We propose a flexible computational EDFA dynamic model for amplified modulated probes used in long-distance distributed sensors based on pulse coding, employing Rayleigh, Raman and Brillouin Scattering phenomena. The EDFA dynamics is studied numerically solving the differential equations of the reservoir model for Erbium ion concentrations. The model allows one to identify the optimal choice of gain parameters as well as the gain control mechanism needed for gain stabilization, minimizing both the code-words output power fluctuations and avoiding nonlinear effects which can degrade the distributed sensor performance when using pulse coding techniques such as Simplex, Golay and Cyclic-Simplex. The technique allows distributed sensors to be robust against fluctuations induced by long amplified code sequences, ensuring at the same time enough optical gain to enhance their performance, especially in terms of sensing distance, without overcoming the threshold of nonlinear propagation effects.