http://41.89.164.27:8080/xmlui/handle/123456789/210 2026-09-15T04:43:13Z 2026-09-15T04:43:13Z Ashibambo, Nancy Shichika, Julius Bii, Albert http://41.89.164.27:8080/xmlui/handle/123456789/2805 2026-09-08T13:21:56Z 2025-08-01T00:00:00Z

Mathematical Modelling of Malaria Transmission Dynamics in Kenya: The Role of Seasonality, Drug Resistance, and Human Movement Ashibambo, Nancy; Shichika, Julius; Bii, Albert Background: Although there has been a remarkable improvement in controlling malaria, the clinical problem is still of public health importance in Kenya and especially in areas where there is climatic variation, which affects the transmission pattern. Seasonal rainfall has been explored as a central factor in the breeding of mosquitoes and the ensuing outbreaks of malaria, but most models have not included these ecological forces together with drug resistance and human mobility. Objective: The purpose of the study is to formulate and examine a seasonally driven malaria transmission model to represent the interaction of the dynamics of mosquito infection, antimalarial drug resistance, and human mobility in the Kenyan setting. Methods: We developed a compartmental model with drug-susceptible and drug-resistant parasite strains, categorised by stages of human infections, and mosquitoes. The model proposes seasonalforcing in a sinusoidal representation, which is staggered with the Kenyan rainfall pattern, which drives the mosquito recruitment. Inter-regional human migration is thought to take the form of a toggling migration parameter. The deSolve package in R was then used to simulate the model within a 2-year horizon. Monthly averages were then used to determine the peaks of the infection rates, and these were equated to the long (March to May) and short (October to December) rainy seasons in Kenya. Results: It was found that the results of simulations identified clear infection spikes closely corresponding to two periods of rainfall in Kenya (bimodal). The post-rainy periods when mosquitoes infected with the malaria parasites reach their peak (Q), as well as when humans are infected, were consistent, making a difference to resistant infections, which do not drop as fast as susceptible infections. The circulation of human movements enhanced the continuation and propagation of resistant infections. This indicated the environmental drivers of seasonal forcing that explained the time and magnitude of outbreaks. Conclusion: Noting the inclusion of seasonality, drug resistance, and movement in the models of malaria transmission increases their reality and predictability to a great extent. The syncing of the most significant infection-containing seasons with rainy seasons necessitates climate-tactful surveillance and intervention time. In Kenya, where the mobility of the population is high based on trade, labour migration, and between urban and rural regions, the modelling of such mobility is very important in gaining an understanding of the management of the epidemic. The model can be of great benefit in optimising vector control, deploying drugs and allocating resources regionally to malaria-endemic countries such as Kenya.

2025-08-01T00:00:00Z Ruto, Faith Bii, Albert Shichikha, Maremwa http://41.89.164.27:8080/xmlui/handle/123456789/2803 2026-09-08T09:30:37Z 2026-08-01T00:00:00Z

Navier-stokes Based Modelling of Airflows in Forest Canopies and Its Influence on Local Climate Dynamics Ruto, Faith; Bii, Albert; Shichikha, Maremwa Background: Forest canopies strongly influence atmospheric airflow, turbulence generation, heat exchange, water transport, and carbon dioxide distribution, thereby regulating the local climate. However, accurately representing airflow dynamics within forests remains challenging because of vegetation drag and turbulent mixing. Aims: This study developed a mathematical model based on the Navier–Stokes equations to investigate airflow behaviour within forest canopies and assess its influence on local climate dynamics. Study Design: This was a computational fluid dynamics (CFD)-based modelling study employing the Reynolds-averaged Navier–Stokes (RANS) equations coupled with the standard k–ε turbulence model.Place and Duration of Study: Department of Mathematics and Computer Science, University of Eldoret, Kenya, between July 2025 and April 2026. Methodology: The incompressible Navier–Stokes equations were used to model airflow within and above forest canopies. Vegetation effects were represented using a canopy drag-force term based on leaf area density. Turbulence was simulated using the standard k–ε model, while additional transport equations described temperature, water vapour, and carbon dioxide dynamics. The governing equations were discretised using the Finite Volume Method (FVM) and solved numerically in MATLAB. Simulations were performed for dense, medium, and sparse canopy configurations over a 30 m computational domain. Results: Airflow velocity increased with height in all canopy configurations, with dense canopies showing the greatest attenuation. At canopy height, velocities were approximately 1.45 m/s, 1.95 m/s, and 2.65 m/s for dense, medium, and sparse canopies, respectively. Turbulent kinetic energy (TKE) peaked near the canopy top, reaching approximately 66 m2/s2, 44 m2/s2, and 22 m2/s2, respectively. Temperature increased with height, while moisture and carbon dioxide concentrations decreased because of enhanced turbulent mixing. Dense canopies retained higher moisture and carbon dioxide levels than medium and sparse canopies. Conclusion: Forest canopy density significantly influenced airflow structure, turbulence production, and scalar transport. Dense canopies provided stronger microclimatic regulation through enhanced momentum attenuation, moisture retention, and carbon storage. The developed modelling framework provides a useful tool for studying canopy–atmosphere interactions and local climate dynamics.

