Modeling the spread of contagiousness is well known in epidemiology. However, theapplication of spread modeling to the banking system is quite recent.Optimal control theory analyzes the properties of controlled systems, ie systems on which one canact by means of a command.In this work, we present a liquidity risk problem in the banking system with an optimal controlterm is formulated in order to study the impact of a possible central bank measure in the economy,simulating data from the largest European banks.Then, the proposed approach allows qualitative specifications of contagion in obtaining bankingand adequate analysis and prognosis within the development of the financial and macroeconomicsector as a whole. We show that our model de-reflects the reality of the largest European banks.The simulations were done with optimal control python, and the main results are taken for threedistinct scenarios.