Maximal Sensitive Dependence and the Optimal Path to Epidemic Extinction

TL;DR

This paper links the optimal path to epidemic extinction with the maximum sensitivity to initial conditions, using finite-time Lyapunov exponents to analyze stochastic epidemic models within a dynamical systems framework.

Contribution

It establishes a novel connection between the optimal extinction path and finite-time Lyapunov exponents in stochastic epidemic models.

Findings

Optimal extinction paths exhibit maximum sensitivity to initial conditions.

Finite-time Lyapunov exponents can be used to identify the optimal extinction trajectory.

Dynamical systems analysis provides new insights into stochastic epidemic extinction processes.

Abstract

Extinction of an epidemic or a species is a rare event that occurs due to a large, rare stochastic fluctuation. Although the extinction process is dynamically unstable, it follows an optimal path that maximizes the probability of extinction. We show that the optimal path is also directly related to the finite-time Lyapunov exponents of the underlying dynamical system in that the optimal path displays maximum sensitivity to initial conditions. We consider several stochastic epidemic models, and examine the extinction process in a dynamical systems framework. Using the dynamics of the finite-time Lyapunov exponents as a constructive tool, we demonstrate that the dynamical systems viewpoint of extinction evolves naturally toward the optimal path.