A deterministic model of tuberculosis dynamics incorporating available hospital resources is formulated and studied. The model analysis reveals the existence of a disease-free equilibrium that is stable when the basic reproduction number R_0 is less than 1 and several endemic equilibria appear when R_0 is greater than 1. Two types of bifurcations were identified: a Hopf bifurcation, which suggests an oscillatory behavior in the disease dynamics, and a transcritical bifurcation that indicates the change in stability between equilibrium points according to the variations of R_0. A sensi- tivity analysis was conducted to study the most influential parameters of the model. Numerical simulations were performed to validate the theoretical results. This study highlights the crucial importance of efficient hospital resource management to keep the basic reproduction number R_0 below 1, which is essential to eradicate tuberculosis within the population.

Tuberculosis, Model, Basic reproduction number, Hospital resources, Numerical simulation