Browsing by Author "Mbogo, Rachel Waema"

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    HIV Drug Resistance: Insights From Mathematical Modelling
    (Applied Mathematical Modelling, 2019) Ngina, Purity; Mbogo, Rachel Waema; Luboobi, Livingstone S.
    In 2013 the World Health Organization recommended the initiation of antiretroviral ther- apy (ART) to any person who tests HIV positive irrespective of his/her CD4 + count. How- ever, 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 vi- rologic 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 op- timal 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 ob- jective 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 in- hibitor and protease inhibitor. The forward backward sweep method is applied to numer- ically solve the optimality system. From the numerical simulations, it is evident that pro- tease 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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    Mathematical Model for the In-Host Malaria Dynamics Subject to Malaria Vaccines
    (Letters in Biomathematics, 2018) Orwa, Titus Okello; Mbogo, Rachel Waema; Luboobi, Livingstone Serwadda
    Despite the success of the existing malaria control strategies, reported malaria cases are still quite high. In 2016, the WHO reported about 216 million malaria cases; 90% of which occurred in the WHO African Region. In this paper, a mathematical model for the in-host Plasmodium falciparum malaria subject to malaria vaccines is formulated and analysed. An efficacious pre-erythrocytic vaccine is shown to greatly reduce the severity of clinical malaria. Based on the normalized forward sensitivity index technique, the average number of merozoites released per bursting blood schizont is shown to be the most sensitive parameter in the model. Numerical simulation results further suggest that an efficacious blood stage vaccine has the potential to reduce the burst size of the blood schizonts and maximize the rate of activation of CD8+ T cells during malaria infection. Moreover, vaccine combinations that are efficacious might help in achieving a malaria free population by the year 2030. This paper provides useful insights in malaria vaccine control and a unique opportunity to intensify support and funding for malaria vaccine development.