Phase Boundary of a Stochastic Watts-Threshold SIS Model on Random Networks
For researchers studying complex contagion on networks, this provides the first quantitative phase diagram for threshold models with SIS-like recovery, analogous to the classical SIS epidemic threshold.
This work maps the extinction-persistence phase boundary of a stochastic Watts-threshold SIS model on random networks, finding a sharp transition (10-90% extinction band spanning Δθ ≈ 0.005-0.008) and showing that the adoption threshold is the dominant parameter governing epidemic feasibility.
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.