Explicit solutions of the SI and Bass models on sparse Erdős-Rényi and regular networks

2024/11/18 by Gadi Fibich, Fibich, Gadi, Yonatan Warman +1 · 1 citation
Mathematics · Physics and Astronomy · #Bass (fish) #Biology #Computer science #FOS: Mathematics #FOS: Physical sciences #Fishery #Mathematics #Opinion Dynamics and Social Influence #Physics and Society (physics.soc-ph) #Probability (math.PR) #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2411.12076

openalex publication_date 2024/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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