The critical infection rate of the high-dimensional two-stage contact process

TL;DR

This paper investigates the critical infection rate of a high-dimensional two-stage contact process on a lattice, providing a limit theorem as the dimension increases, using a linear system and a two-stage SIR model.

Contribution

It establishes a limit theorem for the critical infection rate of the process as the lattice dimension tends to infinity, advancing understanding of high-dimensional epidemic models.

Findings

Derived a limit theorem for the critical infection rate as dimension grows

Utilized a linear system and a two-stage SIR model in the analysis

Provides insights into epidemic thresholds in high-dimensional lattices

Abstract

In this paper we are concerned with the two-stage contact process on the lattice $\mathbb{Z}^d$ introduced in \cite{Krone1999}. We gives a limit theorem of the critical infection rate of the process as the dimension $d$ of the lattice grows to infinity. A linear system and a two-stage SIR model are two main tools for the proof of our main result.