Epidemic Threshold in Dynamic Switching Networks

In this paper, we analyze dynamic switching networks where the networks switch arbitrarily among a set of topologies. For this class of dynamic networks, we derive an epidemic threshold considering the SIS epidemic model. First, an epidemic probabilistic model based on assumption of independence between states of nodes is developed. We identify conditions for the epidemic dying out by linearizing the underlying dynamical system and analyzing its asymptotic stability around the origin. The concept of joint spectral radius is then used to derive the epidemic threshold which we validate using a myriad of networks (Watts-Strogatz, Barabasi-Albert, MIT reality mining graphs, Regular, and Gilbert). A simplified version of epidemic threshold is proposed for undirected networks. Moreover, in the case of static networks, it is shown that the derived epidemic threshold matches with the conventional analytical results. Then, it is proved that analytical results for epidemic threshold of dynamic networks are applicable to periodic networks. We demonstrate for dynamic regular networks, the epidemic threshold is the same as the epidemic threshold for static regular networks. An upper bound for the probability of epidemic spread out in dynamic Gilbert networks is also derived and verified using simulation.