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CDAM Research Report, LSE-CDAM-2006-14October 2006 |
Laws of Large Numbers for Epidemic Models with Countably Many Types
A. D. Barbour and M. J. Luczak
In modelling parasitic diseases, it is natural to distinguish hosts according to the number of parasites that they carry, leading to a countably infinite type space. Proving the analogue of the deterministic equations, used in models with finitely many types as a `law of large numbers' approximation to the underlying stochastic model, has previously either been done case by case, using some special structure, or else not attempted. In this paper, we prove a general theorem of this sort, and complement it with a rate of convergence in the $\ell_1$-norm.A PDF file (262 kB) with the full contents of this report can be downloaded by clicking here.
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