Epidemics with mutating infectivity on small-world networks

Author(s)

Ruediger, Sten ^[1] ; Plietzsch, Anton ^{[2, 1]} ; Sagues, Francesc ^[3] ; Sokolov, Igor M. ^{[1, 4]} ; Kurths, Juergen ^{[2, 1, 5]}

Affiliation

^[1] Humboldt Univ, Dept Phys, D-12489 Berlin - Germany

^[2] Potsdam Inst Climate Impact Res PIK, D-14473 Potsdam - Germany

^[3] Univ Barcelona, Dept Quim Fis, Barcelona 08028 - Spain

^[4] IRIS Adlershof, Zum Grossen Windkanal 6, D-12489 Berlin - Germany

^[5] Saratov NG Chernyshevskii State Univ, 83 Astrakhanskaya Str, Saratov 410012 - Russia

• Document type: Journal article
• Source: SCIENTIFIC REPORTS; v. 10, n. 1 APR 3 2020.
• Web of Science Citations: 0

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. (AU)

• FAPESP's process: 15/50122-0 - Dynamic phenomena in complex networks: basics and applications
• Grantee: Elbert Einstein Nehrer Macau
• Support Opportunities: Research Projects - Thematic Grants