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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.18784 |
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| _version_ | 1866918349616709632 |
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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 |