Document Type
Article
Department/Program
Applied Science
Journal Title
Bulletin of Mathematical Biology
Pub Date
2011
Volume
73
Issue
3
First Page
495
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.
Recommended Citation
Forgoston, Eric; Schwartz, Ira B.; Bianco, Simone; and Shaw, Leah B., Maximal Sensitive Dependence and the Optimal Path to Epidemic Extinction (2011). Bulletin of Mathematical Biology, 73(3), 495-514.
10.1007/s11538-010-9537-0
DOI
10.1007/s11538-010-9537-0
