Journal Articles

Permanent URI for this collectionhttp://erepository.kibu.ac.ke/handle/123456789/9624

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A Self Dual and Doubly Even Code Related to Mathieu Group M24
(IRE Journals, 2021-03-07) Marani, Vincent Nyongesa
In this paper, we determine a self-dual and doubly even [24,12,8] code. We determine and discuss the properties of designs related to this code 2010 Mathematics Subject Classification: 94B 05C
Analysis of Generalised Boussinesq Coupled Equations Using Lie Symmetry
(IRE Journals, 2022-03-07) Omari, Sarah; Marani, Vincent Nyongesa; Oduor, Michael
In the last decades, Nonlinear partial differential equations (NPDEs) have become essential tools to model complex phenomena that arise in different aspects of science and engineering such as hydrodynamics. Therefore, constructing exact and approximate solutions of NLPDEs is of great importance in mathematical sciences. Previously authors have done similar work with restriction of K and L to be one. In this paper we solve the generalised Boussinesq coupled equations: 𝒖𝒕 + 𝑲𝒗𝒙 + 𝑳𝒖𝒖𝒙 = 𝟎; 𝑲 > 𝟎; 𝑳 > 𝟎 𝒗𝒕 + 𝒖𝒗𝒙 + 𝒖𝒙𝒙𝒙 = 𝟎 using Lie symmetry of differential equations where u = u (x; t) is the velocity of water and v = v (x; t) the total depth of water and subscripts denote partial derivatives. The positive constants K, L would enable further analysis of optimal water depth and velocity be determined.
An Irreducible and Doubly Even Code of Degree 23 Related to Mathieu Group M23
(IRE Journals, 2021-04-07) Marani, Vincent Nyongesa
In this paper, we determine an irreducible and doubly even code [23,11,8]. We determine and discuss the properties of designs related to this code
Classification of Some Internal Structures of Degree 120 Related To a Group of Extension𝑂8+ 2 : 2
(IRE Journals, 2023-08-07) Maina, Janet Lilian; Matuya, John Wanyonyi; Njuguna, Edward; Marani, Vincent Nyongesa
This paper uses the modular representation method to classify the internal structures of degree 120 related to a group of extension,𝑶𝟖+ 𝟐 : 2.Specifically, we determine the number of binary linear codes and construct their lattice structure, as well as investigate the properties of some linear codes and designs of minimum weights. Our findings reveal that there are 12 binary linear codes, consisting of 4 doubly even codes, 4 projective codes, 2 irreducible codes, and 2 decomposable codes. We also identify 2 primitive 1-designs of minimum weight. The results demonstrate the potential benefits of using linear codes and designs from finite groups of extension with modular representation methods, such as improved error correction, increased data storage capacity, improved security, efficient designs, and improved computational efficiency. However, it is important to note that this topic can be complex and technical, and we recommend that stakeholders collaborate with experts in the field to ensure the accuracy and reliability of the information being used. Overall, this study contributes to the understanding of the modular representation method and its applications in coding theory and related fields.
Conjugacy Classes of the Split Extension 28: U4(2)
(IRE Journals, 2024-08-07) Wekesa, Caroly Wafula; Chikamai, Lucy Walingo; Marani, Vincent Nyongesa
This study presents a comprehensive analysis of the conjugacy classes of the split extension 28: U4(2), where U4(2) is the unitary group of degree 4 over the field with 2 elements. Using a combination of theoretical techniques, including Fischer-Clifford matrices and character theory, along with computational tools such as GAP and MAGMA, we determined and classified all 49 conjugacy classes of this group. Our analysis revealed complex fusion patterns from U4(2) to 28: U4(2), including class splitting and the introduction of new element orders. We found that 28: U4(2) has more than double the number of conjugacy classes compared to U4(2) alone, with class sizes ranging from 5 to over 1.3 million elements. This work addresses significant gaps in the existing literature regarding this specific group extension and provides insights into its structure, representations, and automorphisms. The methodology and results presented here contribute to the broader understanding of group extensions and lay the groundwork for further investigations into the properties and applications of 28: U4(2) in areas such as coding theory and quantum mechanics.
Binding Number Bounds of Zero Divisor Graphs of Classes of Completely Primary Finite Rings
(African Scientific Annual Review, 2024-07-07) Mmasi, Eliud; Ojiema, Michael Onyango; Marani, Vincent Nyongesa
The binding number of a graph is an important graph parameter which measures the distribution of the size of the graph and its related properties including toughness, rapture degree, scattering number and its integrity. For complete graphs G ≃ Kn obtained from commutative finite ring, some results exist on the bounds of binding numbers. In this paper, we consider an incomplete but connected zero divisor graph Γ(R) associated with a class of completely primary finite ring R and use standard procedures to compute the binding number bounds, the average binding number and related graph parameters.
