Maximal Sensitive Dependence and the Optimal Path to Epidemic Extinction

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.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2010
Accession Number
ADA519129

Entities

People

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

Organizations

  • United States Naval Research Laboratory

Tags

Communities of Interest

  • Biomedical

DTIC Thesaurus Topics

  • Chemical Kinetics
  • Disease Outbreaks
  • Diseases And Disorders
  • Dynamics
  • Equations
  • Equations Of Motion
  • Extinction
  • Flow Fields
  • Infectious Diseases
  • Probability
  • Public Health
  • Statistical Analysis
  • Steady State
  • Stochastic Processes
  • Time Intervals
  • Two Dimensional
  • United States

Fields of Study

  • Mathematics

Readers

  • Combustion science or combustion engineering.
  • Control Systems Engineering.
  • Operations Research