This article is the second in a trilogy presenting the S-AI-Health framework — a formally grounded, intrinsically parsimonious, hormonally regulated, and natively explainable clinical intelligence architecture. Building on the theoretical foundations, global architecture, and five canonical health hormones established in Article I, the present article delivers two core formal contributions: the complete typology of the twenty-six specialized clinical agents organized in seven functional families with their hormonal coupling and HL7 FHIR-compatible input-output contracts, and the full mathematical modeling of the hormonal dynamics governing agent orchestration. The mathematical framework provides the reaction-diffusion hormonal dynamics on the dynamic clinical care graph, the clinically grounded cross inhibition matrix, the circadian modulation law, the Euler-Maruyama discretization with Lyapunov stability guarantees, the primal-dual parsimonious orchestration under wearable energy budget constraints, and the symbolic care engram memory equations enabling contextual recall and intrinsic regulatory explainability. Together, Articles I and II provide the complete architectural and mathematical specification of S-AI-Health. Article III presents the full experimental evaluation on the SAI-UT+ Health testbench across ten clinical operational scenarios.