[en] A set of model equations of the dissipative trapped ion instability is derived to confirm Saison, Wimmel and Sardei's infer that modification of the background trapped particle number density may be a possible saturation mechanism. Multiple time scale expansion scheme is applied to the nonlinear fluid equations of Kadomtsev and Pogutse by employing a usual ordering νsub(i) << ω << νsub(e), where νsub(j) is the effective collision frequency of j-th trapped particles and ω is the frequency of the instability. Model equations derived describe the time evolution of the modification of the background trapped particle number density and the amplitude of the dissipative trapped ion mode. (author)