The contact process on a graph adapting to the infection

John Fernley; Peter Morters; Marcel Ortgiese

doi:10.1016/j.spa.2025.104596

The contact process on a graph adapting to the infection

John Fernley, Peter Morters, Marcel Ortgiese

Research output: Contribution to journal › Article › peer-review

Abstract

We find a non-trivial phase transition for the contact process, a simple model for infection without immunity, on a network which reacts dynamically to prevent an epidemic. This network is initially blue distributed as an Erdős–Rényi graph, but is made adaptive via updating in only the infected neighbourhoods, at constant rate. Adaptive dynamics are new to the mathematical contact process literature—in adaptive dynamics the presence of infection can help to prevent the spread and thus monotonicity-based techniques fail. We show, further, that the phase transition in the fast adaptive model occurs at larger infection rate than in the non-adaptive model.

Original language	English
Article number	104596
Number of pages	38
Journal	Stochastic Processes and their Applications
Volume	183
Early online date	7 Feb 2025
DOIs	https://doi.org/10.1016/j.spa.2025.104596
Publication status	E-pub ahead of print - 7 Feb 2025

Funding

JF was supported by the SAMBa centre for doctoral training at the University of Bath under the EPSRC project EP/L015684/1, then by the Unité de mathématiques pures et appliqués of ENS Lyon, and finally by NRDI grant KKP 137490.

Funders	Funder number
Engineering and Physical Sciences Research Council	EP/L015684/1

Keywords

Adaptive graph dynamics
Contact process
Epidemic phase transition
SIS infection

ASJC Scopus subject areas

Statistics and Probability
Modelling and Simulation
Applied Mathematics

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10.1016/j.spa.2025.104596Licence: CC BY

https://arxiv.org/pdf/2312.06251.pdf

Cite this

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The contact process on a graph adapting to the infection

Abstract

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Keywords

ASJC Scopus subject areas

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