Kybernetika 61 no. 6, 741-751, 2025

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

Ruibo Ma, Tai Heng Liu, Baghdadi Othmane and Dong YaoDOI: 10.14736/kyb-2025-6-0741

Abstract:

In the standard SIR model on a graph, infected vertices infect their neighbors at rate $\alpha$ and recover at rate $\mu$. 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.

Keywords:

SIR model, Galton-Watson trees, cooperative interactions

Classification:

60J27, 92D30

paper.pdf

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