A Geospatial Bounded Confidence Model Including Mega-Influencers with an Application to COVID-19 Vaccine Hesitancy

The paper introduces a stochastic geospatial bounded-confidence model with mega-influencers and supports three qualitative claims by simulation: emergent geospatial clustering, eventual stabilization without tight consensus, and greater dispersion in the presence of mega-influencers. It does not provide formal proofs of these claims, relying instead on algorithmic specifications (including the probability kernel puv in eq. (2)) and empirical results (e.g., Fig. 5, Fig. 7) . The candidate solution provides partial mathematical arguments but under a different edge model (deterministic r-proximity rather than the paper’s time-redrawn, weighted, distance-attenuated, confidence-bounded probabilities) and strong extra assumptions (uniform in-degree bound D and b < ε with D·b ≤ ε) that are not part of the paper’s setup and conflict with typical parameter choices (b = ε = 1.5) . Part A of the candidate does not address dynamic, spatially localized clustering (it uses T = 0 on a complete graph), and Part B(i) refutes an “a.s. finite-time stabilization” claim the paper does not make (the paper uses a numerical stopping criterion, not a theorem) . Parts B(ii)–C qualitatively align with trends reported in the paper (more dispersion with mega-influencers), but the proofs apply to a different, more restricted model and cannot be taken as proofs for the paper’s claims.