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Some majorization orderings of heterogeneity in a class of epidemics

Part of: Applications Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Y. L. Tong
Y. L. Tong*
Affiliation:
Georgia Institute of Technology
*
∗Postal address: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332–0160, USA.
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Abstract

The theory of majorization is applied to investigate the effects of heterogeneity in a class of epidemics. In particular, the heterogeneity of the components of the contact vector of a given susceptible is studied. It is shown that if the heterogeneity can be partially ordered through majorization, then the probability functions of escaping infection can be similarly ordered. The results can be applied to AIDS research on the spread of the HIV virus.

Keywords

MAJORIZATION INEQUALITIESCARRIER-BORNE MODELHETEROGENEITY IN EPIDEMICS

MSC classification

Primary: 60E15: Inequalities; stochastic orderings 62P99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 1 , March 1997 , pp. 84 - 93
Copyright
Copyright © Applied Probability Trust 1997 

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References

Bailey, N. T. J. (1975) The Mathematical Theory of Infectious Diseases and Its Applications. Griffin, London.Google Scholar
Ball, F. G. (1985) Deterministic and stochastic epidemics with several kinds of susceptibles. Adv. Appl. Prob. 17, 1–22.Google Scholar
Becker, N. and Marschner, I. (1990) The effect of heterogeneity on the spread of disease. In Stochastic Processes in Epidemic Theory. ed. Gabriel, J.-P., Lefèvre, C. and Picard, P. Springer, Berlin. pp. 90–103.Google Scholar
Eisenberg, B. (1991) The effect of variable infectivity on the risk of HIV infection. Statist. Medicine 9, 131–139.Google Scholar
El-Neweihi, E., Proschan, F. and Sethuraman, J. (1986) Optimal allocation of components in parallel-series and series-parallel systems. J. Appl. Prob. 23, 770–777.Google Scholar
Hickey, R. J. (1983) Majorization, randomness and some discrete distributions. J. Appl. Prob. 20, 897–902.Google Scholar
Lefevre, C. (1994) Stochastic ordering of epidemics. In Stochastic Orders and Their Applications. ed. Shaked, M. and Shanthikumar, G. J. Academic Press, Boston. pp. 323–348.Google Scholar
Lefevre, C. and Malice, M.-P. (1988) Comparison for carrier-borne epidemics in heterogeneous and homogeneous populations. J. Appl. Prob. 25, 663–674.Google Scholar
Malice, M.-P. and Lefevre, C. (1988) On some effects of variability in the Weiss epidemic model. Commun. Statist. - Theory Meth. 17, 3723–3731.Google Scholar
Marshall, A. W. and Olkin, I. (1979) Inequalities: Theory of Majorization and Its Applications. Academic Press, New York.Google Scholar
Tong, Y. L. (1977) An ordering theorem for conditionally independent and identically-distributed random variables. Ann. Statist. 5, 274–277.Google Scholar
Tong, Y. L. (1990) The Multivariate Normal Distribution. Springer, Berlin.Google Scholar
Weiss, G. H. (1965) On the spread of epidemics by carriers. Biometrics 21, 481–490.Google Scholar