  In this paper we present a simplified model of a proportional taxation system
where citizens decide whether to pay taxes or evade them. We initially derive a
dynamic equation for the fraction of evaders and then present both its critical
points and equilibrium stable states for a well-mixed population and for a
fixed audit probability. Our theoretical predictions consider different
possible income distributions (homogeneous and heterogeneous), time-dependent
audit probability and different possible social topologies, by means of
selected complex network configurations. All derived results are validated and
confirmed by extended Monte Carlo simulations. Finally, some policy
implications aimed to reduce tax evasion are suggested, with regards to the tax
and fine rates and the audit probability.
