Incollection,
The reinfection threshold corresponds to the mean field version of the transition between annular and compact growth in spatial epidemic models
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
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. A pair approximation solution is given for the spatial
epidemic model and its phase transition lines.
Tags
- analytics
- epidemiology
- immunity
- lines
- model
- partial
- phase
- processes
- reinfection
- statphys23
- stochastic
- topic-10
- transition