Graph Numbers and Distance Related Parameters of Zero Divisor Graphs
(Science Mundi, 2024-08-06) Mmasi, Eliud; Ojiema, Michael Onyango; Marani, Vincent Nyongesa
Distance-related parameters have applications in the field of pharmaceutical chemistry, network discovery, robot navigation, and optimizations. Cyclic structures exhibit significant topological features that have become important research areas in the field of computer science and mathematics. Due to the inherent algebraic relationship between graph numbers and distance related parameters, this paper characterizes variants of distance related parameters and graph numbers associated with the zero divisor graphs akin to cyclic structures obtained from classes of completely primary finite rings. In particular, we investigate the local fractional metric dimension and provide certain results concerning graph indices namely the Weiner index and the Zagreb index.
Designs and Lattices from Classes of Cyclic Linear Ternary Codes over GF(3)
(Science Mundi, 2025-07-07) Okombo, Mary Immaculate; Ojiema, Michael Onyango; Kivunge, Benard; Marani, Vincent Nyongesa
In this study, we investigate the relationships between code parameters and lattice properties, providing new insights into the structure of ternary codes from a geometric perspective. Our findings extend the existing knowledge of ternary cyclic codes, particularly for lengths exceeding 25. We construct several new codes with favorable parameters, constructed previously unreported combinatorial designs, and characterized lattices with unique properties. The results demonstrate that ternary cyclic codes exhibit high structural regularity and often produce interesting designs and lattices with properties distinct from their binary counterparts. The research reveal strong interconnections between Coding Theory, Combinatorial Design Theory, and Lattice Theory in the context of ternary codes. We provide a multifaceted characterization framework that integrates algebraic, combinatorial, and geometric perspectives, offering a holistic understanding of these codes. This study contributes to the theoretical advancement of non-binary codes and opens new avenues for their practical applications in error correction, cryptography, and communication systems.
On Skew Quasi-P-Class (Q) Operators
(International Journal of Mathematics And its Applications, 2023-07-07) Wanjala Victor; Matuya, John Wanyonyi; Njuguna, Edward; Marani, Vincent Nyongesa
Skew quasi-p-class (Q) operator is introduced. We show that this class satisfies Bishop’s property. We equally show that this class is isoloid and polaroid. Results linking this class to other classes such as class (Q) are also given and a result showing that this class doesn’t preserve similarity of operators is outlined.
A Characterization of Classes of Linear Ternary Codes over the Galois Field GF(3)
(African Scientific Annual Review, 2025-07-07) Okombo, Mary Immaculate; Ojiema, Michael Onyango; Kivunge, Benard; Marani, Vincent Nyongesa
Linear cyclic ternary codes defined over the Galois field GF(3) exhibit several advantages over their binary counterparts. For instance, they provide an extra option for each pulse resulting into a larger set of available codes at any given length. This paper presents a comprehensive study of classes of linear cyclic ternary codes of length 25 ≤ n ≤ 50. While binary codes have been extensively studied, the properties and applications of longer ternary codes remain less explored. This study address this gap by providing an in-depth characterization of these codes for the stated lengths. Using computational methods implemented in Magma software, a diverse set of linear cyclic ternary codes over GF(3) were generated and analyzed. The paper provides a multifaceted characterization framework that integrates algebraic, combinatorial, and geometric perspectives, offering a holistic understanding of these codes. This study contributes to the theoretical advancement of non-binary codes and their practical applications in error correction, cryptography, and communication systems.
Mathematical Modelling and Optimal Controls for Controlling Pneumonia-HIV Co-Infection
(International Journal of Innovative Research & Development, 2021-01-07) Wafula, Nebert Kituni; Kwach, Boniface Otieno; Marani, Vincent Nyongesa
Bacterial infections like Pneumonia have emerged as an important cause of morbidity and mortality in individuals infected with HIV giving rise to their co-infection. There are mathematical models that describe; the co-dynamics, treatment and protection mechanisms of Pneumonia and HIV infections. Therefore, this research is aimed at determining optimal control treatments through developing a deterministic mathematical model Pneumonia-HIV coinfection incorporating the use of anti-pneumonia and ART treatment interventions as controls. The uncontrolled pneumonia-HIV co-infection is presented with its analysis. Finally, the optimal control theory for Pneumonia-HIV coinfection model is derived analytically by applying the Pontryagin’s Maximum Principle.
