| Title:
|
A note on the cooperative two-type SIR processes on Galton-Watson trees (English) |
| Author:
|
Ma, Ruibo |
| Author:
|
Liu, Tai Heng |
| Author:
|
Othmane, Baghdadi |
| Author:
|
Yao, Dong |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
61 |
| Issue:
|
6 |
| Year:
|
2025 |
| Pages:
|
741-751 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
SIR model |
| Keyword:
|
Galton–Watson trees |
| Keyword:
|
cooperative interactions |
| MSC:
|
60J27 |
| MSC:
|
92D30 |
| DOI:
|
10.14736/kyb-2025-6-0741 |
| . |
| Date available:
|
2026-01-07T10:06:22Z |
| Last updated:
|
2026-01-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153261 |
| . |
| Reference:
|
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| . |
