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Global Stability, Optimal Control, and Cost-Effectiveness of Measles Transmission in Ethiopia: A Mathematical Modeling Approach With Convex Convergence

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  • Hailu Tkue Welu

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 (u1) and treatment (u2) 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 R0=1. Calibration against Ethiopian data (2015–2019) yields R0=1.3973 (95% CI: [1.32, 1.48]). Optimized controls reduce Rc 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.

Suggested Citation

  • Hailu Tkue Welu, 2026. "Global Stability, Optimal Control, and Cost-Effectiveness of Measles Transmission in Ethiopia: A Mathematical Modeling Approach With Convex Convergence," Journal of Applied Mathematics, Hindawi, vol. 2026, pages 1-13, September.
    • Handle: RePEc:hin:jnljam:6458291
    DOI: 10.1155/jama/6458291
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