Weighted-Ensemble method for detecting rare events in the SIS model on complex degree-assortative networks

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 (WE) 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 apply the WE method to model Susceptible-Infected-Susceptible (SIS) dynamics on long time scales, where stochasticity and contact heterogeneity lead to large fluctuations and spontaneous infection clearance, known as disease extinction. Traditionally, random networks, which lack correlations between nodes' degrees, were used as baseline models for disease spread. However, real-world networks often exhibit degree assortativity, where nodes with similar degrees are more likely to connect. As a result, we study a wide variety of networks, with varying assortativity and heterogeneity strength. Notably, the WE method enables us to compute the quasi-stationary distribution and mean time to disease extinction in previously inaccessible parameter regimes.