2003/03/21 by Stephan M. Dammer, Haye Hinrichsen · 37 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · Physics and Astronomy · #Biology #Computer science #Condensed matter physics #Crossover #Directed percolation #Evolution and Genetic Dynamics #Genetics #Geometry #Immunization #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematics #Percolation (cognitive psychology) #Phase (matter) #Phase diagram #Phase transition #Physics #Quantum mechanics #Scaling #Statistical physics #Stochastic processes and statistical mechanics #cond-mat.stat-mech #q-bio
paper · pdf · doi:10.1103/physreve.68.016114
published in Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 68(1), 016114 (American Physical Society) · 9 pages, 13 figures
arxiv created 2003/03/21 · openalex publication_date 2003/07/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The spreading of infectious diseases with and without immunization of individuals can be modeled by stochastic processes that exhibit a transition between an active phase of epidemic spreading and an absorbing phase, where the disease dies out. In nature, however, the transmitted pathogen may also mutate, weakening the effect of immunization. In order to study the influence of mutations, we introduce a model that mimics epidemic spreading with immunization and mutations. The model exhibits a line of continuous phase transitions and includes the general epidemic process (GEP) and directed percolation (DP) as special cases. Restricting to perfect immunization in two spatial dimensions, we analyze the phase diagram and study the scaling behavior along the phase transition line as well as in the vicinity of the GEP point. We show that mutations lead generically to a crossover from the GEP to DP. Using standard scaling arguments, we also predict the form of the phase transition line close to the GEP point. The protection gained by immunization is vitally decreased by the occurrence of mutations.