8,643 research outputs found
Stochastic epidemic models: a survey
This paper is a survey paper on stochastic epidemic models. A simple
stochastic epidemic model is defined and exact and asymptotic model properties
(relying on a large community) are presented. The purpose of modelling is
illustrated by studying effects of vaccination and also in terms of inference
procedures for important parameters, such as the basic reproduction number and
the critical vaccination coverage. Several generalizations towards realism,
e.g. multitype and household epidemic models, are also presented, as is a model
for endemic diseases.Comment: 26 pages, 4 figure
Critical scaling of stochastic epidemic models
In the simple mean-field SIS and SIR epidemic models, infection is
transmitted from infectious to susceptible members of a finite population by
independent coin tosses. Spatial variants of these models are proposed, in
which finite populations of size are situated at the sites of a lattice and
infectious contacts are limited to individuals at neighboring sites. Scaling
laws for both the mean-field and spatial models are given when the infection
parameter is such that the epidemics are critical. It is shown that in all
cases there is a critical threshold for the numbers initially infected: below
the threshold, the epidemic evolves in essentially the same manner as its
branching envelope, but at the threshold evolves like a branching process with
a size-dependent drift.Comment: Published at http://dx.doi.org/10.1214/074921707000000346 in the IMS
Lecture Notes Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
Household epidemic models with varying infection response
This paper is concerned with SIR (susceptible infected removed)
household epidemic models in which the infection response may be either mild or
severe, with the type of response also affecting the infectiousness of an
individual. Two different models are analysed. In the first model, the
infection status of an individual is predetermined, perhaps due to partial
immunity, and in the second, the infection status of an individual depends on
the infection status of its infector and on whether the individual was infected
by a within- or between-household contact. The first scenario may be modelled
using a multitype household epidemic model, and the second scenario by a model
we denote by the infector-dependent-severity household epidemic model. Large
population results of the two models are derived, with the focus being on the
distribution of the total numbers of mild and severe cases in a typical
household, of any given size, in the event that the epidemic becomes
established. The aim of the paper is to investigate whether it is possible to
determine which of the two underlying explanations is causing the varying
response when given final size household outbreak data containing mild and
severe cases. We conduct numerical studies which show that, given data on
sufficiently many households, it is generally possible to discriminate between
the two models by comparing the Kullback-Leibler divergence for the two fitted
models to these data.Comment: 29 pages; submitted to Journal of Mathematical Biolog
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