title: A spatially stochastic epidemic model with partial immunization shows in mean field approximation the reinfection threshold.
abstract: 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.
authors.affiliation: Centro de Matemática e Aplicações Fundamentais, Faculdade de Ciências, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal. nico@ptmat.fc.ul.pt
authors.forename: Nico
authors.initials: N
authors.lastname: Stollenwerk
authors.forename: Sander
authors.initials: S
authors.lastname: van Noort
authors.forename: José
authors.initials: J
authors.lastname: Martins
authors.forename: Maíra
authors.initials: M
authors.lastname: Aguiar
authors.forename: Frank
authors.initials: F
authors.lastname: Hilker
authors.forename: Alberto
authors.initials: A
authors.lastname: Pinto
authors.forename: Gabriela
authors.initials: G
authors.lastname: Gomes
mesh_terms: D003198:Computer Simulation; D004198:Disease Susceptibility; D058872:Epidemics / Q000706:statistics & numerical data*; D006801:Humans; D007114:Immunization / Q000706:statistics & numerical data*; D007239:Infections / Q000453:epidemiology*; D008954:Models, Biological; D055502:Secondary Prevention; D013269:Stochastic Processes