2026-08-01T00:00:00Z Obande, Ruth Kandie, Joseph Bii, Albert http://41.89.164.27:8080/xmlui/handle/123456789/2802 2026-09-08T06:21:27Z 2026-08-01T00:00:00Z

Hydrodynamic Modelling of Mixing Efficiency and Optimal Bio-methane Production in Anaerobic Digesters Using a Two-Dimensional Navier–Stokes Framework Obande, Ruth; Kandie, Joseph; Bii, Albert Background: Anaerobic digestion (AD) is a proven technology for renewable bio-methane production, but digester efficiency is often limited by poor hydrodynamic mixing rather than by microbial kinetics alone; most existing models, however, assume idealised, fully homogeneous reactors. Objective: This study investigates the influence of hydrodynamics on mixing efficiency and bio-methane production potential in anaerobic digesters using mathematical modelling. Methods: A two-dimensional incompressible Navier–Stokes model was coupled with a tracer advection– diffusion equation to simulate slurry flow and mixing behaviour. The governing equations were non- dimensionalised using the Reynolds and Péclet numbers, discretised using the finite difference method, and solved numerically in MATLAB. An optimisation framework that treated inlet velocity as the control variable, together with an adjoint sensitivity analysis, was used to evaluate and improve mixing efficiency. Results: At a Reynolds number of 2100, the flow exhibited transitional characteristics, with a dead zone fraction of approximately 35.1%. Velocity contours revealed limited circulation, whereas the tracer distribution showed a non-uniform concentration pattern across the domain. The dead zone fraction declined exponentially as Re increased, with values above 4000 projected to reduce it below 15%. At Pe = 10,000, transport was strongly advection-dominated, and the adjoint sensitivity analysis identified the inlet/impeller region as offering the greatest leverage over mixing performance. Conclusion: Hydrodynamic conditions play a critical role in determining mixing efficiency and, consequently, bio-methane production potential. The developed model provides a computationally efficient framework for analysing and optimising anaerobic digester performance and offers a foundation for future integration with biochemical reaction models.

2026-08-01T00:00:00Z Kegwaro, Winnie King’ang’i, Denis Meli, Collins http://41.89.164.27:8080/xmlui/handle/123456789/2800 2026-09-07T12:01:28Z 2026-06-01T00:00:00Z

On the Norm of Jordan Elementary Operators in Tensor Product of C ∗ -Algebras Kegwaro, Winnie; King’ang’i, Denis; Meli, Collins Elementary operators have been studied over years, with their norms being of significant interest in operator theory. The study includes the derivation of formulas that describe norms in terms of their coefficient operators, which is traced back to Stampfli`s Theorem that used the property of Numerical range as a foundation for the study of norms. Other properties of Elementary operators have been studied ever since, but little is known on Jordan Elementary operators in tensor products of C ∗ - algebras. This paper aims to extend the determination of norms of Jordan Elementary operators in the tensor product of C ∗ - algebra by determining the lower bound of the norm using the maximal numerical range by employing the technique of tensor product, finite rank operator and inner product. A lower bound of Jordan elementary operator in tensor product of C ∗algebras is obtained.

