  Although viral spreading processes taking place in networks are often
analyzed using Markovian models in which both the transmission and the recovery
times follow exponential distributions, empirical studies show that, in many
real scenarios, the distribution of these times are not necessarily
exponential. To overcome this limitation, we first introduce a generalized
susceptible-infected-susceptible (SIS) spreading model that allows transmission
and recovery times to follow phase-type distributions. In this context, we
derive a lower bound on the exponential decay rate towards the infection-free
equilibrium of the spreading model without relying on mean-field
approximations. Based on our results, we illustrate how the particular shape of
the transmission/recovery distribution influences the exponential rate of
convergence towards the equilibrium.
