  Most theoretical tools available for the analysis of spreading processes over
networks assume exponentially distributed transmission and recovery times. In
practice, the empirical distribution of transmission times for many real
spreading processes, such as the spread of web content through the Internet,
are far from exponential. To bridge this gap between theory and practice, we
propose a methodology to model and analyze spreading processes with arbitrary
transmission times using phase-type distributions. Phase-type distributions are
a family of distributions that is dense in the set of positive-valued
distributions and can be used to approximate any given distributions. To
illustrate our methodology, we focus on a popular model of spreading over
networks: the susceptible-infected-susceptible (SIS) networked model. In the
standard version of this model, individuals informed about a piece of
information transmit this piece to its neighbors at an exponential rate. In
this paper, we extend this model to the case of transmission rates following a
phase-type distribution. Using this extended model, we analyze the dynamics of
the spread based on a vectorial representations of phase-type distributions. We
illustrate our results by analyzing spreading processes over networks with
transmission and recovery rates following a Weibull distribution.
