WKB theory of epidemic fade-out in stochastic populations

TL;DR

This paper develops a WKB theoretical framework to analyze the most probable paths and probabilities of epidemic fade-out caused by stochastic effects in populations, providing insights into disease extinction dynamics.

Contribution

It introduces a novel WKB approach to identify the instanton-like paths leading to epidemic fade-out in stochastic population models.

Findings

Identifies the most probable fade-out trajectories in phase space.

Provides a method to calculate fade-out probabilities.

Connects stochastic fade-out with Hamiltonian phase space dynamics.

Abstract

Stochastic effects may cause fade-out of an infectious disease in a population immediately after an epidemic outbreak. We develop WKB theory to determine the most probable path of the system toward epidemic fade-out and to evaluate the fade-out probability. The most probable path is an instanton-like orbit in the phase space of the underlying Hamiltonian flow.