Persistence is the remnant signal that plagues HgCdTe infrared detectors used for astronomy applications after a bright illumination. Briefly, any perturbation on these detectors generates a nonlinear signal with higher amplitude than a dark current and lasts for hours. The traditional hypothesis used to explain this phenomenon is based on trapping/emission processes from deep-level defects in the space charge region (SCR) of the diode. Inspired by deep-level transient spectroscopy formalism, we have developed an analytical model describing the trap emission current from the SCR of the photodiode. We also take into account the intrinsic non-linearity of the source follower per detector ROIC architecture. Compared to data obtained on detectors built in-house at CEA-LETI, the model allows the estimation that a trap density on the order of the residual doping is enough to explain the persistence amplitude. A graded trap density in the SCR is in addition necessary to explain the persistence measurement as a function of the stress amplitude. Limits of the model are also underlined in the case of higher persistence amplitude. In this case, trap density should be close to the doping. This implies that N doping of the diode would be compensated, which is an extreme scenario out of the scope of this model.