Sleep is a recurring state of inactivity in which the brain undergoes a period of rest and restoration; its disturbances can severely affect health. Sleep and wake cycles can be mimicked in vitro: cortical neurons plated on Micro-Electrode Arrays (MEAs) show spontaneously synchronized, low-frequency firing patterns resembling the slow wave oscillations typical of NREM sleep. With specific compounds (e.g., Carbachol, orexin), network activity can be manipulated to switch to a wake state. To reduce the costs and ethical issues related to in vitro studies and to be more sustainable in research, in silico models are a powerful platforms. In this work, we adapted the Digitoids for modelling the electrophysiological features typical of the sleep and wake states observed in vitro. Digitoids are based on Hodgkin-Huxley formalism for membrane potential oscillations and on oxygen diffusion and consumption to fuel neuron metabolism and firing. In this way, it is possible to capture the absence of vascularization in vitro, which makes oxygen crucial for cell viability and functionality, and to reproduce the effect of Carbachol by modulating the calcium channels conductance. To test the accuracy of Digitoids in predicting the in vitro sleep and wake dynamics, human iPSC-derived cortical neurons were coupled to MEAs. Their spontaneous slow-oscillating electrophysiological activity was recorded and characterized. Then, network activity was modulated by delivering Carbachol and the recorded firing patterns are compared to the spontaneous activity. Preliminary results suggested that desynchronized firing patterns appear when the networks are stimulated with Carbachol, both in vitro and in silico.