Incollection,
The analytic expressions of the phase transition lines of the spatial stochastic epidemic model SIRI in the pair approximation scheme
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Abstract
Models for reinfection processes in epidemiology and
models for partial immunization have attracted wide interest.
Transitions between no-growth, annular growth and compact growth have been
observed in both cases.
For the spatial stochastic epidemic model
SIRI (susceptible, infected, recovered and again infected)
we investigate, in the pair approximation scheme, its phase transition lines.
In particular, we also study the limiting cases, like
the SIS model, which corresponds to the case of
equal primary and secondary infectivity,
and the SIR model,
which is the case of vanishing reinfection.
We derive the dynamic equations for the expectation values of total number of
susceptibles, infected and recovered,
using not only the mean field approximation but also the pair approximation scheme.
We go one step ahead, finding the analytic expressions for the phase transition lines between
no-growth and nontrivial stationary equilibria
for the dynamical systems.
The phase transition line for the dynamical system obtained using the
pair approximation scheme, instead of the mean field approach, is a
better qualitative and quantitative approximation of the
phase transition line between no-growth and annular growth
for the spatial stochastic epidemic model.
In particular, the analytic phase transition line for the dynamical system obtained using the
pair approximation scheme, in contrast with the one obtained with the mean field approach,
show that the limiting cases of SIS and SIR do not have the same critical value for the transition from
no-growth to a nontrivial stationary state.\\
Grassberger, P., Chaté, H. & Rousseau, G. (1997)
Spreading in media with long-time memory, Phys. Rev.
E 55, 2488--2495.
Joo, J. & Lebowitz, J. L. (2004)
Pair approximation of the stochastic
susceptible-infected-recovered-susceptible
epidemic model on the hypercubic lattice,
Physical Review E 70, 036114.
Levin, S.A. & Durrett, R. (1996)
From individuals to epidemics,
Phil. Trans. Royal Soc. London B 351, 1615--1621.
Stollenwerk, N., Martins, J. & Pinto, A. (2007)
The phase transition lines in pair approximation
for the basic reinfection model SIRI, submitted.
Tags
- analytics
- approximation
- epidemiology
- lines
- model
- pair
- phase
- processes
- reinfection
- statphys23
- stochastic
- topic-10
- transition
