We performed extra-cellular recordings simultaneously from the whisker primary sensory cortex (wS1) and the medial prefrontal cortex (mPFC) of mice performing a tactile detection task and then fit a recurrent spiking neural network (RSNN) to the recorded activity. We assume that neural dynamics are defined by standard conductance-based spiking neurons with adaptation. We optimize the entire connectivity matrix (within and across areas) using back-propagation through time (BPTT) for spiking neural networks [1, 2] and synaptic rewiring [3] while respecting Dale’s law. After optimization, the resulting matrix provides a possible connectivity pattern that explains the recorded activity statistics in wS1 and mPFC. To validate this modelling approach, we perform a virtual ablation on the fitted model and compare the resulting activity with experimental manipulations affecting the late response component in wS1. Our model reproduces the finding that a secondary-late response of the whisker stimulation is due to feedback from higher-order cortical areas [4, 5]. Since many other areas are involved in this task in a real mouse brain, we cannot claim that we built a full model of wS1 and mPFC. However, we believe that this modelling approach can help us to understand better the activity in cortical circuits and test hypotheses concerning possible neural computations such as the importance of feedback from high-order areas to wS1.