The time-dependent plasma discharge ionization region model (IRM) has been under continuous development during the past decade and used in several studies of the ionization region of high-power impulse magnetron sputtering (HiPIMS) discharges. In the present work, a complete description of the most recent version of the IRM is given, which includes improvements, such as allowing for returning of the working gas atoms from the target, a separate treatment of hot secondary electrons, addition of doubly charged metal ions, etc. To show the general applicability of the IRM, two different HiPIMS discharges are investigated. The first set concerns 400 mu s long discharge pulses applied to an Al target in an Ar atmosphere at 1.8 Pa. The second set focuses on 100 mu s long discharge pulses applied to a Ti target in an Ar atmosphere at 0.54 Pa, and explores the effects of varying the magnetic field strength. The model results show that Al2+-ions contribute negligibly to the production of secondary electrons, while Ti2+-ions effectively contribute to the production of secondary electrons. Similarly, the model results show that for an argon discharge with Al target the contribution of Al+-ions to the discharge current at the target surface is over 90% at 800 V. However, at 400 V the Al+-ions and Ar+-ions contribute roughly equally to the discharge current in the initial peak, while in the plateau region Ar+-ions contribute to roughly 2/3 of the current. For high currents the discharge with Al target develops almost pure self-sputter recycling, while the discharge with Ti target exhibits close to a 50/50 combination of self-sputter recycling and working gas-recycling. For a Ti target, a self-sputter yield significantly below unity makes working gas-recycling necessary at high currents. For the discharge with Ti target, a decrease in the B-field strength, resulted in a corresponding stepwise increase in the discharge resistivity.