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Applied Mathematics

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Browsing Applied Mathematics by Author "Achia, Thomas Noel Ochieng."

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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.