SIR Epidemics on Evolving Erd\H{o}s-R\'enyi Graphs
Wenze Chen, Yuewen Hou, Dong Yao

TL;DR
This paper characterizes the precise conditions under which the SIR-$$ model on evolving Erd51s-Re9nyi graphs exhibits a discontinuous phase transition in epidemic size, advancing understanding of epidemic dynamics on adaptive networks.
Contribution
It provides a necessary and sufficient condition for the emergence of discontinuous phase transitions in the SIR-$$ model on Erd51s-Re9nyi graphs, closing previous gaps in theoretical understanding.
Findings
Identifies the exact condition for discontinuous phase transition.
Shows the phase transition behavior depends on network rewiring parameters.
Clarifies the relationship between outbreak probability and epidemic size.
Abstract
In the standard SIR model, infected vertices infect their neighbors at rate independently across each edge. They also recover at rate . In this work we consider the SIR- model where the graph structure itself co-evolves with the SIR dynamics. Specifically, connections are broken at rate . Then, with probability , rewires this edge to another uniformly chosen vertex; and with probability , this edge is simply dropped. When the SIR- model becomes the evoSIR model. Jiang et al. proved in \cite{DOMath} that the probability of an outbreak in the evoSIR model converges to 0 as approaches the critical infection rate . On the other hand, numerical experiments in \cite{DOMath} revealed that, as , (conditionally on an outbreak) the fraction of infected vertices may not…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsComplex Network Analysis Techniques · Evolutionary Game Theory and Cooperation · Stochastic processes and statistical mechanics
