  Measurements of the per-event charged-particle yield as a function of the
charged-particle transverse momentum and rapidity are performed using $p+$Pb
collision data collected by the ATLAS experiment at the LHC at a centre-of-mass
energy of $\sqrt{s_{NN}}=5.02$ TeV. Charged particles are reconstructed over
pseudorapidity $|\eta|<2.3$ and transverse momentum between $0.1$ GeV and $22$
GeV in a dataset corresponding to an integrated luminosity of $1$ $\mu b^{-1}$.
The results are presented in the form of charged-particle nuclear modification
factors, where the $p+$Pb charged-particle multiplicities are compared between
central and peripheral $p+$Pb collisions as well as to charged-particle cross
sections measured in pp collisions. The $p+$Pb collision centrality is
characterized by the total transverse energy measured in $-4.9<\eta<-3.1$,
which is in the direction of the outgoing lead beam. Three different
estimations of the number of nucleons participating in the $p+$Pb collision are
carried out using the Glauber model and two Glauber-Gribov colour-fluctuation
extensions to the Glauber model. The values of the nuclear modification factors
are found to vary significantly as a function of rapidity and transverse
momentum. A broad peak is observed for all centralities and rapidities in the
nuclear modification factors for charged-particle transverse momentum values
around $3$ GeV. The magnitude of the peak increases for more central collisions
as well as rapidity ranges closer to the direction of the outgoing lead
nucleus.
