Positron Emission Tomography (PET) is a functional quantitative medical imaging modality with main applications in oncology and treatment of neurodegenerative diseases. The reconstruction step solves a tomographic ill-posed inverse problem with Poisson noise, with particularly high intensity for dynamic protocols. The injected dose, radioactive tracer distribution, and noise level, are also varying across the exams, which requires to devise a sophisticated regularization scheme adapted to the protocol. In this work, we focus on constructing a parametric model of the dose-dependence with a large number of hyperparameters in regularized dynamic PET reconstruction. Our objective is to emphasize the interpretability of the learned parameters. Classical grid search becomes inefficient to explore such a highdimensional space of hyperparameters. This work investigates a new approach based on the Deep Equilibrium (DEQ) framework. Starting from an iterative algorithm, DEQ performs learning on the fixed point of this algorithm seen as a (deep) sequence of parameterized iterations. The dose-dependence model is then built from a series of DEQ estimates obtained for a constant number of detected events. The proposed method is validated on a synthetic 2D+t database derived from acquired data of a dynamic PET protocol.