Mathematical Taxonomy of Health Insurance Models: Conventional Approaches and the Emergent C&C Paradigm

This paper introduces a formal mathematical taxonomy of four principal health insurance models: Bismarckian, Beveridgean, Commercial, and Collaborative & Contributive (C&C). Each model is analyzed for its structural characteristics, sustainability conditions, and demographic resilience under stress. Unique to the C&C model is the incorporation of trust as a variable affecting sustainability and participation. By comparing the equilibrium and value functions across models, the paper reveals fundamental differences in their capacity to withstand demographic and financial pressures. The proposed taxonomy enhances both theoretical understanding and practical evaluation of global health insurance systems.