2010/03/03 by Eric Forgoston, Forgoston, Eric, Simone Bianco +5 · 1 citation
Biochemistry, Genetics and Molecular Biology · Medicine · Physics and Astronomy · Social Sciences · #Biological Physics (physics.bio-ph) #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #FOS: Biological sciences #FOS: Physical sciences #Mathematical and Theoretical Epidemiology and Ecology Models #Populations and Evolution (q-bio.PE) #physics.bio-ph #q-bio.PE
paper · pdf · doi:10.48550/arxiv.1003.0912
21 pages, 5 figures, Final revision to appear in Bulletin of Mathematical Biology
openalex publication_date 2010/03/03 · arxiv created 2010/03/24 · arxiv updated 2010/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.