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Masters Degrees (Applied Mathematics)

Permanent URI for this collectionhttps://hdl.handle.net/10413/7108

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Browsing Masters Degrees (Applied Mathematics) by Author "Chirove, Faraimunashe."

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    Impact of exogenous reinfection on TB infection in a genetically susceptible population.
    (2013) Mwangi, Wangari Isaac.; Chirove, Faraimunashe.; Achia, Thomas Noel Ochieng.
    In this study we investigated the impact of exogenous reinfection on genetically resistant and genetically sensitive sub populations. We qualitatively analysed the dynamics of TB by assuming that TB is transmitted in two ways namely homogeneous and heterogeneous modes of transmission. Analytically, we computed the fundamental thresholds used to measure disease persistence; the basic reproduction number R₀; and found that the exogenous reinfection parameters do not appear in the basic reproduction number. Hence, basic reproduction number derived in presence of exogenous reinfection does not adequately predict the course of a TB epidemic. We obtained the exogenous reinfection threshold which indicated that exogenous reinfection complicates TB dynamics. Both analytical and simulation results disclosed that when exogenous reinfection is above exogenous reinfection threshold TB dynamics were governed by a backward bifurcation implying TB may continue to invade the population despite basic reproduction number being less than one. We computed critical value of basic reproduction numbers Rᴄ and found that TB can only be eradicated if basic reproduction number is reduced below critical value Rc. Furthermore, we incorporated TB therapy in heterogeneous model among individuals with clinically active TB and performed sensitivity and uncertainty analysis using Latin Hypercube Sampling. The sensitivity and uncertainty results showed that transmission rates, reactivation rates and proportion that is genetically resistant greatly infuenced outcome variables of our TB model.
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    Using spectral methods on HIV infection with TAT and SSU72 activation.
    (2016) Mungwe, S'yanda Nkanyiso.; Chirove, Faraimunashe.; Motsa, Sandile Sydney.
    HIV dynamics within the host are complex especially when a reservoir of latently infected CD4+ T cells are present. The failure of the immune system and antiviral therapy to suppress the virus has been suggested to be enhanced by the latently infected CD4+ T cells which are responsible for persistence of HIV within the host. Cells remaining in latent state have been shown to lack suffcient levels of Tat and associated activation-dependent host factor that are necessary for processive transcription of the virus. Tat is a protein that is capable of activating the latently infected CD4+ T cells. Recently, as a protein, Ssu72 was found to be responsible for activation and replication of the virus. Ssu72 enhances the effects of Tat activation in a mutualistic interactive manner. The interaction of Tat and Ssu72 thus, enhances the activation of the latently infected CD4+ T cells which may in turn expose the virus for possible attack by the immune system reaction. In the current study, we modify a constant virus HIV model to incorporate the effects of Tat and Ssu72 on latently infected CD4+ T cells. We analyze the models using both analytic and numerical techniques. Important threshold was derived and model analysis carried out. The incorporation of Tat and Ssu72 proteins on the HIV-1 model with a constant virus shows that, with time the unifected and infectious classes decrease to zero for a threshold value of 30-40 copies of each protein.