Does propagation of chaos hold for coloured epidemic models with heterogeneous infectivity when the infection kernel has long-range dependence, and if so, at what rate does the empirical measure converge to the mean-field limit?

The coloured epidemic paper establishes functional law of large numbers and propagation of chaos for structured epidemic models where individuals carry distinct types or colours affecting their susceptibility and infectivity. However, the results rely on kernels that decay fast enough to ensure well-posedness and tightness of the particle system. The open problem is whether propagation of chaos survives when the infection kernel encodes long-range dependence, analogous to the correlations studied in Hermite processes and fractional Brownian motion settings, and what the precise rate of convergence of the N-particle empirical measure to the limiting nonlinear Fokker-Planck type equation is as a function of N and the dependence parameter.