Maximal Sensitive Dependence and the Optimal Path to Epidemic Extinction
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 2010
- Accession Number
- ADA519129
Entities
People
- Eric Forgoston
- Ira B. Schwartz
- Leah B. Shaw
- Simone Bianco
Organizations
- United States Naval Research Laboratory