Epilepsies are characterized by electrophysiological crises in the brain, which were first observed thanks to electroencephalograms. However, it is known that seizures originating from one or more specific regions may or may not spread to the rest of the brain, while the exact mechanisms are unclear. We propose three computational models at the neural network scale to study the underlying dynamics of seizure propagation, understand which specific features play a role, and relate them to clinical or experimental observations. We consider both network features, such as the internal connectivity structure and single neuron model, and input properties in our characterization. We show that a paroxysmal input leads to a dynamical heterogeneity inside the network, non-trivially related with its architecture, which may or may not entrain it into a seizure. Although hard to anticipate because of the intricate nature of the instability involved, the seizure propagation might be circumvented upon acting on the network during a specific time window. As we deal with a complex system, which seems to depend non trivially on various parameters, we propose a probabilistic approach to the propagative/non-propagative scenarios, which may serve as a guide to control the seizure by using appropriate stimuli.SignificanceOur computational study shows the specific role that the inhibitory population can have and the possible dynamics regarding the propagation of seizure-like behavior in three different neuronal networks. The study conducts in this paper results from the combination of structural aspects and time-continuous measures, which helps us unravel the internal dynamics of the network. We show the existence of a specific time window favorable to the reversal of the seizure propagation.