Faculty Of Science
Permanent URI for this collection
Browse
Recent Submissions
Item Multivariate Analysis of Economic Indicators Related to External Public Debt: A Case Study of Rwanda(THE CATHOLIC UNIVERSITY OF EASTERN AFRICA, 2024-08) GAEL MUGISHAThe rapid rise of the national borrowings level around the world Due to the financial crisis of 2007/2008 has led to several government fiscal issues. In Rwanda alone, the level of borrowed funds rose from19.4% in 2010 to 59.7% in 2019; thus, more studies to understand how different economic indicators affect the public borrowings are needed. The current study analyzed the economic indicators related to government debt accumulation in Rwanda by applying a multivariate time series analysis. The goals of the research were; to check for stationarity of the variables, to perform co-integration analysis and to forecast the external government borrowings level in the next five years. In this study, stationarity, co-integration and forecasting methods were executed. Historical data covering the period from 1973 to 2022. Data collection involved obtaining information from World Bank (W.B) and National Institute of Statistics of Rwanda (N.I.S.R.). The research conducted Augmented Dickey-Fuller test (ADF) for unit root to check for stationarity but also Johansen co-integration technique was utilized before applying Vector Autoregressive model (VAR) for forecasting the state borrowings. This study aimed to ascertain the influence of each selected variable on the state borrowings accumulation. This research found all the variable under the consideration to be stationary after first differentiation and there was no long-term association found between them. The forecasting techniques expect the foreign national borrowings to rise up to 74.20027 % in 2027 of the gross national income.Item MODELLING DEPENDENCE BETWEEN GOVERNMENT DEBT AND BANK NON-PERFORMING LOANS, A COPULA APPROACH(THE CATHOLIC UNIVERSITY OF EASTERN AFRICA, 2023-06) FLORIANE NSABIMANAThis study sought to model dependence between government debt and bank’s non-performing loans. The objectives of this study were to formulate a bivariate copula model which captures the dependence between government debt and bank non-performing loans and to measure the tail and asymmetric dependence between the two variables, the study used quarterly data sourced from World Bank. The data collection includes yearly observations for the following emerging economies: Burundi, Central Africa, Chad, Kenya, Madagascar, Rwanda, and Seychelles; it also includes information on the government debt-to-GDP ratio. The sample spans the years 2010 through 2020.To model the dependence between debt and bank non-performing, different methods have been used. The study estimated the dependence using copula GARCH, an approach that combines copula functions and GARCH models. According to forming the effect of local government debt and bank’s non-performing loans, copula models have been applied to analyze the asymmetry of tail dependence structure between government debt exposure and bank non-performing loans. We used R programming language and Excel to plot and analyze data. The results confirm that a large government debt in relation with non-performing loans has increased significantly from 2012 up to 2020, in all the countries apart of Seychelles. It showed that student t copula parameter provided the best fit for the marginal distributions. The results show the influence of government debt on bank non-performing loans. There appears to be a considerable association between the quick rise in bank non-performing loans and the extraordinary expansion of government debt, as indicated by the high and positive tail dependency. These nations’ larger tail dependency coefficients suggest that bank non-performing loans are more susceptible to the growth in public debt over the course of our sample period. Further researchers should focus on time to ensure the effectiveness of risk measurement and management.Item Statistical Modeling and Forecasting of Mobile Money Transactions in Kenya: Analysis with Hybrid ARIMA-XGBOOST Model(THE CATHOLIC UNIVERSITY OF EASTERN AFRICA, 2024-07) STEPHEN OMONDI ODHIAMBOMobile money services stand out as the revolutionary practices in the changing financial section in Kenya by revolutionizing conventional transaction practices as well as improving the rates of financial inclusion. This study aimed at conducting an assessment and forecasting of mobile money transactions in Kenya whereby a hybrid of ARIMA and XGBOOST was used to identify intricate patterns. The study looks at time variations in mobile money using CBK data collected over the period and identifies temporal trends in mobile money transactions. Therefore, while the use of mobile money services has rapidly expanded in Kenya over