Hostname: page-component-84b7d79bbc-g5fl4 Total loading time: 0 Render date: 2024-07-30T06:42:08.573Z Has data issue: false hasContentIssue false
  • English
  • Français

Carrier-borne epidemics with immigration. I — Immigration of both susceptibles and carriers

Published online by Cambridge University Press:  14 July 2016

K. Dietz  and
F. Downton
K. Dietz
Affiliation:
Institut für Medizinische Statistik und Dokumentation, Freiburg
F. Downton
Affiliation:
University of Birmingham
Get access Rights & Permissions [Opens in a new window]

Extract

Much of the theory of epidemics (see Bailey, 1957) has been concerned with models for their behaviour in closed populations. In such models the epidemic ultimately dies out, and interest has been concentrated on, for example, the ultimate size of the epidemic and its duration in time. In practice a population is rarely completely closed, and for many diseases an endemic model rather than an epidemic model is appropriate. To create models for endemic diseases it is necessary to introduce both new persons susceptible to the disease into the population and new sources of infection. For the so-called general stochastic epidemic, Ridler-Rowe (1967) has obtained certain limiting properties of the population where immigration of both susceptibles and infectives into the population takes place, but much work remains to be done to obtain, for example, the general equilibrium behaviour of this model.

Type
Research Papers
Information
Journal of Applied Probability , Volume 5 , Issue 1 , April 1968 , pp. 31 - 42
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

Bharucha-Reid, A. T. (1960) Elements of the Theory of Markov Processes and their Applications. McGraw-Hill, New York.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
Ridler-Rowe, C. J. (1967) On a stochastic model of an epidemic. J. Appl. Prob. 4, 19–33.CrossRefGoogle Scholar
Rushton, S. and Lang, E. D. (1954) Tables on the confluent hypergeometric function. Sankhya 13, 377–411.Google Scholar
Weiss, G. H. (1965) On the spread of epidemics by carriers. Biometrics 21, 481–490.Google Scholar