Browsing by Author "Mbogo, Rachel Waema"
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- ItemManaging chronic conditions through hosted medical records in KenyaMbogo, Rachel Waema; Mbogo, SalesioComplex medical conditions are rising in developing countries at very alarming rates. E.g. projections from the World Health Organization’s global burden of disease and risk factors report chronic diseases are responsible for up to 50% of disease burden in selected countries. Diseases hitherto associated with the developed countries like diabetes, cancer and Hypertension are in the increase in developing countries. Management of these medical conditions calls for a new way of delivering health care services in these countries. Long term therapeutic management of these diseases requires availability of medical records to a provider when a patient presents him/herself at a medical facility. Advances in technology present opportunities for informing systematic management of these chronic conditions within constraints of resources that these countries face.
- ItemMathematical model for HIV and CD4+ cells dynamics in vivo(IJAPM, ) Mbogo, Rachel Waema; Luboobi, Livingstone S.; Odhiambo, John W.Mathematical models are used to provide insights into the mechanisms and dynamics of the progression of viral infection in vivo. Untangling the dynamics between HIV and CD4+ cellular populations and molecular interactions can be used to investigate the effective points of interventions in the HIV life cycle. With that in mind, we develop and analyze a stochastic model for In-Host HIV dynamics that includes combined therapeutic treatment and intracellular delay between the infection of a cell and the emission of viral particles. The unique feature is that both therapy and the intracellular delay are incorporated into the model. We show the usefulness of our stochastic approach towards modeling combined HIV treatment by obtaining probability generating function, the moment structures of the healthy CD4+ cell, and the virus particles at any time t and the probability of virus clearance. Our analysis show that, when it is assumed that the drug is not completely effective, as is the case of HIV in vivo, the predicted rate of decline in plasma HIV virus concentration depends on three factors: the initial viral load before therapeutic intervention, the efficacy of therapy and the length of the intracellular delay.
- ItemMathematical modelling of in-vivo dynamics of HIV subject to the influence of the CD8+T-Cells(Strathmore University, 2017) Ngina, Purity; Luboobi, Livingstone S.; Mbogo, Rachel WaemaThere have been many mathematical models that analyses in-vivo dynamics of HIV. However, in most cases the attention has been on the interaction of the HIV virions and the CD4+T-cells. This paper brings in the intervention of the CD8+T-cells in seeking, destroying and killing the infected CD4+T-cells. The paper presents and analyses a non-linear ordinary differential equations model and applies the results in investigating the in-vivo dynamics of HIV in presence of the CD8+Tcells. It is assumed that the CD8+T-cells are activated by presence of the infected CD4+T-cells. Both the disease-free and endemic equilibria are established and their stability investigated. In addition, the basic reproductive number is determined and its sensitivity with respect to the parameters of the model established. The results show that in acute infection the CD8+T-cells play a paramount role in reducing HIV viral replication. We also observe that the model exhibits backward and trans critical bifurcation for some set of parameters implying the existence of multiple endemic equilibrium when basic reproductive number is less than unity. The results therefore, suggest the need for more study on how to eliminate backward bifurcation.
- ItemPerformance modeling of web serversMbogo, Rachel Waema; Acosta (Dr.), Freddie
- ItemSemi-Markov model for evaluating the HIV patient treatment costMbogo, Rachel Waema; Luboobi, Livingstone S.; Odhiambo, John W.The aim of this study is to model the progression of HIV/AIDS disease and evaluate the cost of the anti-retroviral therapy for an HIV infected patient under ART follow-up using Non homogeneous semi-Markov processes. States of the Markov process are defined by the seriousness of the sickness based on the clinical scores. The five states considered are: Asymptomatic (CD$^{+}_{4}$ count > 500 cells/microliter); Symptomatic 1 (350 < CD$^{+}_{4}$ count ≤ 500 cells/microliter); Symptomatic 2 (200 < CD$^{+}_{4}$ count ≤ 350 cells/microliter); AIDS (CD$^{+}_{4}$ count ≤ 200 cells/microliter) and Death (Absorbing state). The first four states are named as good or alive states. The models formulated can be used to gain insights on the transition dynamics of the HIV patient given the follow-up time. The transition probability Model, when fitted with data will give insights on the conditional probability of a patient moving from one disease state to another, given the current state and the follow-up time. This model will also give the probability of survival for the HIV patient under treatment given the current state and follow-up time. The total Lifetime Treatment Cost model obtained, when applied to real data will give the cost of managing an HIV patient given the starting state, the treatment combination which incurs minimum cost and which treatment combination is most effective at each state. The treatment reward model also when applied to real data will give the state, which a patient should be maintained so that they remain healthy, noninfectious and productive to the society. Also the model will show the optimal/effective time to initiate treatment, which can be used to give advice on how to handle the HIV infecteds given their states.
