The threshold and quasi-stationary distribution for the SIS model on networks

2025-09-15

AI Summary

This study addresses the epidemic threshold and quasistationary infection distribution of the SIS model on arbitrary networks. We propose a dynamic state-space expansion method incorporating temporal memory, explicitly encoding the infection–recovery history of nodes within a mean-field framework—contrasting with conventional pair approximation, which neglects node-level temporal dynamics. Theoretically and numerically, our approach significantly improves accuracy in predicting both the epidemic threshold and the quasistationary prevalence across finite and infinite random graphs. It consistently outperforms classical pair approximation and heterogeneous mean-field methods on diverse synthetic and real-world networks. By bridging analytical tractability with empirical fidelity, this work establishes a novel, principled paradigm for modeling infectious disease spread on complex networks.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Reasoning under Uncertainty: Relational Probabilistic Models
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

We study the Susceptible-Infectious-Susceptible (SIS) model on arbitrary networks. The well-established pair approximation treats neighboring pairs of nodes exactly while making a mean field approximation for the rest of the network. We improve the method by expanding the state space dynamically, giving nodes a memory of when they last became susceptible. The resulting approximation is simple to implement and appears to be highly accurate, both in locating the epidemic threshold and in computing the quasi-stationary fraction of infected individuals above the threshold, for both finite graphs and infinite random graphs.

Problem

• Improving epidemic threshold prediction for SIS model
• Enhancing quasi-stationary infection rate computation accuracy
• Developing dynamic state expansion with node memory

Innovation

• Dynamic state space expansion
• Memory of susceptibility timing
• Improved pair approximation accuracy