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Abstract
Tuberculosis (TB) has been a human infectious disease for a long time. Yet, there are currently 2 billion persons infected with TB in the world. About 2 million people died in 2008 due to TB. It is essential to study why TB can survive a long time in human history and explore TB controls that might help eliminate TB in the future. This thesis is composed of three projects of mathematical studies of TB transmission and controls. The first project explores the possible reason for TB persistence. Simulation results suggest that TB has the optimal strength for persistence with a prolonged latency period. The second project studies the impact of HIV prevalence on TB epidemic. Simulation results show that the majority of TB cases are HIV negative when the HIV prevalence is below 25%. The number of HIV positive TB cases outnumbers the number of HIV negative TB cases when the HIV prevalence is over 25%. The third project analyzes the cost effectiveness of active case finding (ACF) in urban and rural Uganda areas. Results suggest that ACF implementation is more cost effective in the urban area than in the rural in terms of cost per TB case averted and ACF is more cost effective if implemented for a longer period.