Coupling a branching process to an infinite dimensional epidemic process

TL;DR

This paper demonstrates that in a Markovian parasitic infection model, a coupling method ensures the epidemic process closely follows a branching process with high probability until a significant number of infections occur, extending understanding of early epidemic dynamics.

Contribution

It introduces a coupling technique that aligns the epidemic and branching processes with high probability during initial infection stages in a Markovian model.

Findings

Coupling achieves high-probability coincidence until o(N^{2/3}) infections

Provides a probabilistic bound on epidemic process approximation

Extends classical epidemic threshold results

Abstract

Branching process approximation to the initial stages of an epidemic process has been used since the 1950's as a technique for providing stochastic counterparts to deterministic epidemic threshold theorems. One way of describing the approximation is to construct both branching and epidemic processes on the same probability space, in such a way that their paths coincide for as long as possible. In this paper, it is shown, in the context of a Markovian model of parasitic infection, that coincidence can be achieved with asymptotically high probability until o(N^{2/3}) infections have occurred, where N denotes the total number of hosts.