Competition between evidence-based and alternative medical paradigms in non-infectious diseases

Abstract

Standard epidemiological models coupled with evolutionary game theory (e.g., vaccination games) typically rely on the free-rider dilemma inherent to infectious diseases. In this paper, we present a coupled behavior-disease model where the underlying disease is non-infectious, and transmission occurs strictly at the cultural level. We model the competition between two medical paradigms, namely evidence-based medicine ($M$) and alternative medicine ($A$), using replicator dynamics driven by treatment-specific social-amplification coefficients. We show analytically that the nonlinearity of the coupled system arises from social feedback rather than from the underlying biological dynamics. Crucially, the stability analysis reveals that the system lacks isolated fixed points; instead, it converges to a one-dimensional continuous manifold of non-hyperbolic neutral equilibria, generating persistent path dependence in the cultural composition. Furthermore, we derive an explicit constant of motion that constrains each trajectory to a distinct invariant level set. Restricting this invariant to the equilibrium manifold yields a strictly monotonic selection function, uniquely determining the equilibrium selected from any given initial state. Our findings show that derivative-based cultural feedback is sufficient to generate a continuum of coexisting health paradigms, while asymmetric social amplification modifies this selection. Because transient interventions that directly alter paradigm adoption break this invariant, they shift the system to a different level set, producing persistent changes in the long-run cultural composition. The model thus reveals how societies retain a deterministic memory of prior health and treatment states, demonstrating that both misinformation shocks and targeted public health interventions can leave lasting structural changes long after the perturbation has ended.