Stability and sensitivity analysis of a nonlinear compartmental model for banking risk contagion

Articles in Press

Document Type : Research Article

Authors

Soukaina IBNOU KADY ¹

Adil Meskaf ²

Karam Allali ³

¹ Experimental Laboratory of Innovation in Technology and Simulations, Faculty of Sciences, Chouaib Doukkali University, El Jadida, Morocco.

² Department of SEG, Faculty of Economic and Social Legal Sciences, Chouaib Doukkali University, El Jadida, Morocco.

³ Laboratory of Mathematics, Computer Science and Applications, Faculty of Sciences and Technologies, Hassan II University of Casablanca, Mohammedia, Morocco.

10.22067/ijnao.2026.99100.1885

Abstract

In this work, we study a mathematical model that describes the dynamics of a nonlinear financial system and explains how systemic risk propagates within a banking system. The proposed model is formulated as a system of differential equations structured into five compartments: unexposed, exposed, distressed, recovered, and liquidated. Two mechanisms are incorporated: a direct early-intervention pathway that allows distressed banks to return directly to the unexposed state and a reintegration channel from the liquidated state to the unexposed state. Using the next-generation matrix approach, we derive the risk reproduction number and establish the system’s stability properties. We analyse the equilibrium points and prove the global asymptotic stability of the risk-free equilibrium via a Lyapunov function and the local and global asymptotic stability of the persistent-risk equilibrium via the Routh-Hurwitz criterion and a Lyapunov function. Finally, the numerical simulations and the LHS-PRCC sensitivity analysis illustrate the effects of contagion, intervention, and reintegration on the dynamics of the system.

Keywords

Systemic risk

Banking contagion

Mathematical modelling

Stability analysis

Risk reproduction number

Subjects

• Modeling and Simulation

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