Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-22T05:01:30.906Z Has data issue: false hasContentIssue false
  • English
  • Français

The transition probabilities of the extended simple stochastic epidemic model and the Haskey model

Published online by Cambridge University Press:  14 July 2016

Richard J. Kryscio
Richard J. Kryscio*
Affiliation:
State University of New York, Buffalo
*
* Present address: National Cancer Institute, Bethesda, Maryland.
Get access Rights & Permissions [Opens in a new window]

Abstract

We present a solution to a special system of Kolmogorov forward equations. We use this result to present a useful expression for the transition probabilities of the extended simple stochastic epidemic model and an epidemic model involving cross-infection between two otherwise isolated groups.

Keywords

SIMPLE STOCHASTICEPIDEMIC MODELHASKEY MODELTRANSITION FUNCTIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 3 , June 1972 , pp. 471 - 485
Copyright
Copyright © Applied Probability Trust 1972 

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

This paper is part of the author's doctoral dissertation which was completed at the State University of New York, Buffalo, under the supervision of Professor Norman C. Severo. The research was partially supported by NIH Fellowship 1 FO1 GM43719.

References

Bailey, N. T. J. (1957) The Mathematical Theory of Epidemics. Charles Griffin and Co., Ltd., London.Google Scholar
Bailey, N. T. J. (1963) The simple stochastic epidemic: a complete solution in terms of known functions. Biometrika 50, 235–240.Google Scholar
Chiang, C. L. (1968) Introduction to Stochastic Processes in Biostatistics. J. Wiley and Sons Inc., New York.Google Scholar
Feller, W. (1939) Die Grundlagen Der Volterraschen Theorie Des Kampfes Ums Dasein in Wahrscheinlichkeitstheoretischen Behandlung. Acta Biotheoritica 5, 11–40.Google Scholar
Haskey, H. W. (1957) Stochastic cross-infection between two-otherwise isolated groups. Biometrika 44, 193–204.Google Scholar
Kryscio, R. J. and Severo, N. C. (1969) Some properties of an extended simple stochastic epidemic involving two additional parameters. Math. Biosciences 5, 1–8.Google Scholar
Severo, N. C. (1969a) A recursion theorem on solving differential-difference equations and applications to some stochastic processes. J. Appl. Prob. 6, 673–681.Google Scholar
Severo, N. C. (1969b) Generalizations of some stochastic epidemic models. Math. Biosciences 4, 395–402.Google Scholar