Epidemic Processes Over Time-Varying Networks

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 provide insights that lead to long-term societal benefits. Prior research has focused mainly on network models with static graph structures; however, the systems being modeled typically have dynamic graph structures. In this paper, we consider virus spread models over networks with dynamic graph structures, and we investigate the behavior of these systems. We perform a stability analysis of epidemic processes over time-varying networks, providing sufficient conditions for convergence to the disease-free equilibrium (the origin, or healthy state), in both the deterministic and stochastic cases. We present simulation results and discuss quarantine control via simulation.