تقرير
Monotone convergence of spreading processes on networks
| العنوان: | Monotone convergence of spreading processes on networks |
|---|---|
| المؤلفون: | Fibich, Gadi, Golan, Amit, Schochet, Steven |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics Physics (Other) Quantitative Biology |
| مصطلحات موضوعية: | Mathematics - Classical Analysis and ODEs, Computer Science - Social and Information Networks, Physics - Physics and Society, Quantitative Biology - Populations and Evolution, 91D30 (Primary), 34E10, 92D30, 60J80, 92D25 (Secondary) |
| الوصف: | We analyze the Bass and SI models for the spreading of innovations and epidemics, respectively, on homogeneous complete networks, circular networks, and heterogeneous complete networks with two homogeneous groups. We allow the network parameters to be time dependent, which is a prerequisite for the analysis of optimal strategies on networks. Using a novel top-down analysis of the master equations, we present a simple proof for the monotone convergence of these models to their respective infinite-population limits. This leads to explicit expressions for the expected adoption or infection level in the Bass and SI models, respectively, on infinite homogeneous complete and circular networks, and on heterogeneous complete networks with two homogeneous groups with time-dependent parameters. Comment: 20 pages, 3 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.10816 |
| رقم الأكسشن: | edsarx.2407.10816 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |