Monotone convergence of spreading processes on networks. arXiv:2407.10816
Preprint, arXiv:2407.10816 [math.CA] (2024).
Summary: 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.
MSC:
| 91D30 | Social networks; opinion dynamics |
| 34E10 | Perturbations, asymptotics of solutions to ordinary differential equations |
| 92D30 | Epidemiology |
| 60J80 | Branching processes (Galton-Watson, birth-and-death, etc.) |
| 92D25 | Population dynamics (general) |
arXiv data are taken from the
arXiv OAI-PMH API.
If you found a mistake, please
report it directly to arXiv.
