Browsing by Author "Luboobi, S .Livingstone"

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    HIV drug resistance
    (Elsevier Ltd, 2019) Luboobi, S .Livingstone
    In 2013 the World Health Organization recommended the initiation of antiretroviral therapy (ART) to any person who tests HIV positive irrespective of his/her CD4 count. However, implementation of the new guidelines poses a lot of challenges especially in Sub-Sahara Africa such as: drug side effects, drug resistance-mutations and significant financial burdens. Most importantly, it has been established that HIV resistance and subsequent virologic failure occur in a substantial proportion of HIV-infected patients receiving HAART. This study therefore, seeks to investigate the emergence of drug resistant HIV virus during treatment with the aim of determining the proper use of HIV therapy that would lessen drug resistance. To carry out the analysis a ten dimensional in-vivo mathematical model is proposed for HIV dynamics. The model is formulated in such away that it takes into account two virus strain, that is, the wild type as well as the naive type HIV virus. The in-vivo model is shown to be both biologically meaningful and mathematically well posed. The existence of unique infection-free equilibrium point is determined and both its local and global stability investigated. In addition, the basic reproduction number for each viral strain is computed using the next generation matrix method. An optimal control model is proposed and analysed by applying Pontryagin maximum principle, to obtain the optimal drug combination for HIV treatment. Here two drugs, that is, Reverse Transcriptase inhibitor and Protease inhibitor are used as the controls in the model. We provide an objective function for the minimisation of the number of wild type HIV virus and the drug resistant virus as well as the costs associated with the use of Reverse Transcriptase inhibitor and protease inhibitor. The forward backward sweep method is applied to numerically solve the optimality system. From the numerical simulations, it is evident that protease inhibitor is the most effective drug in controlling HIV infection. The results suggest that prolonged use of HAART leads to development of drug resistant and that people with drug-resistant infection could play a core role in the epidemic of HIV.
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    A mathematical model for the dynamics of malaria in a human host and mosquito vector with temporary immunity
    (Elsevier Ltd, 2007) Luboobi, S .Livingstone
    In the paper, we propose a model that tracks the dynamics of malaria in the human host and mosquito vector. Our model incorporates some infected humans that recover from infection and immune humans after loss of immunity to the disease to join the susceptible class again. All the new borne are susceptible to the infection and there is no vertical transmission. The stability of the system is analyzed for the existence of the disease-free and endemic equilibria points. We established that the disease-free equilibrium point is globally asymptotically stable when the reproduction number, and the disease always dies out. For the disease-free equilibrium becomes unstable and the endemic equilibrium is globally asymptotically stable. Thus, due to new births and immunity loss to malaria, the susceptible class will always be refilled and the disease becomes more endemic.
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    Modeling the Impact of Climate Change on the Dynamics of Rift Valley Fever
    (Hindaw, 2014) Luboobi, S .Livingstone
    A deterministic SEIR model of rift valley fever (RVF) with climate change parameters was considered to compute the basic reproduction number and investigate the impact of temperature and precipitation on . To study the effect of model parameters to , sensitivity and elasticity analysis of were performed. When temperature and precipitation effects are not considered, is more sensitive to the expected number of infected Aedes spp. due to one infected livestock and more elastic to the expected number of infected livestock due to one infected Aedes spp. When climatic data are used, is found to be more sensitive and elastic to the expected number of infected eggs laid by Aedes spp. via transovarial transmission, followed by the expected number of infected livestock due to one infected Aedes spp. and the expected number of infected Aedes spp. due to one infected livestock for both regions Arusha and Dodoma. These results call for attention to parameters regarding incubation period, the adequate contact rate of Aedes spp. and livestock, the infective periods of livestock and Aedes spp., and the vertical transmission in Aedes species.