Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-14T11:15:39.740Z Has data issue: false hasContentIssue false
  • English
  • Français

A random allocation model for carrier-borne epidemics

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

D. J. Daley  and
J. Gani
D. J. Daley*
Affiliation:
The Australian National University
J. Gani*
Affiliation:
University of California, Santa Barbara
*
∗ Postal address: Stochastic Analysis Group, School of Mathematical Sciences, Australian National University, Canberra, ACT 0200, Australia.
∗∗ Postal address: Department of Statistics, University of California, Santa Barbara, CA 93106, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

A carrier-borne epidemic is considered in which the carriers, subject to a death process, infect susceptibles by random allocation rather than the classical homogeneous mixing process. An explicit solution for the probability generating function (p.g.f.) of the process is obtained, and a probabilistic analysis of carrier models provided. The sizes and durations of the random allocation and classical carrier epidemics are compared. The strongest comparisons concern sample path results based on the probabilistic analysis; this also gives a sounder basis for computational work.

Keywords

HOMOGENEOUS MIXINGSIZE OF EPIDEMICDURATION OF EPIDEMIC

MSC classification

Primary: 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Secondary: 92D30: Epidemiology
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 4 , December 1993 , pp. 751 - 765
Copyright
Copyright © Applied Probability Trust 1993 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Research carried out with the support of NIH Grant ROI AI 29426 while visiting the Australian National University.

References

Bailey, N. T. J. (1975) The Mathematical Theory of Infectious Diseases and its Applications, 2nd edn. Griffin, London.Google Scholar
Daley, D. J. (1988) The total size of epidemics with variable infectious periods. Technical Report, Statistics Research Section, Australian National University.Google Scholar
Daley, D. J. (1992) Models for the spread of infection via pairing at parties. Unpublished.Google Scholar
Dietz, K. (1966) On the model of Weiss for the spread of epidemics by carriers. J. Appl. Prob. 3, 375–382.Google Scholar
Downton, F. (1967) Epidemics with carriers: a note on a paper of Dietz. J. Appl. Prob. 4, 264–270.Google Scholar
Downton, F. (1968) The ultimate size of carrier-borne epidemics. Biometrika 55, 277–289.CrossRefGoogle Scholar
Feller, W. (1968) An Introduction to Probability Theory and its Applications, Vol. 1, 3rd edn. Wiley, New York.Google Scholar
Gani, J. (1991) A carrier-borne epidemic with two stages of infection. Stoch. Models 7, 83–105.Google Scholar
Gani, J. and Michaletzky, G. (1991) A carrier-borne epidemic with multiple stages of infection. J. Appl. Prob. 28, 1–8.Google Scholar
Henderson, W. (1979) A solution of the carrier-borne epidemic. J. Appl. Prob. 16, 641–645.Google Scholar
Puri, P. S. (1975a) A linear birth and death process under the influence of another process. J. Appl. Prob. 12, 1–17.CrossRefGoogle Scholar
Puri, P. S. (1975b) A stochastic process under the influence of another arising in the theory of epidemics. In Statistical Inference and Related Topics, Vol. 2, ed. Puri, M. L., pp. 235–255. Academic Press, New York.Google Scholar
Puri, P. S. (1977) A simpler approach to derivation of some results in epidemic theory. In Proc. Symp. to honour Jerzy Neyman, pp. 265–275. PWN - Polish Scientific Publishers, Warszawa.Google Scholar
Weiss, G. H. (1965) On the spread of epidemics by carriers. Biometrics 21, 481–490.Google Scholar