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Scaling limits of SIR epidemics with vertex-dependent transition rates on complete graphs

Part of: Limit theorems Special processes

Published online by Cambridge University Press:  18 December 2025

Xiaofeng Xue
Xiaofeng Xue*
Affiliation:
Beijing Jiaotong University
*
*Postal address: School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China. Email: xfxue@bjtu.edu.cn
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Abstract

In this paper we are concerned with susceptible–infected–removed (SIR) epidemics with vertex-dependent recovery and infection rates on complete graphs. We show that the hydrodynamic limit of our model is driven by a nonlinear function-valued ordinary differential equation consistent with a mean-field analysis. We further show that the fluctuation of our process is driven by a generalized Ornstein–Uhlenbeck process. A key step in the proofs of the main results is to show that states of different vertices are approximately independent as the population $N\rightarrow+\infty$.

Keywords

Susceptible–infected–removedhydrodynamicfluctuationapproximate independence

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory

Information

Type
Original Article
Information
Advances in Applied Probability , First View , pp. 1 - 45
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Applied Probability Trust

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