A Delay-Embedded D-SIRS Model for Associated Credit Risk Contagion on Complex Networks: Threshold, Equilibrium, and Robustness Analysis

Abstract

Associated credit risk can propagate through inter-firm credit, trade, asset, and liquidity linkages, particularly when risk recognition and intervention are delayed. Here we develop a delay-embedded delay-embedded susceptible-infected-recovered-susceptible (D-SIRS) model to study credit-risk contagion on complex inter-firm networks. The model combines a degree-based mean-field framework with degree-dependent asset connectedness, allowing network structure and exposure heterogeneity to jointly shape the contagion mechanism. We derive the contagion threshold and identify the conditions under which local credit stress either dies out or becomes persistent. The threshold rises with stronger immunization and recovery, but falls with longer delays, stronger asset connectedness, faster immunity waning, and greater degree heterogeneity. Numerical simulations show that Barabási-Albert (BA) scale-free networks have lower stability boundaries than more homogeneous benchmark networks. Node-level Monte Carlo simulations further show that the threshold-type transition remains visible under stochastic finite-network propagation, while robustness checks show that concentrating asset connectedness among high-degree firms amplifies systemic vulnerability. These results suggest that associated credit-risk governance should combine preventive screening, timely intervention, and post-distress recovery, rather than rely on a single policy instrument.