Hostname: page-component-6bf8c574d5-7jkgd Total loading time: 0 Render date: 2025-02-14T22:40:17.349Z Has data issue: false hasContentIssue false
  • English
  • Français

Epidemics with carriers: The large population approximation

Published online by Cambridge University Press:  14 July 2016

Hugh M. Pettigrew  and
George H. Weiss
George H. Weiss
Affiliation:
National Cancer Institute, Bethesda, Maryland
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper applies the constant population approximation to the study of epidemics which involve more than a single type of infective. An example of this would be a situation in which both clinically infected individuals and subclinically infected individuals or carriers are present.

We derive equations for the expected numbers of clinically infected individuals and carriers at any time t for the model with zero latent period and infectious periods having negative exponential distributions. From these equations we derive conditions under which a unimodal incidence curve can result, and expressions for the expected total epidemic size.

Type
Research Papers
Information
Journal of Applied Probability , Volume 4 , Issue 2 , August 1967 , pp. 257 - 263
Copyright
Copyright © Sheffield: Applied Probability Trust 

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.)

References

[1] Bailey, N. T. J. (1957) The Mathematical Theory of Epidemics. Griffin, London.Google Scholar
[2] Bailey, N. T. J. (1964) Some stochastic models for small epidemics in large populations. Appl. Statist. XIII, 9–19.CrossRefGoogle Scholar
[3] Morgan, R. W. (1964) A note on Dr. Bailey's paper. Appl. Statist. XIII, 20–24.Google Scholar
[4] Williams, T. (1965) The simple stochastic epidemic curve for large populations of susceptibles. Biometrika, 52, 571–579.CrossRefGoogle ScholarPubMed
[5] Bartlett, M. S. (1955) Stochastic Processes. Cambridge University Press.Google Scholar
[6] Whittle, P. (1955) The outcome of a stochastic epidemic — a note on Bailey's paper. Biometrika 42, 116–122.Google Scholar
[7] Kendall, D. G. (1956) Deterministic and stochastic epidemics in closed populations. Proc. Third Berkeley Symp. on Math. Stat. and Prob. 4, 149–165.Google Scholar
[8] Gart, J. J. The mathematical analysis of an epidemic with two kinds of susceptibles (to appear).Google Scholar
[9] Weiss, G. H. (1965) On the spread of epidemics by carriers. Biometrics 21, 481–490.CrossRefGoogle ScholarPubMed
[10] Harris, T. E. (1963) The Theory of Branching Processes. Prentice-Hall, Englewood Cliffs, N.J. Google Scholar
[11] Hawkins, D. and Ulam, S. (1944) Theory of multiplicative processes, I. Los Alamos Scientific Laboratory, LADC-265.Google Scholar