Coupling a branching process to an infinite dimensional epidemic process
Abstract
Branching process approximation to the initial stages of an epidemic process has been used since the 1950's as a technique for providing stochastic counterparts to deterministic epidemic threshold theorems. One way of describing the approximation is to construct both branching and epidemic processes on the same probability space, in such a way that their paths coincide for as long as possible. In this paper, it is shown, in the context of a Markovian model of parasitic infection, that coincidence can be achieved with asymptotically high probability until o(N^{2/3}) infections have occurred, where N denotes the total number of hosts.
 Publication:

arXiv eprints
 Pub Date:
 October 2007
 arXiv:
 arXiv:0710.3697
 Bibcode:
 2007arXiv0710.3697B
 Keywords:

 Mathematics  Probability;
 Quantitative Biology  Populations and Evolution;
 92D30;
 60J85
 EPrint:
 16 pages