Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-28T16:13:27.326Z Has data issue: false hasContentIssue false
  • English
  • Français

Factorial moments and probabilities for the general stochastic epidemic

Published online by Cambridge University Press:  14 July 2016

L. Billard
L. Billard*
Affiliation:
State University of New York at Buffalo
*
*Now at the University of Waterloo, Ontario.
Get access Rights & Permissions [Opens in a new window]

Abstract

By an appropriate partitioning of the matrix of coefficients in the system of differential difference equations for the general stochastic epidemic, the nature of the state probabilities is shown to consist of combinations of factorial terms. Further, factorial moments are readily obtained. In particular, the mean and variance of the number of susceptibles are derived.

Keywords

GENERAL STOCHASTIC EPIDEMICSTATE PROBABILITIESFACTORIAL MOMENTSMEAN AND VARIANCE OF NUMBER OF SUSCEPTIBLES
Type
Research Papers
Information
Journal of Applied Probability , Volume 10 , Issue 2 , June 1973 , pp. 277 - 288
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.Google Scholar
Bartlett, M. S. (1949) Some evolutionary stochastic processes. J. R. Statist. Soc. B 11, 211–222.Google Scholar
Gani, J. (1965) On a partial differential equation of epidemic theory, I. Biometrika 52, 617–622.Google Scholar
Severo, N. C. (1967) Two theorems on solutions of differential-difference equations and applications to epidemic theory. J. Appl. Prob. 4, 271–280.Google Scholar
Severo, N. C. (1969) A recursion theorem on solving differential-difference equations and applications to some stochastic processes. J. Appl. Prob. 6, 673–681.Google Scholar
Siskind, V. (1965) A solution of the general stochastic epidemic. Biometrika 52, 613–616.Google Scholar