Hostname: page-component-76fb5796d-vfjqv Total loading time: 0 Render date: 2024-04-27T22:41:42.736Z Has data issue: false hasContentIssue false
  • English
  • Français

The initial geographical spread of host-vector and carrier-borne epidemics

Published online by Cambridge University Press:  14 July 2016

J. Radcliffe
J. Radcliffe*
Affiliation:
Queen Mary College, London
Get access Rights & Permissions [Opens in a new window]

Abstract

The deterministic and stochastic models developed by Bartlett (1956) to describe the initial spatial spread of an epidemic such as measles are extended to host-vector and carrier-borne epidemics such as malaria and typhoid in which more than one type of individual is involved. If the epidemic does not die out, then the behaviour predicted by the deterministic model and an examination of the mean distributions in the stochastic model is a wave of infection spreading out from the initial source of infection.

Keywords

INITIAL GEOGRAPHICAL SPREADHOST-VECTORCARRIER-BORNE EPIDEMICDETERMINISTIC AND STOCHASTIC MODELSWAVE OF INFECTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 10 , Issue 4 , December 1973 , pp. 703 - 717
Copyright
Copyright © Applied Probability Trust 1973 

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

Bailey, N. T. J. (1957) The Mathematical Theory of Epidemics. Griffin, London; Hafner, New York.Google Scholar
Bailey, N. T. J. (1967) The simulation of stochastic epidemics in two dimensions. Proc. 5th Berkeley Symp. Math. Statist, and Prob. 4, 237–257.Google Scholar
Bartlett, M. S. (1954) Processus stochastiques ponctuels. Ann. Inst. Poincaré 14, 35–60.Google Scholar
Bartlett, M. S. (1956) Deterministic and stochastic models for recurrent epidemics. Proc. 3rd Berkeley Symp. Math. Statist. and Prob. 4, 81–109.Google Scholar
Bartlett, M. S. (1960) Stochastic Population Models in Ecology and Epidemiology. Wiley, New York; Methuen, London.Google Scholar
Bartlett, M. S. (1964) The relevance of stochastic models for large scale epidemiological phenomena. Appl. Statist. 13, 2–8.Google Scholar
Bartlett, M. S. (1966) An Introduction to Stochastic Processes. Cambridge University Press, London and New York.Google Scholar
Griffiths, D. A. (1972) A bivariate birth-death process which approximates to the spread of a disease involving a vector. J. Appl. Prob. 9, 65–75.Google Scholar
Griffiths, D. A. (1973) Multivariate birth-and-death processes as approximations to epidemic processes. J. Appl. Prob. 10, 15–26.Google Scholar
Harris, T. E. (1963) The Theory of Branching Processes. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Kendall, D. G. (1957) Contribution to the discussion in Bartlett, measles periodicity and community size. J. R. Statist. Soc. A 120, 48–70.Google Scholar
Kendall, D. G. (1965) Mathematical models of the spread of infection. In Mathematics and Computer Science in Biology and Medicine. H.M.S.O., London. 213–225.Google Scholar
Lighthill, M. J. (1964) Introduction to Fourier Analysis and Generalised Functions. Cambridge University Press.Google Scholar
Mode, C. J. (1971) Multitype Branching Processes, Theory and Applications. American Elsevier, New York.Google Scholar
Moyal, J. E. (1962) The general theory of stochastic population processes. Acta Math. 108, 1–31.Google Scholar
Moyal, J. E. (1964) Multiplicative population processes. J. Appl. Prob. 1, 267–283.CrossRefGoogle Scholar
Neyman, J. and Scott, E. (1964) A stochastic model of epidemics. In Stochastic Models in Medicine and Biology (ed. Gurland, J.). University of Wisconsin Press. 45–85.Google Scholar
Pettigrew, H. M. and Weiss, G. H. (1967) Epidemics with carriers: the large population approximation. J. Appl. Prob. 4, 257–263.Google Scholar