http://repository.tharaka.ac.ke/xmlui/handle/1/4345 2026-09-05T11:46:25Z http://repository.tharaka.ac.ke/xmlui/handle/1/4502 MATHEMATICALMODELINGOFMALARIATRANSMISSIONAND TREATMENT:ACASEOFCONFLICTZONES NG’ATIA, NGUU A Malaria continues to be among the most pressing public health challenges globally, disproportionately affecting vulnerable populations in tropical and subtropical regions. The infection is spread through the bites of female Anopheles mosquitoes carrying the parasite, with high-risk groups including people with compromised immune systems and travelers to endemic areas. Despite extensive control efforts and the formulation of mathematical models that integrate essential biological and pharmacological components such as human immunity level, vector behavior treatment coverage and drug resistance, significant gaps persisted in understanding malaria transmission and treatment dynamics, particularly in conflict-affected zones. The study develops a mathematical model for malaria transmission and treatment in conflict zones capturing interventions such as full treatment and partial treatment. The model utilizes a system of ordinary differential equations (ODEs) to describe the progression describing malaria transmission and treatment over time, capturing transitions across different human and mosquito compartments. The positivity of solutions was established to ensure biological feasibility. The existence of a Disease-Free Equilibrium (DFE) was determined and found that no infection exist in human population. Stability analysis was conducted to assess the conditions under which malaria can be eliminated, while sensitivity analysis identified key parameters that significantly influenced transmission and treatment outcomes. Numerical simulations were performed using Mathematica and python software to validate the analytical results and examine the effects of control measures under varying conditions. The findings provided insights into the effectiveness of treatment strategies and interventions aimed at reducing malaria transmission and mortality in conflict zones. The study also offered evidence-based recommendations applicable to similar health constrained environments. 2025-11-01T00:00:00Z http://repository.tharaka.ac.ke/xmlui/handle/1/4501 MATHEMATICALMODELINGOFTUBERCULOSISDYNAMICS INCARE INSTITUTIONS:APERSPECTIVEONVARIANCEINTREATMENT KYALO, KAVOYO A Tuberculosis (TB) remains a major global health concern, particularly in overcrowded healthcare and institutional settings where transmission risk is elevated. Mathematical modeling provides insight into disease dynamics and treatment effects in such environments. The study focused on modeling TB spread and treatment variations in care institutions. Care institutions are facilities that offer essential health, social and rehabilitative services to individuals needing ongoing support due to age, illness, or disability. They include hospitals, rehabilitation centers, nursing homes, prisons and shelters where exposure duration and overcrowding are critical factors, and aim to provide treatment, preventive care and daily assistance in a safe environment (Ministry of Health Kenya, 2025). Prior work by Beggs et al. (2003) emphasized TB transmission in confined spaces but lacked detail on treatment variation and duration of exposure common in care settings. The present study develops a compartmental model using ordinary differential equations, simulated in MATLAB and Mathematica. The basic reproduction number (R0) was derived analytically, incorporating variables like infectivity rates, progression probabilities, and relapse dynamics. Using parameter estimates relevant to Kenyan institutions, the calculated R0 was 0.00022, indicating that TB would eventually be eradicated under current conditions. Variation of the parameter values within the range of the parameters had impact on the model and indicated that the model was sensitive and it was graphically illustrated. Sensitivity analysis showed that parameter variations significantly influenced transmission outcomes, enhancing confidence in the model’s predictive accuracy. Robustness of the SV EIeInTnTfR model were achieved using the basic reproduction number. The value obtained from the basic reproduction number after inserting the parameter values given in table 3 in the formula for the basic reproduction number was below unit and indicated that TB disease died out hence the model was stable. Simulations revealed that full treatment regimens significantly reduced TB prevalence compared to partial treatment scenarios. These results suggest that improving treatment adherence and completing full therapy cycles in care institutions can drastically reduce TB transmission. Stakeholders and policymakers should consider these findings to enhance control strategies, optimize resource allocation, and support evidence-based policy interventions within institutional settings. 