# Graphon-based sensitivity analysis of SIS epidemics

arXiv: https://arxiv.org/abs/1912.10330 · HTML: https://mlsanity.com/paper/1912.10330/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Dec 2019.

## Built on by (most cited first, 4 of 4)

- [Learning Graphon Mean Field Games and Approximate Nash Equilibria](https://mlsanity.com/paper/2112.01280/) (2021)
- [Mean Field Games on Weighted and Directed Graphs via Colored Digraphons](https://mlsanity.com/paper/2209.03887/) (2022)
- [Modularity maximisation for graphons](https://mlsanity.com/paper/2101.00503/) (2021)
- [Graphon Particle Systems, Part II: Dynamics of Distributed Stochastic Continuum Optimization](https://mlsanity.com/paper/2407.02765/) (2024)

## Abstract (arXiv)

In this work, we use the spectral properties of graphons to study stability and sensitivity to noise of deterministic SIS epidemics over large networks. We consider the presence of additive noise in a linearized SIS model and we derive a noise index to quantify the deviation from the disease-free state due to noise. For finite networks, we show that the index depends on the adjacency eigenvalues of its graph. We then assume that the graph is a random sample from a piecewise Lipschitz graphon with finite rank and, using the eigenvalues of the associated graphon operator, we find an approximation of the index that is tight when the network size goes to infinity. A numerical example is included to illustrate the results.