  We introduce two dimensional fermionic band models with two orbitals per
lattice site, or one spinful orbital, and which have a non-zero topological
Chern number that can be changed by varying the ratio of hopping parameters. A
topologically non-trivial insulator is then realized if there is one fermion
per site. When interactions in the framework of the Hubbard model are
introduced, the effective hopping parameters are renormalized and the system's
topological number can change at a certain interaction strength, $U=\bar U$,
smaller than that for the Mott transition. Two different situations may then
occur: either the anomalous Hall conductivity $\sigma_{xy}$ changes abruptly at
$\bar U$, as the system undergoes a transition from one topologically
non-trivial insulator to another, or the transition is through an anomalous
Hall metal, and $\sigma_{xy}$ changes smoothly between two different quantized
values as $U$ grows. Restoring time-reversal symmetry by adding spin to
spinless models, the half-filled system becomes a $\mathbb{Z}_2$ topological
insulator. The topological number $\nu$ then changes at a critical coupling
$\bar U$ and the quantized spin Hall response changes abruptly.
