Mixing time for a noisy SIS model on graphs

Abstract: We study the mixing time of the noisy SIS (Susceptible-Infected-Susceptible) model on graphs. The noisy SIS model is a variant of the standard SIS model, which allows individuals to become infected not just due to contacts with infected individuals but also due to external noise. We show that, under strong external noise, the mixing time is of order $O(n \log n)$. Additionally, we demonstrate that the mixing time on random graphs, namely Erd\"os--R\'enyi graphs, regular multigraphs, and Galton--Watson trees, is also of order $O(n \log n)$ with high probability.