Disease Extinction in the Presence of Random Vaccination

2008/01/31 by M. I. Dykman, Mark Dykman, Ira B. Schwartz +1 · 5 citations
Agricultural and Biological Sciences · Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Animal Disease Management and Epidemiology #COVID-19 epidemiological studies #Evolution and Genetic Dynamics #cond-mat.stat-mech #physics.bio-ph #q-bio.PE

paper · pdf · doi:10.1103/physrevlett.101.078101

Accepted for publication to PRL

arxiv created 2008/06/21 · openalex publication_date 2008/08/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate disease extinction in an epidemic model described by a birth-death process. We show that, in the absence of vaccination, the effective entropic barrier for extinction displays scaling with the distance to the bifurcation point, with an unusual critical exponent. Even a comparatively weak Poisson-distributed random vaccination leads to an exponential increase in the extinction rate, with the exponent that strongly depends on the vaccination parameters.

Cited by

• Rare-event extinction on stochastic networks
• Large rare fluctuations in systems with delayed dissipation
• Minimizing the Population Extinction Risk by Migration
• Large deviations of random walks on random graphs
• Stochastic Tunneling and Metastable States During the Somatic Evolution of Cancer

Related

• Stochastic extinction of epidemics in large populations and role of vaccinations
• Speeding up disease extinction with a limited amount of vaccine
• Entropic decay of an epidemic towards herd immunity
• Universal features of epidemic and vaccine models
• Converging towards the optimal path to extinction