Local-density dependent Markov processes on graphons with epidemiological applications
Probability
2020-11-24 v3
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, the evolution of the process in the transient regime converges to the solution of a set of non-local integro-partial differential equations. We also provide rigorous derivation for the epidemic threshold in the case of the Susceptible-Infected-Susceptible (SIS) process on such graphons.
Keywords
Cite
@article{arxiv.2008.08109,
title = {Local-density dependent Markov processes on graphons with epidemiological applications},
author = {Daniel Keliger and Illes Horvath and Balint Takacs},
journal= {arXiv preprint arXiv:2008.08109},
year = {2020}
}