Laws of large numbers for epidemic models with countably many types.
A.D. Barbour (Universität Zürich, Switzerland) and M. Luczak (London School of Economics)
Many epidemic models can be formulated naturally as density dependent particle systems with mean field interactions. T. G. Kurtz (1970–76) 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 l1-norm.