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

In this paper we perform the stability analysis of the risk-free equi- librium 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 repre- sents a period of financial immunity got after risk infection. In addition, contagion phenomenon is modelled by employing a Holling Type II func- tional 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 clas- sical approach. Our results highlight the crucial role of the incubation time in establishing whether risk crisis can be eliminated from the eco- nomic sector at the long run or it continues to exist in.