Explicit solutions of the SI and Bass models on sparse Erdős-Rényi and regular networks
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909394742018048 |
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| author | Fibich, Gadi Warman, Yonatan |
| author_facet | Fibich, Gadi Warman, Yonatan |
| contents | We derive explicit expressions for the expected adoption and infection level in the Bass and SI models, respectively, on sparse Erdős-Rényi networks and on $d$-regular networks. These expressions are soloutions of first-order ordinary differential equations, which are fairly easy to analyze. To prove that these expressions are exact, we show that the effect of cycles vanishes as the network size goes to infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12076 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Explicit solutions of the SI and Bass models on sparse Erdős-Rényi and regular networks Fibich, Gadi Warman, Yonatan Probability Physics and Society We derive explicit expressions for the expected adoption and infection level in the Bass and SI models, respectively, on sparse Erdős-Rényi networks and on $d$-regular networks. These expressions are soloutions of first-order ordinary differential equations, which are fairly easy to analyze. To prove that these expressions are exact, we show that the effect of cycles vanishes as the network size goes to infinity. |
| title | Explicit solutions of the SI and Bass models on sparse Erdős-Rényi and regular networks |
| topic | Probability Physics and Society |
| url | https://arxiv.org/abs/2411.12076 |