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arXiv · 2602.18784

A note on the cooperative two-type SIR processes on Galton-Watson trees

Ruibo Ma·Tai Heng Liu·Baghdadi Othmane·Dong Yao
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Abstract

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.

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Ruibo Ma, Tai Heng Liu, Baghdadi Othmane, Dong Yao. 2026-02-21. A note on the cooperative two-type SIR processes on Galton-Watson trees. https://doi.org/10.14736/kyb-2025-6-0741

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