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 finitetime 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 finitetime Lyapunov exponents as a constructive tool, we demonstrate that the dynamical systems viewpoint of extinction evolves naturally toward the optimal path.
 Publication:

arXiv eprints
 Pub Date:
 March 2010
 DOI:
 10.48550/arXiv.1003.0912
 arXiv:
 arXiv:1003.0912
 Bibcode:
 2010arXiv1003.0912F
 Keywords:

 Physics  Biological Physics;
 Quantitative Biology  Populations and Evolution
 EPrint:
 21 pages, 5 figures, Final revision to appear in Bulletin of Mathematical Biology