Browsing by Author "Luboobi, Livingstone S."

Now showing 1 - 8 of 8
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    The HIV-HCV co-infection dynamics in absence of therapy
    (Strathmore University, 2019-08) Mayanja, Edison; Luboobi, Livingstone S.; Kasozi, Juma; Nsubuga, Rebecca
    HIV-HCV co-infection is whereby an individual is infected with both viruses HIV and HCV. Globally, approximately 4 to 5 million people are co-infected with HIV and HCV. HCV infection significantly causes morbidity and mortality among HIV patients. HCV is known to progress faster and cause more liver-related health problems and death among people who are HIV/AIDS positive than those who are negative. Co-infection with HCV complicates the management of HIV/AIDS. Mathematical modeling generally provides an explicit framework by which we can develop and communicate an understanding of transmission dynamics of an infectious disease. In this article, a deterministic model is used in which ordinary differential equations are formulated and analyzed to study the HIV-HCV co-infection dynamics in absence of therapy. The findings reveal that the basic reproduction number for HIV-HCV co infection dynamics is equal to the maximum of single-disease basic reproduction numbers. This implies that the dynamics of the HIV-HCV co-infection will be dominated by the disease with the bigger basic reproduction number
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    Mathematical 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.
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    Mathematical 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 Waema
    There 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.
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    Mathematical models for Hepatocytic-Erythrocytic dynamics and therapeutic control of Malaria
    (Strathmore University, 2017) Orwa, Titus O.; Mbogo, Rachel W.; Luboobi, Livingstone S.
    Malaria is one of the most frequently occurring infectious diseases worldwide (along with HIV/AIDS and tuberculosis), with almost 1 million deaths and an estimated 243 million clinical cases annually. An in-host model of malaria that describes the dynamics of the malaria parasite in the liver and blood stages and its interaction with liver cells, red blood cells and immune effectors is proposed. Conditions for existence of the diseases free equilibrium are derived. An in-host basic reproductive number is derived based on the next generation matrix method. For effective control of parasitemia, controls (antimalarials and vaccines) should target both the sporozoite and merozoite at the liver and blood stages respectively.
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    Modeling optimal control of Cholera disease under the interventions of vaccination, treatment and education awareness
    (Strathmore University, 2017) Obuya, Emmanuel; Namawejje, Hellen; Luboobi, Livingstone S.
    In this work, our main purpose is to formulate and analyse a mathematical model of the dynamics and optimal control strategies of cholera epidemic. We present and analyze a cholera model with controls, u1 for vaccination of the human population, u2 for treatment and u3 for health education campaigns. The basic reproductive number, R0, the effective reproductive number, Re as well as disease free equilibrium and endemic equilibrium points are computed. We derive and analyze the conditions for optimal control of the cholera disease using the Pon- tryagin’s maximum principle and simulated it for different control strategies. The results show that vaccination and education campaigns should be applied from the start of the epidemic followed by treatment.
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    "Stochastic model for In-Host HIV dynamics with therapeutic intervention
    (Hindawi Publishing Corporation, ) Odhiambo, John W.; Luboobi, Livingstone S.; Mbogo, Rachel Waema
    Untangling 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.
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    Stochastic model for In-Host HIV dynamics with therapeutic intervention
    Mbogo, 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.
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    Stochastic Model for Langerhans cells and HIV Dynamics in Vivo
    Mbogo, 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.