This paper presents a theoretical analysis of the optimal control structure for a class of nonlinear biological systems characterized by a cascade configuration. Using Pontryagin’s Minimum Principle, the qualitative proper- ties of the optimal intervention policy are derived. Two fundamental theorems are established: first, it is proven that classical singular arcs are excluded near the terminal time under a quadratic cost functional, thereby ensuring a unique and well-defined interior control. Second, the necessity of treatment persistence in the final phase of the intervention is rigorously established, demonstrating that terminating therapy prematurely is mathematically suboptimal when the objective includes minimizing the terminal state. These analytical findings are applied to the biomarker dynamics of Alzheimer’s disease. The results indicate that an abrupt discontinuation of anti-amyloid therapy at the end of the treatment horizon is inconsistent with the derived optimal structure, providing a theoretical basis for sustaining therapeutic intervention in progressive neurodegenerative disorders

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