Measuring the Effect of Different Modes of Mobile Phone-Based Antenatal Family Planning Counseling on the Intention for Early Postpartum Family Planning Uptake in Western Kenya: A Pragmatic Factorial Randomized Control Trial
(Ethiopian Journal of Reproductive Health (EJRH), 2025-01-24) Shisanya, Morris Senghor; Kipmerewo, Mary; Morema, Everlyne; Ouma, Collins
INTRODUCTION: The Maternal and Child Health care continuum offers a key opportunity to integrate postpartum family planning (PPFP) interventions, particularly through antenatal counseling. This study assessed the impact of mobile phone-based antenatal family planning counseling on the intention for early PPFP among postpartum mothers in Western Kenya. METHODOLOGY: This pragmatic factorial randomized controlled trial assessed the effectiveness of family planning counseling delivered by nurses and community health workers using a mobile phone-based tool, compared to routine counseling, on the intention for early postpartum family planning among postpartum mothers in Kisumu County, Western Kenya. Ordinal regression identified predictors of intention, while ANOVA evaluated the effectiveness of counseling modalities, with significance set at P < 0.05. Tukey’s post hoc test and partial eta² were used to determine differences between study arms and effect size, respectively. RESULTS: The mean intention for early PPFP on a 7-point Likert scale was 6.59±0.87 for the nurses’ arm, 6.05±0.86 for the community arm, and 6.03±0.69 for the control arm. ANOVA revealed a significant difference in mean intention scores between the arms (F(2,243)=12.43, P<0.0001). Tukey’s post hoc test showed significantly higher mean intention in the nurses’ arm compared to both the community (P<0.0001) and control arms (P<0.0001) with a medium effect size (partial eta² = 0.06 to <0.14). The combined mean intention for the two intervention arms (6.22±0.85) was significantly higher than the control arm (P=0.012) with a small effect size (partial eta² = 0.026). There was no significant difference between the community and control arms (P=0.986).CONCLUSION: Mobile phone-based antenatal family planning counseling by nurses was more effective in increasing intention for early postpartum family planning for participants in Kisumu County compared to community-based and routine delivery of counseling. Therefore, more efforts should be directed toward empowering nurses with mobile phone-based antenatal family planning counseling tools to enhance intention for early postpartum family planning.
KESOZI Digital Twin: Physics-Informed Neural Network for Independent Estimation and Prediction of Childhood Diarrheal Disease Burden in Kenya, Somaliland, and Zimbabwe
(2026-06-24) Agumba, John Onyango; Namusonge, Lucy Natecho; Ogendo, Joshua Ondura; Takavarasha, Musiiwa; Mohamad Ahmed Hassan; Senghor, Morris Shisanya; Waswa, Lydia; Pembere, Anthony
Childhood diarrheal disease remains a leading cause of morbidity and mortality among children under five years in sub-Saharan Africa, particularly in settings affected by inadequate sanitation, climate variability, malnutrition, and limited healthcare access. Conventional forecasting approaches are often constrained by sparse surveillance data, weak spatial representation, and limited incorporation of mechanistic disease dynamics. This study presents a Physics-Informed Multimodal Artificial Intelligence Digital Twin framework that integrates Physics-Informed Neural Networks, Graph Neural Networks, diffusion-reaction epidemiological modeling, multimodal fusion learning, and Digital Twin simulation to estimate and predict childhood diarrheal disease burden in Kenya, Somaliland, and Zimbabwe. Using public epidemiological, environmental, climate, sanitation, and synthetic proof-of-concept datasets, the framework modeled temporal disease dynamics, spatial transmission, pathogen-attributed burden, and outbreak trajectories while enforcing epidemiological consistency through physics-informed optimization. Results demonstrated robust forecasting performance, enhanced spatial transmission modeling, uncertainty-aware predictions, and realistic outbreak simulations across the three countries. Rotavirus, Shigella, and Cryptosporidium were identified as major contributors to modeled mortality burden, while unsafe water exposure, poor sanitation, malnutrition, and climate-sensitive transmission substantially increased disease risk. Compared with a Bayesian baseline model, the multimodal framework achieved superior nonlinear risk characterization, geospatial learning, and temporal prediction. These findings highlight the potential of scientific machine learning and digital twin systems for infectious disease surveillance, outbreak forecasting, climate-health analytics, and evidence-based public health decision-making in low-resource African settings.
