This paper characterizes the systemic dynamics of risk contagion within interconnected supply chain ecosystems by developing a degree-resolved susceptible-exposed-Infectious-recovered-susceptible (SEIRS) framework on heterogeneous network topologies. Utilizing the heterogeneous mean-field theory, we analytically derived a spectral threshold, the basic reproduction number $ \mathcal{R}_0 $, which governs the phase transition of risk cascades. We established that $ \mathcal{R}_0 = 1 $ constitutes a transcritical bifurcation point: the network resides in a distress-free state when $ \mathcal{R}_0 < 1 $, whereas a unique, globally attractive endemic equilibrium emerges when $ \mathcal{R}_0 > 1 $, signifying the onset of chronic systemic fragility. Sensitivity analysis revealed that the risk threshold is predominantly driven by the contagion intensity across business ties and the duration of latent vulnerability, while metabolic clearing mechanisms, such as firm exit and market attrition, effectively truncate the infectious window. Furthermore, we formulated an optimal control problem to identify targeted intervention strategies that minimize the aggregate social cost of disruptions against fiscal constraints. Numerical simulations on scale-free topologies demonstrated that targeted recovery stimulus effectively fosters a Ⅴ-shaped resilience rebound, starving the contagion of susceptible hosts. Our results provide a theoretical foundation for re-engineering supply chain resilience and designing cost-effective regulatory stabilizers in the presence of network externalities.
Citation: Shufen Wei, Yannan Su, Zhanyu Wang, Xinze Lian, Feng Rao. Systemic resilience in heterogeneous supply chains: optimal targeted interventions against risk contagion[J]. Journal of Industrial and Management Optimization, 2026, 22(6): 2912-2941. doi: 10.3934/jimo.2026107
This paper characterizes the systemic dynamics of risk contagion within interconnected supply chain ecosystems by developing a degree-resolved susceptible-exposed-Infectious-recovered-susceptible (SEIRS) framework on heterogeneous network topologies. Utilizing the heterogeneous mean-field theory, we analytically derived a spectral threshold, the basic reproduction number $ \mathcal{R}_0 $, which governs the phase transition of risk cascades. We established that $ \mathcal{R}_0 = 1 $ constitutes a transcritical bifurcation point: the network resides in a distress-free state when $ \mathcal{R}_0 < 1 $, whereas a unique, globally attractive endemic equilibrium emerges when $ \mathcal{R}_0 > 1 $, signifying the onset of chronic systemic fragility. Sensitivity analysis revealed that the risk threshold is predominantly driven by the contagion intensity across business ties and the duration of latent vulnerability, while metabolic clearing mechanisms, such as firm exit and market attrition, effectively truncate the infectious window. Furthermore, we formulated an optimal control problem to identify targeted intervention strategies that minimize the aggregate social cost of disruptions against fiscal constraints. Numerical simulations on scale-free topologies demonstrated that targeted recovery stimulus effectively fosters a Ⅴ-shaped resilience rebound, starving the contagion of susceptible hosts. Our results provide a theoretical foundation for re-engineering supply chain resilience and designing cost-effective regulatory stabilizers in the presence of network externalities.
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Shufen Wei, Yannan Su, Zhanyu Wang, Xinze Lian, Feng Rao. Systemic resilience in heterogeneous supply chains: optimal targeted interventions against risk contagion[J]. Journal of Industrial and Management Optimization, 2026, 22(6): 2912-2941. doi: 10.3934/jimo.2026107
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