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A recursion theorem on solving differential-difference equations and applications to some stochastic processes

Published online by Cambridge University Press:  14 July 2016

Norman C. Severo
Norman C. Severo*
Affiliation:
State University of New York, Buffalo
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Summary

A recursive procedure leading to the solution of triangular systems of differential-difference equations is presented. It is shown that the equations for special families of multi-dimensional pure birth processes and pure death processes can be represented as such a system. The theory is used to resolve a difficult problem of stochastic cross-infection among groups. Additional applications to problems in epidemic theory are discussed.

Type
Research Papers
Information
Journal of Applied Probability , Volume 6 , Issue 3 , December 1969 , pp. 673 - 681
Copyright
Copyright © Applied Probability Trust 

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References

Bailey, N. T. J. (1963) The simple stochastic epidemic: a complete solution in terms of known functions. Biometrika 50, 235–240.Google Scholar
Downton, F. (1968) The ultimate size of carrier-borne epidemics. Biometrika 55, 277–289.Google Scholar
Gani, J. (1965) On a partial differential equation of epidemic theory. I. Biometrika 52, 617–622.Google Scholar
Gani, J. (1967) On the general stochastic epidemic. Proc. 5th Berkeley Symp. Math. Stat. Prob. University of California Press, 4, 271–279.Google Scholar
Gart, J. J. (1968) The mathematical analysis of an epidemic with two kinds of susceptibles. Biometrics 24, 557–565.Google Scholar
Haskey, H. W. (1957) Stochastic cross-infection between two otherwise isolated groups. Biometrika 44, 193–204.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) The probabilities of some epidemic models. Biometrika 56, 197–201.Google Scholar
Siskind, V. (1965) A solution of the general stochastic epidemic. Biometrika 52, 613–616.CrossRefGoogle ScholarPubMed