A Compartmental Model for Financial Systemic Risk‎: ‎Extending‎ ‎an‎ ‎SIRS‎ ‎Model‎ ‎to Capture Mitigation and Protection Dynamics

Document Type : Original Scientific Paper

Authors

1 ‎Department of Mathematics and Computer Science, ‎School of Natural Sciences‎, ‎Great Zimbabwe University‎, ‎‎Masvingo‎, ‎Zimbabwe

2 ‎Department of Mathematics and Applied Mathematics‎, Faculty of Science‎, ‎Pretoria‎, ‎South Africa and Institute of Research and Professional Training, Emirates Aviation University, Dubai International Academic City, UAE

10.22052/mir.2025.256837.1520

Abstract

‎Financial systemic risk refers to the transmission of distress among financial institutions‎, ‎posing a significant threat to economic stability‎. ‎Inspired by epidemiological modelling‎, ‎this study develops an extended compartmental framework based on the classical SIRS model to analyse the spread and control of financial systemic risk within a banking network‎. ‎The model introduces six compartments‎: ‎susceptible‎, ‎immune‎, ‎infected‎, ‎curated‎, ‎mitigated‎, ‎and removed to capture the diverse states of banks under systemic stress and regulatory intervention‎. ‎Central bank actions such as curatorship‎, ‎mitigation‎, ‎and temporary protection are explicitly incorporated‎. ‎The model is formulated as a system of ordinary differential equations‎, ‎and analytical techniques are employed to derive the risk reproduction number‎, ‎$R_{sr}$‎, ‎which serves as a threshold parameter governing the system’s long-term behaviour‎. ‎Two equilibrium points are identified‎: ‎the risk-free equilibrium‎, ‎which is locally and globally asymptotically stable when $R_{sr} < 1$‎, ‎and the endemic equilibrium‎, ‎which persists when $R_{sr} > 1$‎. ‎Numerical simulations demonstrate how variations in key parameters such as the rate of curatorship‎, ‎mitigation‎, ‎and protection affect the prevalence of financial contagion‎. ‎While the model does not yield fundamentally new theoretical insights‎, ‎it offers a structured framework for evaluating the impact of regulatory interventions‎. ‎The findings underscore the utility of epidemiological modelling in financial risk analysis and highlight the importance of timely and targeted control measures to prevent cascading failures in the banking sector‎.

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References

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Mathematics Interdisciplinary Research
Volume 11, Issue 1
March 2026
Pages 43-64

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