METASTABILITY OF THE CONTACT PROCESS ON FAST EVOLVING SCALE-FREE NETWORKS

Emmanuel Jacob (1) , Amitai Linker (2) , Peter Mörters (3)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
2 USACH - Universidad de Santiago de Chile [Santiago]
3 Mathematisches Institut, Universität zu Köln

We study the contact process in the regime of small infection rates on finite scale-free networks with stationary dynamics based on simultaneous updating of all connections of a vertex. We allow the update rates of individual vertices to increase with the strength of a vertex, leading to a fast evolution of the network. We first develop an approach for inhomoge-neous networks with general kernel and then focus on two canonical cases, the factor kernel and the preferential attachment kernel. For these specific networks we identify and analyse four possible strategies how the infection can survive for a long time. We show that there is fast extinction of the infection when neither of the strategies is successful, otherwise there is slow extinction and the most successful strategy determines the asymptotics of the metastable density as the infection rate goes to zero. We identify the domains in which these strategies dominate in terms of phase diagrams for the exponent describing the decay of the metastable density. MSc Classification: Primary 05C82; Secondary 82C22.

Mots clés: Phase transitions; metastable density; evolving network; temporal network; dynamic network; inhomogeneous random graph; preferential attachment network; network dynamics; SIS infection

Domaines: Probabilités [math.PR]

Emmanuel Jacob, Amitai Linker, Peter Mörters. METASTABILITY OF THE CONTACT PROCESS ON FAST EVOLVING SCALE-FREE NETWORKS. 2018. ⟨hal-01957185⟩