Situation Analysis of HIV, Hepatitis B, and Syphilis among Pregnant Women: A Case of Burco General Hospital, Somaliland
(East African Journal of Health and Science, 2025-06-05) Osman, Abdirisaq Muse; Namusonge, Lucy Natecho
Background: Sexually transmitted diseases like HIV, Hepatitis B and Sexually Transmitted Diseases like syphilis remain a public health concern, with 2.3 million deaths per year and 1 million people newly infected per day. This accounts for about 14% of deaths from infectious and parasitic diseases globally. These diseases can be vertically transmitted and have a particular burden on pregnant and newborns, especially in low-income countries. Objectives: This study aims to determine the seroprevalence and determinants of HIV, Hepatitis B and Syphilis among pregnant women attending the obstetric department of Burco General Hospital, Somaliland. Methodology: quantitative research with a cross-sectional study design using semi-structured questionnaires and rapid test kits were used to screen 271 pregnant women attending the hospital. Both descriptive and analytic statistics were calculated using SPSS v20. Adjusted odds ratios (AOR) and their 95% confidence interval (CI) were calculated with a level of significance set at 5%. Results: the prevalence of HIV, Hepatitis B, and Syphilis among pregnant women attending Burco General Hospital was 0.4%, 4.1%, and 3% respectively. The cross-reactivity of HIV/HBV was 9.1%. There was no significant risk factor outcome regarding sociodemographic and obstetric characteristics. Conclusion and recommendations: Infectious diseases are a public health burden among pregnant women in Burao. However, antenatal care provides an excellent opportunity to screen women for infections that are common and treatable and can be transmitted vertically. Ministry of Health should adopt proper prevention and control intervention guidelines to reduce the risk of these three infections in line with WHO triple elimination guidelines.
Level of Water Governance in Schools and its Effect on Student Participation in Education
(International Journal of Research and Innovation in Social Science, 2021-06-12) Wambeye, K. M.; Wasike, D. W.; Ong’anyi, Paul Obino
Adequate access to water, hygiene and sanitation is every human’s and child’s right. These do not reflect national policies aspirations and are not adequate to student’s needs, affecting their health, well-being, performance and participation at school in Kenya. A cross-sectional survey design was adopted to sample from boarding schools that were sampled to take part in a study conducted in Bungoma County in the Western region of Kenya. Stratified sampling was employed in choosing the Schools while questionnaires, interview schedules, document analysis and focus groups were used to gather data. The model was not able to significantly predict the level of water governance in schools and its effect on student participation in education and hence concluded that every boarding secondary school should develop a drinking water access plan. This study provides an empirical pattern of participation in education influenced by WASH in schools.
Mechanism of Waste Management in Schools and its Effect on Student Participation in Education
(International Journal of Development Research, 2022-01-12) Wambeye, K. M.; Wasike, D. W.; Ong’anyi, Paul Obino
Waste management is pausing challenges to the environment especially in schools world over. In schools, water, sanitation and hygiene do not reflect national policies aspirations and are not adequate to student’s needs and hence affecting their health, well-being, performance and participation at school. An investigation into the mechanism of waste management in schools and its effect on student participation in education in Bungoma County, Kenya was done using a cross-sectional survey design approach. A sample of sixty five (65) boarding schools was chosen to take part while stratified sampling was employed in choosing the boarding Schools from the targeted population of 289 secondary schools. Questionnaires, interview schedules, document analysis and focus groups to gather data. Standard multiple linear regressions at α= .05 was used to examine waste disposal to see if it could predict participation in education in school. The model was not able to significantly predict the effect of waste management in schools on participation in education. It was concluded that engagement of school related groups need to encourage students to make waste reduction a part of their everyday life while increasing the flow of reusable and recyclable materials can even generate extra funds for school departments and groups.
An Investigation into Collaborative Stakeholder Engagement’s Effect on Teacher Professional Development Implementation in Kenya
(East African Journal of Education Studies, 2024-08-09) Wafula, Samuel Mabele; Likoko, Sarah Naliaka; Ong’anyi, Paul Obino
Quality education is attributed to the quality of teaching. Teacher Professional Development (TPD) is vital towards improved quality of teaching in Kenya. To achieve this, Teachers Service Commission (TSC) rolled out TPD, whose successful implementation is at risk due to criticism from various stakeholders. This study sought to investigate the effect of stakeholder collaboration on implementation of TPD in Kenya. It adopted a descriptive survey study design. The study targeted a population of 327349 teachers from public schools and 188 TPD coordinators from accredited TPD service providers. Using the Krejcie and Morgan Table of 1970, a sample of 384 teachers, and 8 TPD coordinators was adequate for the study. However, to increase the statistical power of the study, the researcher used a sample of 404 respondents. Simple random sampling was used to identify one institution accredited to offer TPD. Each accredited institution enrolled teachers across Kenya. Exponential non-discriminative snowball sampling was used to select teacher respondents. TPD coordinators were selected by purposive sampling. Cluster sampling was used to ensure all the regions were included in the study. Both quantitative and qualitative data were collected using questionnaires and interviews respectively. Data was analyzed using descriptive statistics by way of frequencies, mean and standard deviations as well as inferential statistics including Pearson correlation and simple linear regression. The findings showed a significant positive effect of stakeholder collaboration on implementation of TPD. Effects of stakeholder collaboration explained a significant proportion of variation in implementation of TPD with, (t=2.536, B =.285, p<.0001). The study concluded that an increase in stakeholder collaboration positively influenced implementation of TPD. It recommended establishment of an institution mandated to conduct TPD-related activities in Kenya and work in collaboration with relevant education sector stakeholders in order to effectively implement TPD.
