A spatially stochastic epidemic model with partial immunization shows in mean field approximation the reinfection threshold

• Type: Article in International Scientific Journal
• Date: 2010

Authors

N. Stollenwerk (Author) Other; S. van Noort (Author) Other; J. Martins (Author) Other; M. Aguiar (Author) Other; F. Hilker (Author) Other; A. A. Pinto (Author) FCUP; G. Gomes (Author) Other

Journal

Title: Journal of Biological Dynamics

Vol. 4 No. 6

Pages: 634-649

ISSN: 1751-3758

Publisher: Taylor & Francis

Indexing

Scopus - 22 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-007-Z76

DOI: 10.1080/17513758.2010.487159

Resumo (PT): Recently, the notion of a reinfection threshold in epidemiological models of only partial immunity has been debated in the literature. We present a rigorous analysis of a model of reinfection which shows a clear threshold behaviour at the parameter point where the reinfection threshold was originally described. Furthermore, we demonstrate that this threshold is the mean field version of a transition in corresponding spatial models of immunization. The reinfection threshold corresponds to the transition between annular growth of an epidemics spreading into a susceptible area leaving recovered behind and compact growth of a susceptible-infected-susceptible region growing into a susceptible area. This transition between annular growth and compact growth was described in the physics literature long before the reinfection threshold debate broke out in the theoretical biology literature.

Abstract (EN): Recently, the notion of a reinfection threshold in epidemiological models of only partial immunity has been debated in the literature. We present a rigorous analysis of a model of reinfection which shows a clear threshold behaviour at the parameter point where the reinfection threshold was originally described. Furthermore, we demonstrate that this threshold is the mean field version of a transition in corresponding spatial models of immunization. The reinfection threshold corresponds to the transition between annular growth of an epidemics spreading into a susceptible area leaving recovered behind and compact growth of a susceptible-infected-susceptible region growing into a susceptible area. This transition between annular growth and compact growth was described in the physics literature long before the reinfection threshold debate broke out in the theoretical biology literature.

Language: English

Type (Professor's evaluation): Scientific