Explicit solutions of the SI and Bass models on sparse Erd\H{o}s-R\'enyi and regular networks

Gadi Fibich; Yonatan Warman

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arXiv · 2411.12076

Explicit solutions of the SI and Bass models on sparse Erd\H{o}s-R\'enyi and regular networks

Gadi Fibich·Yonatan Warman

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Abstract

We derive explicit expressions for the expected adoption and infection level in the Bass and SI models, respectively, on sparse Erd\H{o}s-R\'enyi 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.

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Gadi Fibich, Yonatan Warman. 2024-11-18. Explicit solutions of the SI and Bass models on sparse Erd\H{o}s-R\'enyi and regular networks. https://arxiv.org/abs/2411.12076

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