Epidemic Processes over Time-Varying Networks

TL;DR

This paper studies how viruses spread over networks with changing connections, analyzing stability and control strategies to better understand and mitigate epidemics in dynamic systems.

Contribution

It introduces a stability analysis framework for epidemic processes on time-varying networks, extending prior static network models to dynamic graph structures.

Findings

Stability conditions for disease-free states in dynamic networks

Simulation results demonstrating epidemic behavior over time-varying graphs

Proposed quarantine control strategies based on model insights

Abstract

The spread of viruses in biological networks, computer networks, and human contact networks can have devastating effects; developing and analyzing mathematical models of these systems can be insightful and lead to societal benefits. Prior research has focused mainly on network models with static graph structures, however the systems being modeled typically have dynamic graph structures. Therefore to better understand and analyze virus spread, further study is required. In this paper, we consider virus spread models over networks with dynamic graph structures, and investigate the behavior of diseases in these systems. A stability analysis of epidemic processes over time-varying networks is performed, examining conditions for the disease free equilibrium, in both the deterministic and stochastic cases. We present simulation results, propose a number of corollaries based on these simulations, and discuss quarantine control via simulation.