A nonlinear dynamics for risk contagion: analyzing the risk-free equilibrium

In this paper we perform the stability analysis of the risk-free equilibrium point which characterizes a financial contagion dynamics. The model is formulated in the Susceptible-Infected-Recovered approach by employing an analogy between economic sectors and ecosystems. The dynamics is nonlinear and characterized by a time delay which represents a period of financial immunity got after risk infection. In addition, contagion phenomenon is modelled by employing a Holling Type II functional response taking into account an incubation time for risk infection. The analysis around the risk-free steady state is performed in terms of both local asymptotic stability and global asymptotic stability by classical approach. Our results highlight the crucial role of the incubation time in establishing whether risk crisis can be eliminated from the economic sector at the long run, or it continues to exist in.