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

Maximal Sensitive Dependence and the Optimal Path to Epidemic Extinction