- Item"Stochastic model for In-Host HIV dynamics with therapeutic intervention(Hindawi Publishing Corporation, ) Odhiambo, John W.; Luboobi, Livingstone S.; Mbogo, Rachel WaemaUntangling the dynamics between HIV and CD4 cellular populations and molecular interactions can be used to investigate the e fective points of interventions in the HIV life cycle. With that in mind,we propose and show the usefulness of a stochastic approach towards modeling HIV and CD4 cells Dynamics in Vivo by obtaining probability generating function, the moment structures of the healthy CD4 cell and the virus particles at any time t and the probability of HIV clearance. The unique feature is that both therapy and the intracellular delay are incorporated into the model. Our analysis show that, when it is assumed that the drug is not completely eff ective, as is the case of HIV in vivo, the probability of HIV clearance depends on two factors: the combination of drug effi cacy and length of the intracellular delay and also education to the infected patients. Comparing simulated data for before and after treatment indicates the importance of combined therapeutic intervention and intracellular delay in having low, undetectable viral load in HIV infected person.
- ItemStochastic model for In-Host HIV dynamics with therapeutic interventionMbogo, Rachel Waema; Odhiambo, John W.; Luboobi, Livingstone S.;Mathematical models are used to provide insights into the mechanisms the dynamics between HIV and CD4+ cellular populations and molecuar interactions can be used to investigate the eff ective points of interventions in the HIV life cycle. With that in mind, we develop and analyze a stochastic model for In-Host HIV dynamics that includes combined therapeutic treatment and intracellular delay between the infection of a cell and the emission of viral particles, which describes HIV infection of CD4+ T-cells during therapy. The unique feature is that both therapy and the intracellular delay are incorporated into the model. Models of HIV infection that include intracellular delays are more accurate representations of the biological data. We show the usefulness of our stochastic approach towards modeling combined HIV treatment by obtaining probability distribution, variance and co-variance structures of the healthy CD4+ cell, and the virus particles at any time t. Our analysis show that, when it is assumed that the drug is not completely eff ective, as is the case of HIV in vivo, the predicted rate of decline in plasma HIV virus concentration depends on three factors: the death rate of the virons, the e cacy of therapy and the length of the intracellular delay.
- ItemStochastic Model for Langerhans cells and HIV Dynamics in VivoMbogo, Rachel Waema; Luboobi, Livingstone S.; Odhiambo, John W.Many aspects of the complex interaction between HIV and the human immune system remain elusive. Our objective is to study these inter-actions, focusing on the speci c roles of langerhans cells (LCs) in HIV infection. In patients infected with HIV, a large amount of virus is as-sociated with LCs in lymphoid tissue. To assess the influence of LCs on HIV viral dynamics during anti-retroviral therapy, we present and analyse a stochastic model describing the dynamics of HIV, CD4+ T-cells, and LCs interactions under therapeutic intervention in vivo. We per-form sensitivity analyses on the model to determine which parameters and/or which interaction mechanisms strongly affect infection dynamics.
- ItemStochastic modeling of HIV dynamics within an individual and its managementMbogo, Rachel WaemaMathematical models can facilitate the understanding of complex biomedical systems such as in HIV/AIDS. Untangling the dynamics between HIV and CD4+ cellular populations and molecular interactions can be used to investigate the effective points of interventions in the HIV life cycle. With that in mind, we will develop state transition systems dynamics and stochastic model that can be used to examine various alternatives for the control and treatment of HIV/AIDS, and also determine the cost of treating an HIV patient such that the expected lifetime or quality-adjusted lifetime of the patient is maximized. The AIDS epidemic is extremely dynamic; this dynamism orthogonally complicates interventions embraced for the management of the epidemic. This research is mostly motivated by the fact that eradication of the HIV virus is not attainable with the current available drugs and now the focus is not virus eradication but the management and control of the virus progression. We will develop and analyze Non-Homogeneous Semi-Markov Stochastic (NHSMS) Models of HIV biological process and compute internal transition probabilities. Specifically the models will target: the HIV internal dynamics in an infected person, defined by CD4+ levels and Viral load, and the disease control and management strategies put in place. Secondly we will use Non-Homogeneous Semi-Markov Reward (NHSMR) processes to determine the cost of treating an HIV patient, and lastly, we consider the revenue generated by such person (as well as the expert advice by such infected person into various projects) such that the Cost Benefit Analysis (CBA) can also be conducted.
- ItemUse of generating functions in HIV/AIDS transmission modelsMbogo, Rachel Waema; OTTIENO, J. A.M. Prof.This study is concerned with the mathematical modeling for human immunodeficient virus (HIV) transmission epidemics. The mathematical models are specified by stochastic differential equations. The differential equations are solved by use of Generating Functions (GF).In the process of literature review, a conceptual framework is drawn which summarizes the literature on HIV/ AIDS transmission epidemic models. Models based on Mother to child transmission (MTCT) (age group 0-5 years), Heterosexual transmission (age group 15 and more years) and combined case (incorporating all groups and the two modes of transmission) are developed and the expectations and variances of Susceptible (S) persons, Infected (I) persons and AIDS cases found. It is shown from the combined model that MTCT and Heterosexual models are special cases of the combined model.General aspects of modeling HIV/ AIDS are described in chapter 1, Chapter 2 focuses on the literature review. MTCT model is formulated in chapter 3. Heterosexual model is developed in chapter 4, Chapter 5 focuses on the development of the Combined model. Chapter 6 concludes the study.