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Applications of martingale theory to some epidemic models, II

Published online by Cambridge University Press:  14 July 2016

Philippe Picard
Philippe Picard*
Affiliation:
Université de Lyon 1
*
∗Postal address: Université Claude Bernard (Lyon 1), Mathématiques Appliqueés, 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne Cedex, France.
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Abstract

We consider Weiss's and Downton's models with parametersπ, αand β depending on i number of susceptibles and j number of carriers. A martingale argument is performed when πand α /β only depend on i or, in Weiss's case, when α /β is the product of a function of i by a function of j. In these cases the martingale approach proves very valuable and gives explicit results quite easily. In particular it shows that well-known relations between moments and integrals along a trajectory are still true for any stopping time and for more general models than the classic ones.

Keywords

CARRIER-BORNEEND AND DIMENSION OF EPIDEMICINTEGRAL ALONG A TRAJECTORYSTOPPING TIME
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 4 , December 1984 , pp. 677 - 684
Copyright
Copyright © Applied Probability Trust 1984 

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References

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