  We considered the Asynchronous SIR (susceptible-infected-removed) model on
Penrose and Ammann-Beenker quasiperiodic lattices, and obtained its critical
behavior by using Newman-Ziff algorithm to track cluster propagation by making
a tree structure of clusters grown at the dynamics, allowing to simulate SIR
model on non-periodic lattices and measure any observable related to
percolation. We numerically calculated the order parameter, defined in a
geographical fashion by distinguish between an epidemic state, characterized by
a spanning cluster formed by the removed nodes and the endemic state, where
there is no spanning cluster. We obtained the averaged mean cluster size which
plays the role of a susceptibility, and a cumulant ratio defined for
percolation to estimate the epidemic threshold. Our numerical results suggest
that the system falls into two-dimensional dynamic percolation universality
class and the quasiperiodic order is irrelevant, in according to results for
classical percolation.
