  The presence of erratic or unstable paths in standard kinetic Monte Carlo
simulations significantly undermines the accurate simulation and sampling of
transition pathways. While typically reliable methods, such as the Gillespie
algorithm, are employed to simulate such paths, they encounter challenges in
efficiently identifying rare events due to their sequential nature and reliance
on exact Monte Carlo sampling. In contrast, the weighted ensemble method
effectively samples rare events and accelerates the exploration of complex
reaction pathways by distributing computational resources among multiple
replicas, where each replica is assigned a weight reflecting its importance,
and evolves independently from the others. Here, we implement the highly
efficient and robust weighted ensemble method to model
susceptible-infected-susceptible (SIS) dynamics on large heterogeneous
population networks. In particular, we explore the interplay between
stochasticity and contact heterogeneity which gives rise to large fluctuations,
leading to extinction (spontaneous clearance of infection). By studying a wide
variety of networks characterized by fat-tailed degree distributions, we are
able to compute the mean time to extinction as function of the various network
and epidemic parameters. Importantly, this method allows exploring
previously-inaccessible parameter regimes.
