2008/03/06 by David A. Kessler, David A Kessler, Nadav M. Shnerb +1 · 1 citation
Mathematics · Medicine · Physics and Astronomy · #COVID-19 epidemiological studies #Mathematical and Theoretical Epidemiology and Ecology Models #Stochastic processes and statistical mechanics #cond-mat.stat-mech
paper · pdf · doi:10.1088/1751-8113/41/29/292003
arxiv created 2008/03/06 · openalex publication_date 2008/06/27 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
The quasi-deterministic limit of the generic extinction transition is considered within the framework of standard epidemiological models. The susceptible-infected-susceptible (SIS) model is known to exhibit a transition from extinction to spreading, as the infectivity is increased, described by the directed percolation equivalence class. We find that the distance from the transition point, and the prefactor controlling the divergence of the (perpendicular) correlation length, both scale with the local population size, N , with two novel universal exponents. Different exponents characterize the large- N behavior of the susceptible-infected-recovered (SIR) model, which belongs to the dynamic percolation class. Extensive numerical studies in a range of systems lead to the conjecture that these characteristics are generic and may be used in order to classify the high density limit of any stochastic process on the edge of extinction.