Probability seminar: Júlia Komjáthy

Monday, 15 June 2026, 2pm to 3pm

Title: How communities help epidemics survive

Abstract: Real-world contact networks are rarely just homogeneous collections of individuals: they contain households, workplaces, classrooms, social groups, and many other overlapping communities. In this talk, I will discuss a toy model for understanding how such local community structure changes the spread of an epidemic.

The network model will be a random intersection graph, where individuals belong to one or more microscopic-to-mesoscopic communities, and two individuals are connected if they share a community. On this graph we run a Markovian Susceptible-Infected-Susceptible epidemic, or equivalently the contact process: infected vertices recover at rate 1, while healthy vertices are infected by each infected neighbour at rate lambda.

The main question is how the presence of communities changes the epidemic threshold. More precisely, we compare the contact process on a random intersection graph with the corresponding “community-free” random graph having the same/similar degree distribution. How does community structure affect the critical infection rate for long survival? And when the infection does survive for a long time, how can we describe the metastable density of infected individuals in terms of the community-size and membership distributions? In this model, these questions can be answered quite explicitly, giving a mathematically clean picture of how small local clusters can have a macroscopic effect on epidemic persistence.

Joint work with Marco Seiler and Daniel Valesin.

Speaker(s): Júlia Komjáthy (TU Delft)

Series: Probability seminar

Venue: Mathematical Institute - L5 - L5 Mathematical Institute Woodstock Road Oxford Oxfordshire OX2 6GG United Kingdom

Department: Statistics (Department)

Organiser: Christina Goldschmidt, James Martin, Julien Berestycki