# Survival probabilities of high-dimensional stochastic SIS and SIR models with random edge weights

## TL;DR

This paper analyzes the survival probabilities of high-dimensional stochastic SIS and SIR epidemic models with random edge weights, deriving mean field limits as the dimension increases, extending previous results for the SIS model.

## Contribution

It provides the first mean field limit results for both SIS and SIR models with random edge weights in high dimensions, generalizing prior work on the SIS model.

## Key findings

- Mean field limits for survival probabilities as dimension grows
- Extension of previous SIS results to SIR models with randomness
- Demonstrates the impact of random edge weights on epidemic survival

## Abstract

In this paper, we are concerned with the stochastic SIS (susceptible-infected-susceptible) and SIR (susceptible-infected-recovered) models on high-dimensional lattices with random edge weights, where a susceptible vertex is infected by an infectious neighbor at rate proportional to the weight on the edge connecting them. All the edge weights are assumed to be i.i.d.. Our main result gives mean field limits for survival probabilities of the two models as the dimension grows to infinity, which extends the main conclusion given in \cite{Xue2017} for classic stochastic SIS model.