Mathematical analysis of the effects of BCG vaccination and treatment on tuberculosis transmission dynamics

Tuberculosis is an infectious disease caused by the bacterium Mycobacterium tuberculosis (MTB) that enters the body through the respiratory system and is mainly spread through the air. This study develops and analyzes a non-linear deterministic SVEITRS compartmental model and this framework explicitly integrates two critical clinical realities: the rate of treatment failure where individuals fail to clear the infection and return to an active infectious state and a specific TB-induced death rate operating directly within the treatment class. We analytically derive the basic reproduction number, , which serves as the fundamental threshold parameter for disease elimination.