Based on the 2024 report from the World Health Organization, tuberculosis continues to pose a global threat. In response to this, we developed a modified five-compartmental SVIMDR model to evaluate the stability of the disease, specifically considering multi-drug-resistant patients, within a feasible human population. The stability analysis was conducted in relation to the reproduction number (R0) using the generalized Hyers Ulam stability, Jacobi method and modified Lyapunov-Volterra stability. The model was validated qualitatively using a modified Banach fixed point theorem and Lipchitz contraction condition approach. To assess the impact of multi-drug resistance on the infection dynamics, two relapse rates were incorporated to check the effect on the model which negatively impacts it. The model was estimated numerically using a modified Adam’s Bashforth predictor-corrector method. The graphical solutions revealed that the introduced inhibitory effect (saturation factor) within the model demonstrated that as saturation increases, the infection become more stable (R0<1). According to the findings in this research, we will have fewer multi-drug-resistant patients provided the saturation factor is implemented properly.