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Applications of martingale theory to some epidemic models

Published online by Cambridge University Press:  14 July 2016

Philippe Picard
Philippe Picard*
Affiliation:
Université de Lyon I
*
∗Postal address: Mathématiques Appliquées, 43, Boulevard du 11 Novembre 1918, 69621 Villeurbanne, France.
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Abstract

The purpose of this paper is to give some very simple applications of martingales to epidemics. The results are all connected with stopping times T (for instance the classical end of epidemic) and include the expression of the joint generating function Laplace transform of and and simple relations between moments of these three variables. (Here Xt and Yt respectively denote the numbers of susceptibles and carriers.) We also give several relations between different types of epidemics. Although this paper only deals with Downton's model, some of the methods are still valid for more general models.

Keywords

EPIDEMICSEND AND DIMENSION OF EPIDEMICMARTINGALESTOPPING TIMEAREA UNDER TRAJECTORY OF CARRIERSPARAMETER ESTIMATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 3 , September 1980 , pp. 583 - 599
Copyright
Copyright © Applied Probability Trust 1980 

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