Affordable Access

Access to the full text

Epidemics with mutating infectivity on small-world networks

Authors
  • Rüdiger, Sten1
  • Plietzsch, Anton1, 2
  • Sagués, Francesc3
  • Sokolov, Igor M.1, 4
  • Kurths, Jürgen1, 2, 5
  • 1 Humboldt-Universität zu Berlin, Berlin, 12489, Germany , Berlin (Germany)
  • 2 Potsdam Institute for Climate Impact Research (PIK), Potsdam, 14473, Germany , Potsdam (Germany)
  • 3 Universitat de Barcelona, Barcelona, 08028, Spain , Barcelona (Spain)
  • 4 IRIS Adlershof, Zum Großen Windkanal 6, Berlin, 12489, Germany , Berlin (Germany)
  • 5 Saratov State University, 83, Astrakhanskaya Str., Saratov, 410012, Russia , Saratov (Russia)
Type
Published Article
Journal
Scientific Reports
Publisher
Springer Nature
Publication Date
Apr 03, 2020
Volume
10
Issue
1
Identifiers
DOI: 10.1038/s41598-020-62597-5
Source
Springer Nature
License
Green

Abstract

Epidemics and evolution of many pathogens occur on similar timescales so that their dynamics are often entangled. Here, in a first step to study this problem theoretically, we analyze mutating pathogens spreading on simple SIR networks with grid-like connectivity. We have in mind the spatial aspect of epidemics, which often advance on transport links between hosts or groups of hosts such as cities or countries. We focus on the case of mutations that enhance an agent’s infection rate. We uncover that the small-world property, i.e., the presence of long-range connections, makes the network very vulnerable, supporting frequent supercritical mutations and bringing the network from disease extinction to full blown epidemic. For very large numbers of long-range links, however, the effect reverses and we find a reduced chance for large outbreaks. We study two cases, one with discrete number of mutational steps and one with a continuous genetic variable, and we analyze various scaling regimes. For the continuous case we derive a Fokker-Planck-like equation for the probability density and solve it for small numbers of shortcuts using the WKB approximation. Our analysis supports the claims that a potentiating mutation in the transmissibility might occur during an epidemic wave and not necessarily before its initiation.

Report this publication

Statistics

Seen <100 times