This study addresses a current research gap in Medicine concerning Mental Health First Aid Training for Senegalese Police Officers' Effectiveness in Reducing Post-Traumatic Stress Disorder (PTSD) Rates in Gambia. The objective is to formulate a rigorous model, state verifiable assumptions, and derive results with direct analytical or practical implications. A mixed-methods design was used, combining survey and interview data collected over the study period. 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. Mental Health First Aid Training for Senegalese Police Officers' Effectiveness in Reducing Post-Traumatic Stress Disorder (PTSD) Rates, Gambia, Africa, Medicine, longitudinal 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.