2026-06-01T00:00:00Z CHEPSERGON, KENNETH http://41.89.164.27:8080/xmlui/handle/123456789/2772 2026-06-11T09:15:20Z 2025-01-01T00:00:00Z

MODELING RISK FACTORS ASSOCIATED WITH SNAKEBITE MORBIDITY USING MULTIVARIATE ANALYSIS:A RETROSPECTIVE STUDY IN CHEMALINGOT IN BARINGO COUNTY. CHEPSERGON, KENNETH Snake bite envenomation is a major but neglected public health problem especially in resource poor rural areas. In Kenya, the burden of morbidity attributable to snakebite has been increasing in many areas. Chemalingot in Baringo County is one of the region in kenya where venomous snakes are common.This has resulted to cases of morbidity to go high due to victims inability to access timely and effective health care. The aim of the study was to model the main risk factors related to the morbidity of snakebite using a multivariate analytical framework, in an attempt to provide locally appropriate interventions. A retrospective cross-sectional research methodology was used and medical records of the identified dispensaries in Chemalingot were employed. Patient demographics and clinical outcomes were summarized in terms of descriptive statistics. To determine the predictors significantly correlated with morbidity after snakebite, the multivariate logistic regression analysis was used. In the results analysis, it was found that there was a morbidity of snakebites of 30.0%. The average age of adults with the disease is 19.26 years and the average length of stay in a hospital is 4 days. The rates of morbidity depended on the time of the bite, and those that occurred in the evening and night had higher rates of complications vs. Multivariate modeling indicated that prolonged stay in hospitals was significantly correlated with high morbidity with each day increasing chances by 9% . In addition, patients arriving to a health institution over 12 hours after the bite were triple likely to have morbidity than those who were presented to health center in less than 12 hours . The results demonstrate the importance of early treatment and available health care services to decrease the outcomes of the problem of snakebites. The study will be of immense importance in terms of providing evidence to the epidemiology of snakebites in Chemalingot and will also act as a basis of formulating specific intervention measures that will be directed at lessening morbidity among snakebite victims who are rural poor people.

2025-01-01T00:00:00Z MURERE, JOHN http://41.89.164.27:8080/xmlui/handle/123456789/2749 2026-06-08T12:10:56Z 2025-01-01T00:00:00Z

MACHINE LEARNING BASED CERVICAL CANCER DETECTION MODEL IN WESTERN KENYA MURERE, JOHN Cervical cancer is the leading cause of cancer-related deaths among Kenyan women, with approximately 3,200 deaths reported annually, driven mainly by low screening uptake (16%) and late diagnosis. The aim of this study was to develop a machine learning based model that would enhance the detection of cervical cancer in Western Kenya, a region that has limited healthcare resources. This study used a cross-sectional study design where data from 968 women were collected, including information on demographics, reproduction, and clinical characteristics. Data was collected from health facilities. The study showed that 93.7% (n = 907) had no biopsy-confirmed abnormalities, while 6.3% (n = 61) had abnormalities. There were five machine learning models (Logistic Regression, Random Forest, Decision Tree, Support Vector Machine, and Artificial Neural Network) that were trained on 70% of the data (training set) and tested on 30% of the data (testing set). The random forest model achieved the highest accuracy (94.33%) and specificity (98.37%), which outperformed the other models and traditional methods like Human papilloma virus (HPV) testing (70-80% specificity) and Pap smear (>90% specificity) for confirming negative cancer cases. The logistic regression model had the highest sensitivity of 70% which was comparable to the Pap-smear method (60-95% sensitivity), but it was lower than the HPV testing, with a sensitivity greater than 90% which makes it suitable for initial cervical cancer screening. The Pap smear results and use of hormonal contraceptives emerged as the key significant predictors of cervical cancer, which supports targeted screening strategies. The findings from this study confirmed there was a significant difference in model performance with partial superiority over existing methods and the influence of key cervical cancer risk factors. The combined approach of using a random forest model for confirmation and logistic regression for screening could optimize cervical cancer screening further in the resource-constrained Western setting. This study has underscored the potential that machine learning has in addressing cervical cancer disparities in Western Kenya, with implications for both public and private health interventions and future research work.

2025-01-01T00:00:00Z MOMANYI, MOGIRE KRIFIX http://41.89.164.27:8080/xmlui/handle/123456789/2644 2026-05-11T10:09:01Z 2025-01-01T00:00:00Z

