Global Stability, Optimal Control, and Cost‐Effectiveness of Measles Transmission in Ethiopia: A Mathematical Modeling Approach With Convex Convergence
Hailu Tkue Welu
Source abstract
Measles remains a persistent threat in Ethiopia, affecting thousands of families despite ongoing vaccination efforts. Previous models have not simultaneously addressed global stability with disease‐induced mortality ( d > 0), optimal control tailored to Ethiopian data, or cost‐effectiveness. We fill these gaps through a deterministic SEIR model with vaccination ( u 1 ) and treatment ( u 2 ) controls. Using Lyapunov functions and the geometric approach of Li and Muldowney, we establish global stability for both equilibria without the restrictive assumption d = 0, extending prior Ethiopian studies. Bifurcation analysis confirms forward transcritical behavior at . Calibration against Ethiopian data (2015–2019) yields (95% CI: [1.32, 1.48]). Optimized controls reduce to 0.4167, avert 68.7% of infections, and achieve a cost‐effectiveness ratio of $2.73 per infection averted. A 2D surface visualization illustrates the convex convergence of the optimal control algorithm. These findings provide rigorous evidence supporting combined vaccination and treatment for measles elimination in Ethiopia.
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