Mixing time for an epidemic model on graphs with external sources of infection
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917489304141824 |
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| author | KhudaBukhsh, Wasiur R. Xiang, Yangrui |
| author_facet | KhudaBukhsh, Wasiur R. Xiang, Yangrui |
| contents | We study the mixing time of a Susceptible--Infected--Susceptible (SIS) model on graphs with external sources of infection, which we refer to as the noisy SIS model. Under suitable assumptions on the parameters of the dynamics, we show that the mixing time is of the order $Θ(n\log n)$ with respect to the number of vertices $n$. We further investigate the model on random graph families, including Erd{ö}s--R{é}nyi graphs, random regular multigraphs, and Galton--Watson trees. By identifying high-probability structural properties of these graphs and conditioning on typical realizations, we prove that the mixing time remains of order $Θ(n\log n)$ with high probability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07738 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mixing time for an epidemic model on graphs with external sources of infection KhudaBukhsh, Wasiur R. Xiang, Yangrui Probability Mathematical Physics Statistics Theory Populations and Evolution 60J10, 60J20, 92D25 We study the mixing time of a Susceptible--Infected--Susceptible (SIS) model on graphs with external sources of infection, which we refer to as the noisy SIS model. Under suitable assumptions on the parameters of the dynamics, we show that the mixing time is of the order $Θ(n\log n)$ with respect to the number of vertices $n$. We further investigate the model on random graph families, including Erd{ö}s--R{é}nyi graphs, random regular multigraphs, and Galton--Watson trees. By identifying high-probability structural properties of these graphs and conditioning on typical realizations, we prove that the mixing time remains of order $Θ(n\log n)$ with high probability. |
| title | Mixing time for an epidemic model on graphs with external sources of infection |
| topic | Probability Mathematical Physics Statistics Theory Populations and Evolution 60J10, 60J20, 92D25 |
| url | https://arxiv.org/abs/2501.07738 |