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Main Authors: Ma, Ruibo, Liu, Tai Heng, Othmane, Baghdadi, Yao, Dong
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2602.18784
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author Ma, Ruibo
Liu, Tai Heng
Othmane, Baghdadi
Yao, Dong
author_facet Ma, Ruibo
Liu, Tai Heng
Othmane, Baghdadi
Yao, Dong
contents In the standard SIR model on a graph, infected vertices infect their neighbors at rate $α$ and recover at rate $μ$. We consider a two-type SIR process where each individual in the graph can be infected with two types of diseases, $A$ and $B$. Moreover, the two diseases interact in a cooperative way so that an individual that has been infected with one type of disease can acquire the other at a higher rate. We prove that if the underlying graph is a Galton-Watson tree and initially the root is infected with both $A$ and $B$, while all others are susceptible, then the two-type SIR model has the same critical value for the survival probability as the classic single-type model.
format Preprint
id arxiv_https___arxiv_org_abs_2602_18784
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle A note on the cooperative two-type SIR processes on Galton-Watson trees
Ma, Ruibo
Liu, Tai Heng
Othmane, Baghdadi
Yao, Dong
Probability
60J27, 92D30
In the standard SIR model on a graph, infected vertices infect their neighbors at rate $α$ and recover at rate $μ$. We consider a two-type SIR process where each individual in the graph can be infected with two types of diseases, $A$ and $B$. Moreover, the two diseases interact in a cooperative way so that an individual that has been infected with one type of disease can acquire the other at a higher rate. We prove that if the underlying graph is a Galton-Watson tree and initially the root is infected with both $A$ and $B$, while all others are susceptible, then the two-type SIR model has the same critical value for the survival probability as the classic single-type model.
title A note on the cooperative two-type SIR processes on Galton-Watson trees
topic Probability
60J27, 92D30
url https://arxiv.org/abs/2602.18784