School Seminars and Colloquia

Laws of large numbers for epidemic models with countably many types

Complex Systems Seminar

by Professor Andrew D Barbour

Institution: Universitaet Zuerich
Date: Thu 30th August 2007
Time: 1:15 PM
Location: Russel Love Theatre, Richard Berry Building, Uni of Mel

Abstract: Many epidemic models can be formulated naturally as density
dependent particle systems with mean field interactions. T.G. Kurtz
1970 to 1976 gave a general theory, including laws of large numbers and
central limit theorems, for finite dimensional systems Ch. L eonard
1988 introduced an explicit spatial component. However, models of parasitic infections give rise to systems with countably infinitely many types, in that hosts are naturally distinguished according to the number of parasites that they carry. In this context, even laws of large numbers
can be difficult to establish, and are usually only proved using special
properties of individual systems. In this talk, we shall discuss an approach which works in some generality, and gives a rate of approximation for the law of large numbers in an l 1 norm. Joint work with Malwina Luczak.

For More Information: Konstantin Borovkov