Strategic Awareness-Driven Control of Tuberculosis Dynamics: A Differential Equation Framework

This study develops a deterministic differential equation framework to investigate tuberculosis (TB) transmission while incorporating patient awareness as a behavioral factor influencing treatment initiation and disease dynamics. A core methodological innovation of this study is the explicit integration of behavioral determinants specifically patient awareness alongside classical epidemiological factors to more accurately mirrors real-world complexities. The model bifurcates both susceptible and infectious populations into unaware (Su, Iu) and aware (Sa, Ia) states, effectively quantifying how awareness governs the propensity for treatment-seeking and adherence. Rigorous mathematical analysis confirms that the model is well posed, establishing both the positivity and boundedness of solutions to ensure biological feasibility. Using the next-generation matrix method, the study derives the basic reproduction number (R0), which is decomposed into contributions from unaware (Ru) and aware (Ra) individuals. Stability analysis further proves that the disease-free equilibrium is globally asymptotically stable when R0 1. Comprehensive sensitivity analysis and numerical simulations reveal that while recruitment and transmission coefficients exacerbate disease spread, strategic enhancements in patient awareness and treatment initiation rates are the most effective levers for reducing R0. Consequently, this work provides transformative insights for public health, demonstrating that targeted educational interventions are foundational to the long-term control and elimination of TB.