🤖 AI Summary
This study characterizes the extinction–persistence phase transition boundary of complex contagion models with recovery mechanisms on random networks. Focusing on the Watts threshold SIS model, the authors perform over 180,000 Monte Carlo simulations on Erdős–Rényi and Barabási–Albert networks, combining adaptive Delaunay sampling with weighted logistic regression to quantitatively reconstruct— for the first time—the phase boundary in the joint parameter space of transmission rate, adoption threshold, and infectious duration. The results reveal an exceptionally sharp transition, with the 10%–90% extinction probability bandwidth spanning only 0.005–0.008, and a phase boundary structure invariant across network topologies. The adoption threshold dominates the transition, while transmission rate and infectious duration play secondary, asymmetric roles. This work establishes a benchmark analogous to the classical SIS epidemic threshold for complex contagion and develops a high-precision six-parameter interaction model.
📝 Abstract
Complex contagion models, in which adoption requires reinforcement from multiple neighbors, have been extensively studied in the monotone (no-recovery) setting, but the phase diagram of threshold models with SIS-like recovery on networks remains unmapped. We study a stochastic Watts-threshold SIS model on Erdos-Renyi and Barabasi-Albert networks and reconstruct its extinction-persistence phase boundary in the joint parameter space of transmission rate $β$, adoption threshold $θ$, and infectious duration $d$. Using adaptive Delaunay-based sampling and weighted logistic regression on over 180,000 Monte Carlo trials, we find that: (i) the boundary is well described by a six-parameter interaction model whose structure is invariant across both topologies; (ii) the transition is sharp, with the 10-90\% extinction-probability band spanning only $Δθ\approx 0.005$-$0.008$; and (iii) the adoption threshold is the dominant parameter governing epidemic feasibility, with transmission rate and infectious duration playing secondary and asymmetric roles. The characterization provides a quantitative reference for the complex-contagion analogue of the classical SIS epidemic threshold.