The University of Nottingham
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Division of Statistics, School of Mathematical Sciences
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SEMINAR:
Time: 2pm, Thurs 13th Jan
Venue: Room C19, Maths and Physics Building
Speaker: Dr. Tom Britton, Uppsala University
Title: Stochastic Epidemics in Dynamic Populations: Quasi-stationarity
and Extinction
Abstract:
Empirical evidence shows that childhood diseases persist in large
communities whereas in smaller communities the epidemic goes extinct
(and is later reintroduced by immigration). The present paper treats a
stochastic model describing the spread of an infectious disease giving
life-long immunity, in a community where individuals die and new
individuals are born. In a large population the epidemic process may be
approximated by a diffusion process. The time to extinction starting in
(quasi-)stationarity is shown to be exponentially distributed and an
approximate expression for the mean parameter $\tau$ is obtained from the
diffusion approximation. The expression is used to study how $\tau$
depends on the community size but also on certain properties of the
disease/community: the basic reproduction number and the means and
variances of the latency period, infectious period and life-length.
Effects of introducing a vaccination program are also discussed.
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For further details contact Dr. P.D. O'Neill ([log in to unmask],
tel 0115 951 4939), or see
http://www.maths.nottingham.ac.uk/seminars/Statistics.html
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Philip D. O'Neill School of Mathematical Sciences,
University of Nottingham, University Park, Nottingham,
England NG7 2RD
Tel: +44 (0)115 951 4939 (Direct)
Tel: +44 (0)115 951 4949 (School)
Fax: +44 (0)115 951 4951
Email: [log in to unmask]
WWW: http://www.maths.nott.ac.uk/personal/pdo/index.html
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