Maximal Sensitive Dependence and the Optimal Path to Epidemic Extinction

Details Maximal Sensitive Dependence and the Optimal Path to Epidemic Extinction Maximal Sensitive Dependence and the Optimal Path to Epidemic Extinction

2010-03-03

arxiv.org/abs/1003.0912v2

Physics

Biological Physics

21 pages, 5 figures, Final revision to appear in Bulletin of Mathematical Biology

Scientific paper

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.

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