Browsing by Author "Muriithi, D. K."

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Mathematical Analysis of a Comprehensive HIV AIDS Model: Treatment versus Vaccination
(HIKARI Ltd,, 2013) Okongo, M. O.; Kirimi, J.; Murwayi, A. L. Murwayi; Muriithi, D. K.
A comprehensive deterministic HIV/AIDS transmission model incorporating social behaviour, treatment, vaccination, stages of infection, age structures, discrete time delay and vertical transmission is presented and rigorously analyzed. Two age structures are considered with group one consisting of children aged (0 - a) years and group two consisting of adults aged (a) years and above. In this study we investigate wether a trade-off exists between vaccination and treatment. Numerical simulations shows that treatment that does not reduce infectiousness is worse than when the treatment is not applied at all, however when coupled with effective counseling, then it is very effective in combating the spread of the disease and finally eliminating it. A trade off seems to exists between vaccination and treatment and therefore careful considerations should be made when vaccination and treatment is to be applied together because a combination of the two could be counterproductive or helpful depending on how it is implemented.
Ordinal Logistic Regression Versus Multiple Binary Logistic Regression Model for Predicting Student Loan Allocation
(2012) Muriithi, D. K.; Kihoro, J.; Waititu, A.
This paper examines two different methodologies to a classification problem of higher education loan applicants. The paper looks into the allocations made by the Higher Education Loans Board (HELB) relative to the economic status of the applicant. In this article, we modeled Higher Education Loans Board (HELB) loan application data from three public universities to determine whether the loan was allocated based on the needs of the respective applicants. The data was classified into two natural categories of those not allocated the loan (0) and those allocated the loan (1). This paper classified further to consider the amounts awarded by the HELB. This was possible since we observed that HELB loans were awarded in distinct categories (Kshs 0, Kshs 35,000, Kshs 40,000, Kshs 45,000, Kshs 50,000), Kshs 55,000 Kshs 60,000). In this study, we used ordinal logistic regression and multiple binary logistic regressions in classifying the applicants into the identified categories. The models were generated that included all predictor variables that were useful in predicting the response variable. This study found that HELB allocate a loan amount to Kshs 40,000 but anything behold Kshs 40,000 is based on information provided by an applicant. The study revealed that the loans were not awarded based on the need of respective applicants. This has led to misclassification when allocating loan. The study found that wealth and amount of fees paid for siblings were other factors that could be considered to identify needy applicants. This results show that an ordinal regression model gives accurate estimates that can enable HELB make a viable awarding decision. It is expected that proper determination of the most accurate model will go a long way in minimizing the number of mis-classifications when awarding HELB loan. The study raises questions on the criteria used by HELB in loan allocation but further studies may be commissioned to confirm or disapprove our findings.
Singular Spectrum Analysis: An Application to Kenya’s Industrial Inputs Price Index
(EJ-MATH, European Journal of Mathematics and Statistics., 2022) Emmanuel, K. K.; Wagala, A.; Muriithi, D. K.
Time series modeling and forecasting techniques serve as gauging tools to understand the time-related properties of a given time series and its future course. Most financial and economic time series data do not meet the restrictive assumptions of normality, linearity, and stationarity of the observed data, limiting the application of classical models without data transformation. As non-parametric methods, Singular Spectrum Analysis (SSA) is data- adaptive; hence do not necessarily consider these restrictive assumptions as in classical methods. The current study employed a longitudinal research design to evaluate how SSA fist Kenya’s monthly industrial inputs price index from January 1992 to April 2022. Since 2018, reducing the costs of industrial inputs has been one of Kenya’s manufacturing agendas to level the playing field and foster Kenya’s manufacturing sector. It was expected that Kenya’s Manufacturing Value Added hit a tune of 22% by 2022. The study results showed that the SSA (L = 12, r =7) (MAPE = 0.707%) provides more reliable forecasts. The 24-period forecasts showed that the industrial inputs price index remains high above the index in 2017 before the post-industrial agenda targeting a reduction in the cost of industrial inputs. Thus, the industrial input prices should be reduced to a sustainable level.