Demographic Factors affecting Dual Contraception Preference among Seropositive Women in Discordant Relationships in Nyatike Sub-County, Kenya
(Journal of the Kenya National Commission for UNESCO, 2024-06-12) Ouma, Mark Okungu Kadenyo; Ong’anyi, Paul Obino
Dual contraception is an effective strategy of achieving zero HIV transmission and unwanted pregnancy among discordant couples. Despite the double benefit, dual contraception use is still limited among seropositive women particularly in Nyatike Sub County, Kenya. Further, no research had been done on dual contraception preference or use among discordant couples in Nyatike Sub County. To fill this gap, this study aimed to establish the relationship between socio-demographic factors including age, parity, level of education, monthly income and dual contraception preference among seropositive women in discordant marital relationships in Nyatike Sub- County of Migori County, Kenya. This was a facility-based cross-sectional study in fourteen health facilities in Nyatike Sub- County. It involved 188 randomly sampled seropositive women in discordant marital relationships, 14 seronegative men randomly sampled and 14 healthcare providers. Descriptive statistics and chi-square test were used to analyze quantitative data while qualitative data were analyzed using content analysis. The study revealed that Parity (p=.001), level of education (p=.003) and monthly income (p=.026) were statistically significantly associated with dual contraception preference while age (p=.051) was not. The study recommends sensitization of seropositive women on the benefits of dual contraception to increase uptake of dual contraception.
Knowledge and Practice of Responsible Research Ethics among Doctoral Students and Alumni: A Case Study of Kibabii University, Kenya
(IOSR Journal of Research & Method in Education, 2022-10-12) Ong’anyi, Paul Obino; Owoche, Patrick Oduor; Abuya, Joshua Olang’o
Adherence to principles of responsible conduct in research is at the heart of doctoral supervision, and lack of it severely affects the quality and credibility of such study outcomes. Very few studies have investigated the level of knowledge and practice of responsible research ethics in institutions of higher learning in Kenya, a gap this study sought to address. The objective of this study was to investigate the knowledge and practice of responsible research ethics among doctoral students and Alumni at Kibabii University, Kenya. To realize its objective, the study conducted a cross sectional survey using a structured questionnaire to gather relevant information from 25 doctoral students and Alumni of the University. Data obtained was analyzed descriptively. Results indicate 48% of respondents were not knowledgeable about University’s Research Ethics Committee. The majority (54.2%) of the respondents lacked prior training in responsible conduct in research. The study recommends the need for the University to regularly sensitize doctoral students on the existence and roles of the various established institutions in the research process. Training for doctoral students in all areas of responsible conduct in research is critically necessary.
Doctoral Virtual Supervisory Meeting: Engagement Optimization Strategies
(American Journal of Education and Information Technology, 2022-11-16) Owoche, Patrick Oduor; Abuya, Joshua Olang’o; Ong’anyi, Paul Obino
The emergence of COVID-19 has seen widespread adoption and use of virtual interaction in business, academic, and other areas where hitherto their use was not imaginable just a few years ago. The adoption of virtual interactions has also seen growth in a number of service providers as well as enhancement of the quality of interactions. However, this advancement in virtual technologies does not guarantee their optimal use. This qualitative study’s main purpose was to explore discursive practices that impact virtual meeting experiences as they take place during the course of the doctoral supervisory process in Kenyan universities. The study used media richness theory and channel expansion theory to analyze the affordances of computer-mediated communication presented to the user to conduct virtual meetings. Drawing upon survey and interview transcripts, it was found that the choice of virtual meeting channel was based on the availability of technology and past experience enhanced the perception of the effectiveness of virtual meetings. This study proposes strategies for enhancing the virtual supervisory process based on the media richness theory, channel expansion theory, and research data. The strategy addresses the aspects of management of risks, virtual meeting etiquettes, supervisory relationship, and confidentiality as well as after the meeting follow-up. The proposed strategies will enhance academic interaction and can be used in similar interactions in other fields.

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