This paper aims to provide a resiliency management strategy of the air transportation network through network stability theory. To ensure the network to recover quickly from an upset condition, an optimization problem has been introduced through network stability upon the meta-population epidemic process model, which is a low-dimensional approximate model of the air traffic flow network. The delay propagation over air traffic network has been modeled as an epidemic spreading process model, which allows to define the whole network through a few states of the individuals (i.e., flights) and recovery rates of the nodes (i.e., airports). The physical parameters of the network extracted from real flight data set are transformed into a parameter set of the epidemic model enabling to simulate the propagation of delay. Moreover, self-organizing maps are used, generating the discretized representation of the input space through an artificial neural network to analyze the European air traffic network with regard to resiliency metrics. Through examples with historical real flight data, it is shown that the applied methodology to control the infection rates, which has the direct projection to operational applications such as ground holding and flight cancellation, effectively enhances the resiliency of the air traffic network under disruptive events.