the years, there is a dearth of knowledge regarding the development trends and forecast of such transactions. It is essential for the stakeholders to have a good forecast model, so that planning and resource management are efficient. This study focused on this gap through the use of a new model that combines the linear nature of the ARIMA model with the non-linear nature of the XGBOOST algorithm. This study was guided by two specific objectives: Formulate a Hybrid ARIMA-XGBOOST models to identify patterns and movements in Mobile Money Transactions in Kenya; Also, to analyze temporal trends, present in the data and forecast future values in Kenya from the transactional data. The approach included applying the ARIMA on the time series data to get initial forecasts, then applying the XGBOOST on the residuals of the ARIMA to obtain better forecasts. The final result of hybrid model is the integration of the forecasts from the two individual models. ADF was used to test for the stationarity of the data, meanwhile the Box-Jenkins methodology was used to help identify and estimate the parameters of the best fit ARIMA model. An evaluation showed that there was a strong usurp of the both the number of transactions and the value of those being conducted through mobile money. Based on the findings from the ADF coefficient, the stationary condition was met, and therefore we proceeded to develop the ARIMA models. Initial diagnoses included model identification and examination of autocorrelation to determine the ARIMA configurations, whereas the Box-Jenkins test confirmed the models’ adequacy. The forecasting of demand for garments with the help of XGBOOST models with different types of losses proved to be reliable and accurate. When attesting to the concept of mobile money transactions growth in the context of the present study, the decomposition plots and the statistical analysis with reference to the Mann-Kendall test supported the positive trends growth. Based on Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), and Mean Percentage Error (MPE) the performance of the models had high prediction accuracy. The combination model of ARIMA and XGBOOST was useful in establishing a strong methodology for the study and prediction of the mobile money transactions in Kenya. The findings also revealed a strong positive correlation between the development of mobile money services and the economic activities as well as financial sustainability. According to the forecasts of for 2024-2026, cash volume and value both will increase constantly but showing uneven tendencies depending on external conditions. Hence, these observations offered useful directions on efforts toward the alteration of mobile money in Kenya to help decision makers in the m-Chips stakeholders. This research adds knowledge to the theoretical knowledge of mobile money systems and who has significance policy, financial, and business applications for Kenya.Item Mathematical Modelling of HIV/AIDS Dynamics in Relation to Drug Abuse(THE CATHOLIC UNIVERSITY OF EASTERN AFRICA, 2025-09) DOLPHINE MOCHEREThis study has investigated the co-dynamics of HIV/AIDS and drug abuse, focusing on how protection strategies and rehabilitation programmes influence transmission. The problem addressed is the strong interaction between drug abuse and HIV spread, particularly in Kenya, where injection drug use and risky behaviours heighten vulnerability to infection. The primary objective of the study was to create and evaluate a mathematical model that integrates protection and rehabilitation as control strategies. Specifically, the study aimed to investigate the stability of disease-free and endemic equilibria, compute basic and control reproduction numbers, conduct sensitivity analysis, and evaluate the impact of interventions through numerical simulations. A deterministic model with seven compartments, founded on ordinary differential equations, was developed and analyzed. The next-generation matrix method was employed to calculate reproduction numbers, while equilibrium stability was evaluated using the Jacobian method, Routh–Hurwitz criteria, and Lyapunov functions. Sensitivity analysis was performed to determine the most significant parameters, and numerical simulations were executed with Maple software. The findings indicated that the disease-free equilibrium is both locally and globally stable when RC < 1, suggesting that HIV/AIDS and drug misuse can be effectively managed with adequate measures. Simulations confirmed that higher protection and rehabilitation rates significantly reduce the prevalence of drug abusers, HIV-infected, and co-infected individuals. Sensitivity analysis highlighted protection and rehabilitation as the most critical parameters. The study concludes that integrated interventions, combining protection measures with