Title: Equivalence between non-Markovian and Markovian dynamics in epidemic spreading processes,
Abstract: A general formalism is introduced to allow the steady state of non-Markovian
processes on networks to be reduced to equivalent Markovian processes on the
same substrates. The example of an epidemic spreading process is considered in
detail, where all the non-Markovian aspects are shown to be captured within a
single parameter, the effective infection rate. Remarkably, this result is
independent of the topology of the underlying network, as demonstrated by
numerical simulations on two-dimensional lattices and various types of random
networks. Furthermore, an analytic approximation for the effective infection
rate is introduced, which enables the calculation of the critical point and of
the critical exponents for the non-Markovian dynamics.