Abstract
This study investigates the dynamics of tuberculosis transmission through mathematical modeling, incorporating exogenous reinfections and different treatment approaches for latent tuberculosis infections. We examine three types of treatment rates: saturated, unsaturated, and mass screening-then-treatment. Our results reveal that both saturated treatment and mass screening-then-treatment can lead to a backward bifurcation, while unsaturated treatment does not. To determine the global dynamics of the models, we employ a persistent approach that avoids classifying the steady mode. By applying the models to China, we demonstrate that the data favors the use of unsaturated treatment. If unsaturated treatment is not feasible, the optimal strategy is to screen high-risk groups, identify LTBIs, and administer unsaturated treatment. Saturated treatments are not recommended.
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