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VARIABILITY FOR CARRIER-BORNE EPIDEMICS AND REED–FROST MODELS INCORPORATING UNCERTAINTIES AND DEPENDENCIES FROM SUSCEPTIBLES AND INFECTIVES

Published online by Cambridge University Press:  18 March 2010

Eva María Ortega  and
Laureano F. Escudero
Eva María Ortega
Affiliation:
Dept. Estadística, Matemáticas e Informática, Centro de Investigación Operativa, Universidad Miguel Hernández, 03312 Orihuela (Alicante), Spain E-mail: evamaria@umh.es
Laureano F. Escudero
Affiliation:
Dept. Estadística, Matemáticas e Informática, Centro de Investigación Operativa, Universidad Miguel Hernández, 03312 Orihuela (Alicante), Spain E-mail: evamaria@umh.es
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Abstract

This article provides analytical results on which are the implications of the statistical dependencies among certain random parameters on the variability of the number of susceptibles of the carrier-borne epidemic model with heterogeneous populations and of the number of infectives under the Reed–Frost model with random infection rates. We consider dependencies among the random infection rates, among the random infectious times, and among random initial susceptibles of several carrier-borne epidemic models. We obtain conditions for the variability ordering between the number of susceptibles for carrier-borne epidemics under two different random environments, at any time-scale value. These results are extended to multivariate comparisons of the random vectors of populations in the strata. We also obtain conditions for the increasing concave order between the number of infectives in the Reed–Frost model under two different random environments, for any generation. Variability bounds are obtained for different epidemic models from modeling dependencies for a range of special cases that are useful for risk assessment of disease propagation.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 24 , Issue 2 , April 2010 , pp. 303 - 328
Copyright
Copyright © Cambridge University Press 2010

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