Browsing by Author "Wainaina, Mary"

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    Analysis of Transmission Dynamics of Anthrax in Animals: A Modeling Approach
    (Journal of Scientific Research & Reports, 2019) Wainaina, Mary; Githire, George Thiong’o; Kimathi, George
    This paper seeks to develop a SIR model with vaccination compartment in the study of anthrax transmission dynamics in animal population. The model employ ordinary differential equations in the formulation of its equation. The model’s steady states solutions are investigated. The disease free equilibrium and endemic equilibrium of the model are analyzed qualitatively. Vaccination rate below a certain critical value causes the anthrax disease to persist. Recruitment and contact rates are the most sensitive parameters that significantly contribute to the basic reproductive ratio.
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    Bayesian Model Averaging in Modeling of State Specific Failure Rates in HIV/AIDS Progression
    (Mathematics and Statistics, 2022) Mwirigi, Nahashon; Simwa, Richard Onyino ; Wainaina, Mary; Sewe, Stanley
    In modeling HIV/AIDS progression, we carried out a comprehensive investigation into the risk factors for statespecific-failure rates to identify the influential co-variates using Bayesian Model averaging method (BMA). BMA provides a posterior probability via Markov Chain Monte Carlo (MCMC) for each variable that belongs to the model. It accounts for model uncertainty by averaging all plausible models using their posterior probabilities as the weights for model-averaged predictions and estimates of the required parameters. Patients’ age, and gender, among other co-variates, have been found to influence the state-specific-failure rates highly. However, the impact of each of the factors on the state specific-failure was not quantified. This paper seeks to evaluate and quantify the contribution of the patient’s age and gender, CD4 cell count during any two consecutive visits, and state movement on the state-specific-failure rates for patients transiting either to the same, better or worse state. We used R Studio statistical Programming software to implement the method by applying BMS and BMA packages. State movement had a comparatively large coefficient with a posterior inclusion probability (PIP) of 0.8788 (87.88%). Hence, the most critical variable followed by observation-two-CD4-cell-count with a PIP of 0.1416 (14.16%), age and gender were the last with a PIP of 0.0556 (5.56%) and 0.0510 (5.10%) respectively for patients transiting to the same state. For patients transiting to a better state, the patients’ age group dominated with a PIP of 0.9969 (99.69%), followed by patients’ gender with a PIP of 0.0608 (6.08%). Patients’ CD4 cell count during the second observation had the least PIP of 0.0399 (3.99%). For patients transiting to a worse disease state, patients CD4 cell count during the second observation proved to be the most important, with a PIP of 0.6179(61.79%) followed by state movement with a PIP of 0.2599 (25.99%), patients gender tailed with a PIP of 0.0467
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    Mathematical Modeling of Drug Abuse as an Infectious Disease in Secondary Schools Incorporating Guidance and Counseling
    (International Journal of Mathematics Trends and Technology, 2021-09) Wainaina, Mary; Muketo, Cecilia Kalekye; Kimathi, George
    Drug abuse is a major problem that has affected many young people in our society. In this study, we looked at drug abuse as an infectious disease in secondary schools. We developed a SEIGWR model which is a mathematical model of drug abuse as an infectious disease with six compartments; susceptible, exposed, infected, guided and counseled, rehabilitated and recovered. The model stability and the existence of equilibrium points was determined. From the quantitative analysis of the study, it was found out that the local stability existed when R0 < 1. From the numerical analysis of the drug abuse model, we determined that guidance and counseling affects the dynamics of the model. We established that an increase in guidance and counseling leads to a decrease in the number of infections. This suggests that there is a need for all the relevant stakeholders in the secondary schools to increase the rate at which guidance and counseling is offered in the schools. The study suggested that guidance and counseling would serve as a control strategy if given at an early age when the students are still in the primary schools.
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    Weibull Distribution as the Choice Model for State-Specific Failure Rates in HIV/AIDS Progression
    (Mathematics and Statistics, 2022) Mwirigi, Nahashon; Sewe, Stanley; Wainaina, Mary; Simwa, Richard Onyino
    This study considered the problem of selecting the best single model for modeling state-specific failure rates in HIV/AIDS progression for patients on antiretroviral therapy with age and gender as risk factors using exponential, twoparameter, and three-parameter Weibull distributions. CD4 count changes in any two consecutive visits, the mean waiting time (µ), and transitional rates (λ) for remaining in the same state or transiting to a better or a worse state were analyzed. Various model selection criteria, namely, Akaike Information Criteria (AIC), Bayesian Information Criteria (BIC), and Log-Likelihood (LL), were used in each specific disease state. The Maximum Likelihood Estimation (MLE) method was applied to obtain the parameters of the distributions used. Plots of State-specific transition rates (λ) depicted constant, increasing, decreasing, and unimodal trends. Three-parameter Weibull distribution was the best for male patients and patients aged (40-69) years transiting in the states 1-2, 3-4, and 4-5, and 1-2, 3-4, and 5-6, respectively, and for male, female patients, and patients aged (40-69), remaining in the same state. Two-parameter Weibull distribution was the best for female patients and patients aged (20-39) years transiting in the states 1-2, 2-3, 4-5, and 1-2, 2-3, 3-4, respectively. Exponential distribution proved inferior to the other two distributions used.