Efficient weighted-ensemble network simulations of the SIS model of epidemics

TL;DR

This paper introduces an efficient weighted ensemble simulation method for modeling SIS epidemic dynamics on large heterogeneous networks, enabling accurate estimation of disease extinction times in complex scenarios.

Contribution

The study applies the weighted ensemble method to SIS epidemic models on large networks, improving the sampling of rare events like disease extinction.

Findings

Successfully computed mean extinction times in complex network regimes.

Demonstrated robustness of the weighted ensemble method for epidemic simulations.

Explored the impact of contact heterogeneity on disease dynamics.

Abstract

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, and explore the interplay between stochasticity and contact heterogeneity which ultimately gives rise to disease clearance. Studying a wide variety of networks characterized by fat-tailed asymmetric degree distributions, we are able to compute the mean time to extinction and quasi-stationary distribution around it in previously-inaccessible parameter regimes.