations and Gibbs sampling. For model adequacy and forecast accuracy, the analysis made use of Ljung-Box test, partial autocorrelation function, autocorrelation function (ACF), and normality tests among other diagnostic tests. The hierarchical Bayesian vector autoregressive model (BVARX) incorporates monthly incidence and mortality rates (2014-2024, 𝑛 = 120) as the endogenous variables. The exogenous variables comprised ITN access and use, treatment efficacy, and infection prevalence. Ward-level heterogeneity summed the spatial random effects. Hamilton Monte Carlo model estimation with convergence assessed using 𝑅෠ < 1.01 Counterfactual simulations quantified intervention impacts. ITN use reduced incidence (β = −1.43, 95% CrI: −2.21, −0.65) but access increased mortality (β = 1.81, CrI: 0.32, 3.30), suggesting behavioral misuse. VARX outperformed VAR (WAIC: 412 vs. 587), yet residual spatial autocorrelation (Moran’s I = 0.34, *p* = 0.01) indicated unobserved confounders. BVARX forecasts predicted 22% (CrI: 18–27%) higher incidence by 2025 under current interventions. The regression analysis identified that higher ITN use is significantly associated with reductions in both malaria mortality and incidence. While ITNs and treatments show efficacy, their benefits are eroded by suboptimal utilization and ecological feedback. The study recommended the use of ward-level VARX outputs for geospatial targeting of ITN campaigns as well as integrated resistance monitoring through adaptive Bayesian frameworks.

ON THE NORM OF JORDAN ELEMENTARY OPERATOR IN TENSOR PRODUCT OF C*-ALGEBRAS

2025-05-21T09:39:13Z

ON THE NORM OF JORDAN ELEMENTARY OPERATOR IN TENSOR PRODUCT OF C*-ALGEBRAS Muiruri, Peter Guchu; King'ang'i, Denis Njue; Musundi, Sammy Wabomba The norm property of different types of Elementary operators has attracted a lot of researchers due to its wide range applications in functional analysis. From available literature the norm of Jordan elementary operator has been determined in C*-algebras, JB*-algebras, standard operator algebra and prime JB*-triple but not much has been done in tensor product of C*- algebras. This paper, dealt with the norm of Jordan elementary operator in a tensor product of C*-algebras. More precisely, the paper investigated the bounds of the norm of Jordan elementary operator in a tensor product of C*-algebras and obtained that ∥ 𝑼𝑨⨂𝑩,𝑪⨂𝑫 ∥= 𝟐 ∥ 𝑨 ∥∥ 𝑩 ∥∥ 𝑪 ∥∥ 𝑫 ∥. The concept of finite rank operator and properties of tensor product of Hilbert spaces and operators and vectors in Hilbert spaces were used to achieve the paper’s objective