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This paper investigates the dynamics of systemic risk in banking networks by analyzing equilibrium points and stability conditions. The focus is on a model that incorporates interactions among distressed and undistressed banks. The equilibrium points are determined by solving a reduced system of equations, considering both homogeneous and heterogeneous scenarios. Local and global stability analyses reveal conditions under which equilibrium points are stable or unstable. Numerical simulations further illustrate the dynamics of systemic risk, while the theoretical findings offer insights into the behavior of distressed banks under varying conditions. Overall, the model enhances our understanding of systemic financial risk and offers valuable insights for risk management and policymaking in the banking sector. [ABSTRACT FROM AUTHOR]

In recent times, all world banks have been threatened by the liquidity risk problem. This phenomenon represents a devastating financial threat to banks and may lead to irrecoverable consequences in case of negligence or underestimation. In this article, we study a mathematical model that describes the contagion of liquidity risk in the banking system based on the SIR epidemic model simulation. The model consists of three ordinary differential equations illustrating the interaction between banks susceptible or affected by liquidity risk and tending towards bankruptcy. We have demonstrated the bornness and positivity of the solutions, and we have mathematically analyzed this system to demonstrate how to control the banking system's stability. Numerical simulations have been illustrated by using real data to support the analytical results and prove the effects of different system parameters studied on the contagion of liquidity risk. [ABSTRACT FROM AUTHOR]