Bulletin of Mathematical Biology

, Volume 73, Issue 3, pp 495–514 | Cite as

Maximal Sensitive Dependence and the Optimal Path to Epidemic Extinction

  • Eric Forgoston
  • Simone Bianco
  • Leah B. Shaw
  • Ira B. Schwartz
Original Article

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.

Keywords

Stochastic dynamical systems and Lyapunov exponents Optimal path to extinction 

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Copyright information

© Society for Mathematical Biology 2010

Authors and Affiliations

  • Eric Forgoston
    • 1
  • Simone Bianco
    • 2
  • Leah B. Shaw
    • 2
  • Ira B. Schwartz
    • 1
  1. 1.Nonlinear Systems Dynamics Section, Plasma Physics Division, Code 6792US Naval Research LaboratoryWashingtonUSA
  2. 2.Department of Applied ScienceThe College of William & MaryWilliamsburgUSA

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