Mathematical modelling of In-vivo HIV optimal therapy and management

Ngina, Purity Muthoni
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Strathmore University
Human Immunodeficiency Virus (HIV) remains the main cause of premature death globally. In 2013, Kenya was the fourth largest endemic HIV country in the world having over 1.6 million people living with the virus. The fact that there is an increase in the rate of new-HIV infections in Africa and especially in Kenya underscores the need for adequate strategies to cope with this deadly disease and to achieve vision 2020. Where the government envision that, by 2020, 90% of all people living with HIV will know their HIV status, 90% of all people with diagnosed HIV infection will receive sustained antiretroviral therapy and 90% of all people receiving antiretroviral therapy will have viral suppression. Currently, there is no known cure for HIV, hence the most optimal way is the management of HIV infected people to prevent virus progression and HIV transmission. Although there has been progress in management of HIV by the use of antiretroviral drugs (ARTs), long-term use of these ARTs leads to overwhelming challenges. These challenges are: toxicity of the medication, nonadherence problems as a result of inaccessibility of comprehensive care centres, drug resistance-mutations and significant financial burdens. This study aimed at formulating and analysing mathematical in-vivo models for the interaction between HIV virions, CD4+ T-cells, CD8+ T-cells and the optimal control for effective therapy, whose numerical simulations would assist in giving more insight about the challenges aforementioned.Various mathematical methods including ordinary differential equations, Runge-Kutta forth order scheme and optimal control theory have been applied in the development and the analysis of the model. Analysis of the formulated model indicates existence of multiple equilibria whose stability and bifurcation analysis have been presented. From the simulated results, we have noted that early initiation of HIV treatment reduce viral replication in HIV infected people. In particular, highly active antiretroviral therapy (HAART) which include the combination therapy of Fusion inhibitor (FI), Reverse Transcriptase inhibitor (RTI) and Protease inhibitor (PI) in different proportions have been found to be more effective in treating HIV than a single drug therapy. The model simulations show how to best choose the proportions of FI, RTI and PI in order to maintain an acceptable level of CD4+ T-cells and, at the same time, reduce the side effects associated with their long term use. In addition, the most optimal way of administering ART drugs that lead to maximum benefit has been predicted from optimal control simulation. The findings give a significant explanation of why late initiation of ARTs might not be helpful to an HIV infected person and suggest that the controls ought to be optimal at the acute phase of infection where the viral replication is extremely high. If the controls are well implemented, many potential infections would be averted by lowering the viral load and increasing the number of the T-helper cells. This, in turn, will also lead to reduction in HIV transmission. Therefore, there is need for increased awareness campaigns to encourage people to know their HIV status and adhere to the prescribed treatment.The research outcomes in this study emphasizes the importance of “Anza Sasa”campaign that was launched on 15th July 2016 by the Government of Kenya through the Ministry of Health in collaboration with the National AIDS and STI Control program.
Thesis submitted in total fulfillment of the requirements for the Degree of Doctor of Philosophy in Biomathematics of Strathmore University
Human Immunodeficiency Virus, CD4+ T-cells, CD8+ T-cells, Antiretroviral Drugs, ART's, In-vivo HIV, In-vivo