effective rehabilitation, are essential for reducing the dual burden of HIV/AIDS and drug abuse. These findings offer significant insights for policymakers and health practitioners in formulating targeted public health interventions.Item Modeling and Forecasting Performance of ARIMA and ANN Models in the Presence of High-Frequency Data. Application to the East African Currency Exchange Rates(THE CATHOLIC UNIVERSITY OF EASTERN AFRICA, 2024-09) ROSELINE ONDIEKIMore and more high frequency time series (instead of quarterly/monthly) are being encountered and have resulted to longer and complex time series data. In modeling such data, more parameters are expected hence the need to use approaches which can capture the inherent structure of the data accurately. Existing models such as ARIMA and ANN have been applied to model mostly monthly and annual time series data with no focus on how the time series data frequency affects both their modeling and predictive performance and remedies established. This study sought to establish the modeling and forecasting performance of the two methodologies in the presence of high-frequency data and justify the need for Mixture models to model and predict such data. The study also applied the methods studied to modeling and forecasting the currency exchange rates for the East African countries. Additionally, the study endeavored to enrich the existing literature on mixture modeling approaches and their effectiveness in forecasting high-frequency time series data. The Ljung Box test was used to test for the lack of fit in the ARIMA, ANN, and Mixture models while RMSE and MAPE were used to compare the prediction performance of the models. The results established that ARIMA approach became weaker in accurately modeling and forecasting time series data whose frequency was greater than 48 while ANN was able to precisely handle time series data whose frequency was up to 336. Further, the study results showed that the mixture ARIMA-ANN model provided the best forecast accuracy compared to ARIMA and ANN models for high-frequency data and produced better fitting models even for hourly time series data, a phenomenon that could not be achieved by the single models. When applied to currency exchange rates, the study established ���������� − ������ (1,1,0)(5: 1: 2) 250 , ���������� −������(0,1,1)(5: 1: 2) 250 , ���������� − ������ (0,1,0)(5: 1: 2) 250 and ���������� −������ (1,1,0)(5: 1: 2) 250 respectively for the KSH/RWF, KSH/TSHS, KSH/USHS and KSH/BIF currency exchange rates. The models had lower MAPE and RMSE values compared to the corresponding ARIMA and ANN models.Item MATHEMATICAL MODELING ON TRANSMISSION DYNAMICS OF PNEUMONIA INFECTION WITH INTERVENTION INCORPORATING INTERNATIONAL TRAVELLERS SCREENING(THE CATHOLIC UNIVERSITY OF EASTERN AFRICA, 2024-08) EZEAKA VINCENT IKENNAPneumonia is one of the global pandemics which have afflicted humanity in various aspects of life among the young children and elderly one. In some developed countries like Kenya, it is discovered to be a highly airborne transmitted disease which leads to a high mortality rate of human beings. It has been discovered by the World Health Organization (WHO) that almost 16% deaths of children are due to pneumonia infection in most regions like South Asia and Sub-Sahara Africa. There exist several mathematical models which aimed at mitigating the transmission of Pneumonia infection. We take into consideration the screening of international travellers with intervention seeking to minimize the rate of the circulation of pneumonia infection led by the movement of human beings. The originality of this research lies on International Travellers Screening as a preventive and control mechanism of pneumonia transmission. We create and examine the pneumonia disease dynamics from a mathematical view using SXEIT model. The model includes five non-linear compartments namely; "Susceptible (S), Screened (X), Exposed (E), Infected (I) and Treated (T)". Also, we develop the Basic Reproduction number (Ro) in the study and examine the existence of all the equilibrium points; the Endemic equilibrium and Disease Free equilibrium, and analyze their stabilities. If the basic reproduction number R0 > 1, it records that the endemic equilibrium is globally stable and the disease persists, while if R0 < 1, then the disease will be eradicated out of the population. The model uses the preferred model system of differential equations which is subjected to numerical simulation using Matlab application. The research utilizes data collected from surveys of other writers and related works to parameterize and validate the model. The findings of this study are recommended to the Ministry of Health and World Health Organization (WHO) who may use them to strategize new ways of preventing the spread of Pneumonia infection.