Maximal Sensitive Dependence and the Optimal Path to Epidemic Extinction

Eric Forgoston, Simone Bianco, Leah B. Shaw, Ira B. Schwartz

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


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.

Original languageEnglish
Pages (from-to)495-514
Number of pages20
JournalBulletin of Mathematical Biology
Issue number3
StatePublished - Mar 2011


  • Optimal path to extinction
  • Stochastic dynamical systems and Lyapunov exponents


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