Recent findings indicate that astrocytes might play a functional role in triggering epileptic seizures. To test both the role of astrocytes on neuronal firings under normal conditions and the role they could play in epilepsy, we build here a computational model where four neurons and an astrocyte interact. Based on a mathematical model previously described in the literature, our model allows to investigate the dynamics of neuronal firing in this mini-network. In particular, we describe the conditions that can lead to hypersynchronous firings.