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Limit theorems for the total size of a spatial epidemic

Part of: Limit theorems Markov processes

Published online by Cambridge University Press:  14 July 2016

Håkan Andersson  and
Boualem Djehiche
Håkan Andersson*
Affiliation:
Stockholm University
Boualem Djehiche*
Affiliation:
Royal Institute of Technology, Stockholm
*
∗Postal address: Department of Mathematics, Stockholm University, S-106 91 Stockholm, Sweden.
∗∗Postal address: Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden.
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Abstract

We study the long-term behaviour of a sequence of multitype general stochastic epidemics, converging in probability to a deterministic spatial epidemic model, proposed by D. G. Kendall. More precisely, we use branching and deterministic approximations in order to study the asymptotic behaviour of the total size of the epidemics as the number of types and the number of individuals of each type both grow to infinity.

Keywords

EPIDEMIC PROCESSTOTAL SIZEHILBERT SPACEMARTINGALECOUPLING

MSC classification

Primary: 92D30: Epidemiology
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces 60F05: Central limit and other weak theorems
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 3 , September 1997 , pp. 698 - 710
Copyright
Copyright © Applied Probability Trust 1997 

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References

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