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11	Mathematical modeling of TB disease dynamics in a crowded population. Maku Vyambwera, Sibaliwe January 2020 (has links) Philosophiae Doctor - PhD / Tuberculosis is a bacterial infection which is a major cause of death worldwide. TB is a curable disease, however the bacterium can become resistant to the first line treatment against the disease. This leads to a disease called drug resistant TB that is difficult and expensive to treat. It is well-known that TB disease thrives in communities in overcrowded environments with poor ventilation, weak nutrition, inadequate or inaccessible medical care, etc, such as in some prisons or some refugee camps. In particular, the World Health Organization discovered that a number of prisoners come from socio-economic disadvantaged population where the burden of TB disease may be already high and access to medical care may be limited. In this dissertation we propose compartmental models of systems of differential equations to describe the population dynamics of TB disease under conditions of crowding. Such models can be used to make quantitative projections of TB prevalence and to measure the effect of interventions. Indeed we apply these models to specific regions and for specific purposes. The models are more widely applicable, however in this dissertation we calibrate and apply the models to prison populations. Cross effect Awaiting trial Remand Sentenced convict Two-group TB model Almost sure exponential stability Stochastic TB model Removal rate Inflow of infecteds Prison TB model Crowded environment Multi-drug resistant TB Basic reproduction number Optimal control Lyapunov function Endemic equilibrium Disease-free equilibrium

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Mathematical modeling of TB disease dynamics in a crowded population.