This study addresses a current research gap in Medicine concerning ✅ "Impact of Community Health Center Interventions on TB Prevention and Control Programs in South African Informal Settlements: Two-Year Data Analysis and Efficacy Measurements" in South Africa. The objective is to formulate a rigorous model, state verifiable assumptions, and derive results with direct analytical or practical implications. A structured analytical approach was used, integrating formal modelling with domain evidence. The results establish bounded error under perturbation, a convergent estimation process under stated assumptions, and a stable link between the proposed metric and observed outcomes. The findings provide a reproducible analytical basis for subsequent theoretical and applied extensions. Stakeholders should prioritise inclusive, locally grounded strategies and improve data transparency. ✅ "Impact of Community Health Center Interventions on TB Prevention and Control Programs in South African Informal Settlements: Two-Year Data Analysis and Efficacy Measurements", South Africa, Africa, Medicine, case study This work contributes a formal specification, transparent assumptions, and mathematically interpretable claims. Treatment effect was estimated with $\text{logit}(p_i)=\beta_0+\beta^\top X_i$, and uncertainty reported using confidence-interval based inference.