Who is the infector? General multi-type epidemics and real-time susceptibility processes

TL;DR

This paper models multi-type epidemics using a stochastic process coupled with a directed random graph, providing a theoretical framework to understand infection patterns and type-specific infection fractions in large populations.

Contribution

It introduces a novel coupling of epidemic processes with random graphs and applies multi-type real-time branching process theory to characterize infection fractions.

Findings

Characterizes infection fractions among different types in large populations.

Identifies a special case maximizing same-type infection fractions.

Provides a theoretical basis for understanding multi-type epidemic dynamics.

Abstract

We couple a multi-type stochastic epidemic process with a directed random graph, where edges have random lengths. This random graph representation is used to characterise the fractions of individuals infected by the different types of vertices among all infected individuals in the large population limit. For this characterisation we rely on theory of multi-type real-time branching processes. We identify a special case of the two-type model, in which the fraction of individuals of a certain type infected by individuals of the same type, is maximised among all two-type epidemics approximated by branching processes with the same mean offspring matrix.