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The convergence of a position-dependent branching process used as an approximation to a model describing the spread of an epidemic

Published online by Cambridge University Press:  14 July 2016

J. Radcliffe
J. Radcliffe*
Affiliation:
Queen Mary College, London
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Abstract

A supercritical position-dependent Markov branching process has been used as an approximation to a model describing the initial geographical spread of a measles epidemic (Bartlett (1956)). Let α be its Malthusian parameter, ß its velocity of propagation, Z(A, t) the number of individuals in the set A at time t, and A√(ßt) = [√(ßt) r: r ∈ A]. The mean square convergence of the random variable W(A, t)= e–αtZ(A√(ßt), t) to a limit variable W(A) is established.

Keywords

MEAN-SQUARE CONVERGENCEPOSITION-DEPENDENT BRANCHING PROCESSMEASLES EPIDEMIC
Type
Short Communications
Information
Journal of Applied Probability , Volume 13 , Issue 2 , June 1976 , pp. 338 - 344
Copyright
Copyright © Applied Probability Trust 1976 

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