The evolution of dissipative dust-ion acoustic (DIA) rogue waves is studied in a collisional dusty plasma with superthermal electrons. Multiple-time-scale reduction shows that the nonlinear dynamics of low-frequency waves reduces to a modified nonlinear Schr¨odinger (mNLS) equation. This equation captures the main features of modulated waves and shows a criterion in determining the maximum time for the occurrence of the modulational instability. It is found that the impact of such an energetic tail of electrons is to narrow the stability region in a dusty plasma with source and sink.Within the instability window, we have shown that the mNLS equation in a weakly dissipative plasma is responsible for the formation of DIA rogue waves. The possible region for the existence of dissipative rogue waves is precisely defined for physical parameters. It is shown that the rogue wave profile is very sensitive to any changes in the electron superthermality and dissipative parameters. Index Terms—Low dissipation, modulational
