A Nonlinear Dynamics for Risk Contagion: Theoretical Remarks

We employ an epidemiological approach to explain how risk may spread in a given economic system. Precisely, the analogy between eco- nomic systems and ecosystems is exploited and an original Susceptible- Infected-Recovered model with time delay is adopted to describe risk contagion by a nonlinear dynamic. The economic player population is divided into a set of distinct compartments, which are defined in terms of risk with low and high level. The time delay represents the period of financial immunity that some agents get from recovery after risk infection. Moreover, the contagion phenomenon is modelled by a Holling Type II functional response, which accounts for an incubation time from the contact between susceptible and infected players up to the actual financial distress. The existence of a unique solution of the proposed delay differential system is stated, moreover the main qualitative features are discussed. Actually, we prove that the dynamics remains positive during the whole-time horizon, and it admits two different stationary states.