On the dynamics of a SIR model for a financial risk contagion

This work starts from an analogy between financial systems and ecosystems so that the SIR mathematical approach can be revisited in modeling a kind of risk contagion among financial players. We are interested on a specific type of financial risk contagion which identifies firms as the key participants responsible for propagating this contagion. In this respect, the proposed mechanism facilitating this transmission is the Supply Chain framework. In this direction, we focus on a new SIR dynamic with time delay which represents the “financial immunity” after recovery. A complete and robust analysis about asymptotic stability is performed for both risk-free and not-free-risk steady states at the long run, by applying Lyapunov functional method. The model is applied to perform some simulations with application in different Italian economic sectors.