Mean field limit for survival probability of the high-dimensional contact process

TL;DR

This paper establishes a mean field limit for the survival probability of the high-dimensional contact process on a lattice, providing insights into disease spread in large networks.

Contribution

It introduces a mean field approximation for the survival probability as the lattice dimension tends to infinity, using the binary contact path process as a key tool.

Findings

Mean field limit derived for high-dimensional contact process

Survival probability conditioned on initial infection at origin analyzed

Binary contact path process used as an auxiliary method

Abstract

In this paper we are concerned with the contact process on the squared lattice. The contact process intuitively describes the spread of the infectious disease on a graph, where an infectious vertex becomes healthy at a constant rate while a healthy vertex is infected at rate proportional to the number of infectious neighbors. As the dimension of the lattice grows to infinity, we give a mean field limit for the survival probability of the process conditioned on the event that only the origin of the lattice is infected at t=0. The binary contact path process is a main auxiliary tool for our proof.