  We present the particle method for simulating the solution to the
path-dependent McKean-Vlasov equation, in which both the drift and the
diffusion coefficients depend on the whole trajectory of the process up to the
current time t, as well as on the corresponding marginal distributions. Our
paper establishes an explicit convergence rate for this numerical approach. We
illustrate our findings with numerical simulations of a modified
Ornstein-Uhlenbeck process with memory, and of an extension of the Jansen-Rit
mean-field model for neural mass.
