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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

Information

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

Heyde, C. C. (1984) Robust population models with application in genetic and epidemic theory (abstract). Adv. Appl. Prob. 16, 26.Google Scholar
Picard, Ph. (1980) Applications of martingale theory to some epidemic models. J. Appl. Prob. 17, 583–599.Google Scholar
Picard, Ph. (1981) Applications of martingale theory to carrier-borne epidemic models with time-dependent parameters. Math. Biosci. 55, 205–229.CrossRefGoogle Scholar
Routleff, C. (1982) A variation of Weiss's carrier-borne epidemic model. J. Appl. Prob. 19, 403–407.Google Scholar
Severo, N. C. (1969) Generalizations of some epidemic models. Math. Biosci. 4, 395–402.Google Scholar