  Epidemic models are increasingly used in real-world networks to understand
diffusion phenomena (such as the spread of diseases, emotions, innovations,
failures) or the transport of information (such as news, memes in social
on-line networks). A new analysis of the prevalence, the expected number of
infected nodes in a network, is presented and physically interpreted. The
analysis method is based on spectral decomposition and leads to a universal,
analytic curve, that can bound the time-varying prevalence in any finite time
interval. Moreover, that universal curve also applies to various types of
Susceptible-Infected-Susceptible (SIS) (and Susceptible-Infected-Removed (SIR))
infection processes, with both homogenous and heterogeneous infection
characteristics (curing and infection rates), in temporal and even disconnected
graphs and in SIS processes with and without self-infections. The accuracy of
the universal curve is comparable to that of well-established mean-field
approximations.
