This study addresses a current research gap in African Studies concerning Health Systems Resilience in the Face of Epidemics: Lessons from Africa in Ghana. 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. Health Systems Resilience in the Face of Epidemics: Lessons from Africa, Ghana, Africa, African Studies, qualitative study This work contributes a formal specification, transparent assumptions, and mathematically interpretable claims.