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Funnel theorems for spreading on networks
Gadi Fibich1, Tomer Levin1, Steven Schochet1
1Department of Applied Mathematics, Tel Aviv University, Tel Aviv, Israel.
Chaos (Woodbury, N.Y.)
|July 7, 2025
Summary
New funnel theorems bound susceptibility probabilities in Bass and susceptible-infected models on networks. These theorems offer precise calculations for adoption and infection levels in various network structures.
Area of Science:
- Network Science
- Mathematical Modeling
- Epidemiology
Background:
- Understanding information and disease propagation on networks is crucial.
- Existing models often lack precise analytical solutions for complex network structures.
Purpose of the Study:
- To derive and present novel funnel theorems for Bass and susceptible-infected models.
- To provide bounds for susceptibility probabilities on modified networks.
- To enable exact expressions for adoption/infection probabilities and levels.
Main Methods:
- Derivation of funnel theorems for network models.
- Analysis of susceptibility probabilities on modified networks with restricted incoming edges.
- Application to networks with and without cycles.
Main Results:
- Funnel theorems establish lower and upper bounds for susceptibility differences.
- The theorems allow for simplification by considering single-edge influence.
- Exact explicit expressions for adoption/infection probabilities are obtained.
Conclusions:
- The derived funnel theorems offer a powerful analytical tool for network models.
- These theorems facilitate precise calculations of adoption and infection dynamics.
- The approach is applicable to diverse network types, enhancing predictive capabilities.
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