2025-11-01T00:00:00Z http://repository.tharaka.ac.ke/xmlui/handle/1/4493 ANON-LINEARDYNAMICALMODELOFTUMOUR-HEALTHY-IMMUNE CELLINTERACTIONSUNDERTHERAPEUTICINTERVENTION WAITHEGA, NICHOLAS MURIMI Cancer therapy remains a major biomedical challenge due to the coexistence of healthy,tumour, quiescent, and immune cells that interact in complex and often unpredictableways. This thesis presents a mathematical model of tumour-host interactions underradiotherapy and chemotherapy. The limited understanding of how radiotherapy andchemotherapy when applied singly or in combination, influences tumour-immune dynamics and long-term treatment efficacy is the problem to be addressed. The model incorporates four compartments: healthy cells, tumour cells, quiescent tumour cells,and immune cells. The system of non-linear ordinary differential equations is analysedfor positivity, boundedness, invariant regions, and equilibria. The basic reproductionnumber R0 is derived, and stability analysis establishes conditions for tumour persis tence or eradication. Sensitivity analysis identifies the parameters most influential totreatment outcomes. Numerical simulations, conducted using biologically consistent parameter values, reveal key dynamics. In the absence of therapy, tumour and quiescent populations expand while healthy cells decline, corresponding to R0 > 1. Radiotherapy efficacy ε exerts a threshold effect: low values slow tumour growth without elimination, while sufficiently high values reduce R0 below one, driving eradication.Chemotherapy schedules show similar behavior. In both modalities, continuous administration consistently outperforms pulsed or fractionated delivery. Combination therapy achieves the most rapid and sustained suppression, highlighting non-linear synergy between the two interventions. Timing is also decisive: early treatment stabilizes the system and prevents resurgence, whereas late initiation produces larger oscillations and slower recovery. These findings demonstrate the value of mathematical modelling in oncology by showing how efficacy, scheduling, and timing jointly determine long-term therapeutic success. The results provide quantitative insights that may guide clinical decision-making and the design of optimized cancer treatment strategies. 2025-11-01T00:00:00Z http://repository.tharaka.ac.ke/xmlui/handle/1/4462 IMPEDIMENTS TO YOUTH ENTERPRISE DEVELOPMENT FUND LOAN REPAYMENT AMONG YOUTH GROUPS IN THARAKA NORTH SUB COUNTY, THARAKA NITHI COUNTY, KENYA MUTEGI, JUDITH K This study examined the impediments to youth enterprise development fund loan repayment. Studies show that youths successfully repay loans consistently in the initial months after being awarded loans, but default there-after for reasons that are virtually unknown. Lack of steady repayment until the principal loan sum is fully cleared provides a breach that this study pursued to explore. This study set out to examine how entrepreneurship training, socio-economic factors, and business performance influence loan repayment among youth group beneficiaries. It was grounded in Group Lending Theory and Social Traits Theory; frameworks that explore how shared accountability and individual characteristics shape financial behavior. A descriptive research design was used, drawing on primary data sources. The research targeted 16 registered youth groups, including YEDF beneficiaries and fund officers. From this population, a stratified random sample of 123 respondents was selected. Data were collected through structured questionnaires and interviews, then analyzed using the Statistical Package for Social Sciences (SPSS) 27.0. Both descriptive statistics and thematic analysis were applied to the quantitative data, while qualitative responses were examined through thematic analysis. The findings showed that most beneficiaries reported gains in financial literacy and business management skills following entrepreneurship training. However, several constraints such as limited startup capital, low-income levels, and weak market linkages posed significant barriers to consistent loan repayment. Broader socio-economic challenges also emerged, including high unemployment, a poor culture of saving, and dependence on unstable income streams. In addition, business performance factors like low profitability and inadequate record-keeping were found to have a strong influence on repayment behavior’s study concludes that while the Youth Enterprise Development Fund (YEDF) has expanded access to credit for young people, the sustainability of these gains is undermined by fragile repayment structures and insufficient follow-up after loan disbursement. To address these gaps, the study recommends ongoing entrepreneurship training, increased loan amounts tailored to real business needs, stronger post-loan monitoring systems, and improved collaboration between YEDF and local actors to boost accountability and compliance. These findings offer valuable insights for policymakers, development practitioners, and researchers seeking to strengthen youth credit systems and advance inclusive economic empowerment strategies. 2025-11-01T00:00:00Z