2011/12/21 by Ira B. Schwartz, Schwartz, Ira B., Eric Forgoston +5
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · Physics and Astronomy · #COVID-19 epidemiological studies #Evolution and Genetic Dynamics #FOS: Biological sciences #FOS: Physical sciences #Mathematical and Theoretical Epidemiology and Ecology Models #Populations and Evolution (q-bio.PE) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #q-bio.PE
paper · pdf · doi:10.48550/arxiv.1112.4908
18 pages, 5 figures, Final revision in Journal of the Royal Society Interface. arXiv admin note: substantial text overlap with arXiv:1003.0912
arxiv created 2011/12/21 · openalex publication_date 2011/12/21 · arxiv updated 2011/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Extinction appears ubiquitously in many fields, including chemical reactions, population biology, evolution, and epidemiology. Even though extinction as a random process is a rare event, its occurrence is observed in large finite populations. Extinction occurs when fluctuations due to random transitions act as an effective force which drives one or more components or species to vanish. Although there are many random paths to an extinct state, there is an optimal path that maximizes the probability to extinction. In this article, we show that the optimal path is associated with the dynamical systems idea of having maximum sensitive dependence to initial conditions. Using the equivalence between the sensitive dependence and the path to extinction, we show that the dynamical systems picture of extinction evolves naturally toward the optimal path in several stochastic models of epidemics.