Local-density dependent Markov processes on graphons with epidemiological applications

Abstract

We investigate local-density dependent Markov processes on a class of large graphs sampled from a graphon, where the transition rates of the vertices are influenced by the states of their neighbors. We show that as the average degree converges to infinity (faster than a given threshold), the evolution of the process in the transient regime converges to the solution of a set of non-local integro-partial differential equations depending on the limit graphon. We also provide rigorous derivation for the epidemic threshold in the case of the Susceptible–Infected–Susceptible (SIS) process on such graphons.

Topics & Concepts