  In this paper, we analyze dynamic switching networks, wherein 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 is developed assuming independence
between states of nodes. We identify the conditions under which the epidemic
dies 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 is later validated using
several networks (Watts-Strogatz, Barabasi-Albert, MIT reality mining graphs,
Regular, and Gilbert). A simplified version of the epidemic threshold is
proposed for undirected networks. Moreover, in the case of static networks, the
derived epidemic threshold is shown to match conventional analytical results.
Then, analytical results for the epidemic threshold of dynamic networksare
proved to be applicable to periodic networks. For dynamic regular networks, we
demonstrate that the epidemic threshold is identical to the epidemic threshold
for static regular networks. An upper bound for the epidemic spread probability
in dynamic Gilbert networks is also derived and verified using simulation.
