Phase Boundary of a Stochastic Watts-Threshold SIS Model on Random Networks
2026-06-29 • Social and Information Networks
Social and Information Networks
AI summaryⓘ
The authors studied how ideas or behaviors spread on networks when someone needs several neighbors to adopt before they do, but can also stop adopting later (like recovery). They looked specifically at a model combining this with epidemic-like behavior on two types of networks and mapped when the spreading dies out versus when it persists. They found that the main factor controlling spread is the adoption threshold, while transmission rate and how long someone remains 'infected' matter less. Their results give a clear, detailed map of the conditions needed for sustained spreading in complex contagions with recovery.
complex contagionSIS modelWatts thresholdErdos-Renyi networkBarabasi-Albert networkphase transitionMonte Carlo simulationadoption thresholdtransmission rateinfectious duration
Authors
Yasmine Beji, Heger Arfaoui, Slimane BenMiled
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.