  A microscopic dynamic model is here constructed and analyzed, describing the
evolution of the income distribution in the presence of taxation and
redistribution in a society in which also tax evasion and auditing processes
occur. The focus is on effects of enforcement regimes, characterized by
different choices of the audited taxpayer fraction and of the penalties imposed
to noncompliant individuals. A complex systems perspective is adopted: society
is considered as a system composed by a large number of heterogeneous
individuals. These are divided into income classes and may as well have
different tax evasion behaviors. The variation in time of the number of
individuals in each class is described by a system of nonlinear differential
equations of the kinetic discretized Boltzmann type involving transition
probabilities.
