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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 us to work with very large system sizes, where Monte Carlo simulations are useless due to memory needs. We then study the susceptible-infected-removed 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 us to solve arbitrary epidemiclike models provided that they can be described by mean-field rate equations.
Moreno et al. (2003) studied this question.