Infrared hybridized detectors are widely used in astronomy, and their performance can be degraded by image persistence. This results in remnant images that can persist in the detector for many hours, contaminating any subsequent low-background observations. A different but related problem is reciprocity failure whereby the detector is less sensitive to low flux observations. It is demonstrated that both of these problems can be explained by trapping and detrapping currents that move charge back and forward across the depletion region boundary of the photodiodes within each pixel. These traps have been characterized in one 2.5-μm and two 5.3-μm cutoff wavelength Teledyne H2RG detectors. We have developed a behavior model of these traps using a five-pole infinite impulse response digital filter. This model allows the trapped charge in a detector to be constantly calculated for arbitrary exposure histories, providing a near-real-time correction for image persistence.