  We introduce a numerical method to solve epidemic models on the underlying
topology of complex networks. The approach exploits the mean-field like rate
equations describing the system and allows to work with very large system
sizes, where Monte Carlo simulations are useless due to memory needs. We then
study the SIR epidemiological model on assortative networks, providing
numerical evidence of the absence of epidemic thresholds. Besides, the time
profiles of the populations are analyzed. Finally, we stress that the present
method would allow to solve arbitrary epidemic-like models provided that they
can be described by mean-field rate equations.
