Consider the paper Li, Yang, and Zhou - Global stability of an epidemic model with latent stage and vaccination.

Reading the entire paper isn't required. At the top of page 2168 in the journal, the author splits the region in three cases (C1, C2, C3) as a consequence of (16). This is understood for proving global stability of the disease-free equilibrium.

Next, they went on to prove the endemic equilibrium, the same technique is applied as the disease free equilibrium but this time we have a set of inequalities labelled (22). They then consider 9 cases (C1–C9) but I don't know why they split the region in that particular way. Any ideas? Or was it a typo?