MODELLING TRAFFIC FLOW BEFORE AND AFTER ROUNDABOUT USING NAVIER-STOKES AND ADVECTION-DIFFUSION EQUATIONS MOMANYI, MOGIRE KRIFIX Traffic congestion remains a persistent challenge in urban areas, with roundabouts playing a pivotal role in enhancing road safety, improving traffic flow, and minimizing congestion. Understanding traffic dynamics before and after roundabout implementation is critical for optimizing urban infrastructure. Traditional traffic models lack the precision to account for the complex interactions and flow disruptions associated with roundabouts. These limitations hinder accurate predictions of traffic patterns, requiring more advanced mathematical approaches to model flow dynamics effectively. This study aims to model traffic flow around roundabouts using Navier-Stokes and advection-diffusion equations. Specific objectives include formulating mathematical models, analyzing the influence of roundabout geometry on traffic flow, evaluating disruption and diffusion effects, and identifying critical factors impacting flow stability. The study employed fluid mechanics principles, utilizing the Navier-Stokes and advection-diffusion equations to model traffic as a fluid-like system. Numerical simulations were conducted using the Finite Volume Method and Crank-Nicolson scheme, with Matlab R2023b facilitating sensitivity analyses to evaluate various scenarios. Findings indicate that roundabouts significantly improve traffic flow efficiency by reducing congestion and enhancing speed regulation. The geometric design of roundabouts and their capacity to handle disruptions were identified as key factors influencing performance. Sensitivity analysis revealed optimal configurations for minimizing delays and maximizing output. The integration of roundabouts enhances urban traffic dynamics by mitigating congestion and optimizing vehicle movement. Mathematical models provide a robust framework for analyzing these effects, ensuring informed urban planning. Policymakers should incorporate advanced mathematical modeling in roundabout designs, emphasizing scenario-specific analyses to address diverse traffic conditions. Future research should integrate behavioral and environmental factors to refine predictive capabilities and practical applications

2025-01-01T00:00:00Z NGETICH, LUCY JEROP http://41.89.164.27:8080/xmlui/handle/123456789/2643 2026-05-11T10:04:12Z 2025-01-01T00:00:00Z

MODELLING GEOMETRY INTERRUPTION, VASCULAR STRESS, AND PULSATILITY IN CAROTID ARTERY BLOOD FLOW USING POISEUILLE-BASED EQUATIONS NGETICH, LUCY JEROP The Poiseuille equations are instrumental in modeling blood flow, particularly within large and medium-sized arteries where laminar flow predominates. Derived under the assumption of steady, incompressible, Newtonian flow through cylindrical tubes, these equations effec- tively describe vascular dynamics in geometries approximating cylindrical shapes and at low Reynolds numbers. However, their applicability diminishes in regions characterized by tur- bulence, geometric irregularities, or pulsatile flow, such as those found in the carotid artery. This study identifies three key research gaps in the application of Poiseuille equations to carotid artery hemodynamics: (i) the influence of vascular shear stress under turbulent condi- tions, (ii) the deviation introduced by pulsatile flow from the steady-state assumption inherent in the Poiseuille model, and (iii) the geometric variability of the carotid artery and its under- explored role in altering flow characteristics. To address these gaps, the study introduces a novel formulation of the Poiseuille equation incorporating geometric drag and pulsatile flow through a Womersley function. Governing equations were formulated based on modified Poiseuille flow and solved numerically using the Finite Volume Method (FVM) implemented in MATLAB, with custom code developed to simulate time-dependent blood flow. The nu- merical scheme incorporated discretization of the Navier–Stokes equations and was executed using MATLAB’s built-in solvers and post-processing tools for velocity, pressure, and vascu- lar stress visualization. The simulation results revealed a significant reduction in flow rate and velocity in regions with geometric interruptions. For example, the peak simulated velocity reduced by approximately 28% in stenosed segments compared to normal arterial sections, demonstrating a nonlinear velocity profile consistent with observed clinical behavior. The simulations further indicated that geometric disturbances, such as stenosis and bifurcations, resulted in an increase in vascular stress and a pronounced decrease in flow rate (Q), partic- ularly under turbulent conditions. This inverse relationship between vessel radius and flow dynamics corroborates findings from existing studies on stenotic arteries. Additionally, the analysis demonstrated that as artery radius (r) decreased, vascular stress W(r, t) increased substantially, in line with predictions from Hagen–Poiseuille’s law. Pulsatility during systolic phases further amplified wall shear stress (WSS), thus supporting the third objective of the study. The findings emphasize the limitations of the classical Poiseuille-based model in tur- bulent and pulsatile regimes and highlight the necessity for more robust modeling approaches to accurately capture the complex hemodynamics of carotid artery flow under pathological conditions.

2025-01-01T00:00:00Z OMARE, BRIAN http://41.89.164.27:8080/xmlui/handle/123456789/2583 2026-04-15T05:17:26Z 2025-01-01T00:00:00Z

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.

2025-01-01T00:00:00Z Murere, JF Wangila, S. Koech, J. http://41.89.164.27:8080/xmlui/handle/123456789/2564 2026-03-26T13:36:46Z 2025-06-01T00:00:00Z

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.

2025-06-01T00:00:00Z