Recurrent high-order neural networks (ROHNNs) have been recognized for their great ability to approximate complex and nonlinear functions in the continuous and discrete time domain. Additionally, ROHNNs' architectures are very flexible and allow to incorporate to the neural model a priori information about the system structure. Exploiting these features, we present a discrete-time RHONN-based identification system for the description of a SIR epidemic model with impulsive control, which is assumed to be unknown, and combine the usage of a suitable learning algorithm for neural networks based on the famous extended Kalman filter. Simulation results of the proposed scheme are shown to illustrate its applicability.