Maximal Sensitive Dependence and the Optimal Path to Epidemic Extinction

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

Research output: Contribution to journalArticle

17 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)495-514
Number of pages20
JournalBulletin of Mathematical Biology
Volume73
Issue number3
DOIs
StatePublished - 1 Mar 2011

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Optimal Path
Extinction
Dynamical systems
extinction
Dynamical system
Lyapunov Exponent
Stochastic models
Stochastic Epidemic Models
Rare Events
Initial conditions
Unstable
Maximise
Fluctuations
Demonstrate

Keywords

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

Cite this

Forgoston, Eric ; Bianco, Simone ; Shaw, Leah B. ; Schwartz, Ira B. / Maximal Sensitive Dependence and the Optimal Path to Epidemic Extinction. In: Bulletin of Mathematical Biology. 2011 ; Vol. 73, No. 3. pp. 495-514.
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Maximal Sensitive Dependence and the Optimal Path to Epidemic Extinction. / Forgoston, Eric; Bianco, Simone; Shaw, Leah B.; Schwartz, Ira B.

In: Bulletin of Mathematical Biology, Vol. 73, No. 3, 01.03.2011, p. 495-514.

Research output: Contribution to journalArticle

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