  Complex or hostile environments can sometimes inhibit the movement
capabilities of diffusive particles or active swimmers, who may thus become
stuck in fixed positions. This occurs, for example, in the adhesion of bacteria
to surfaces at the initial stage of biofilm formation. Here we analyze the
dynamics of active particles in the presence of trapping regions, where
irreversible particle immobilization occurs at a fixed rate. By solving the
kinetic equations for run-and tumble motion in one space dimension, we give
expressions for probability distribution functions, focusing on stationary
distributions of blocked particles, and mean trapping times in terms of
physical and geometrical parameters. Different extensions of the trapping
region are considered, from infinite to cases of semi infinite and finite
intervals. The mean trapping time turns out to be simply the inverse of the
trapping rate for infinitely extended trapping zones, while it has a nontrivial
form in the semi-infinite case and is undefined for finite domains, due to the
appearance of long tails in the trapping time distribution. Finally, to account
for the subdiffusive behavior observed in the adhesion processes of bacteria to
surfaces, we extend the model to include anomalous diffusive motion in the
trapping region, reporting the exact expression of the mean-square
displacement.
