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A note on perturbation techniques for epidemics

Published online by Cambridge University Press:  01 July 2016

H. E. Daniels
H. E. Daniels*
Affiliation:
University of Birmingham
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Extract

This note is prompted by the papers of Weiss (this Symposium) and Bailey (1968). Weiss develops a technique for approximation to the moments of an epidemic process by regarding them as expandable in powers of N-1 where N is the size of the population, assumed constant. He first considers the simple stochastic epidemic with no removals and obtains explicit formulae for the terms of order N-1, the zero order terms being the deterministic values. Bailey is concerned with a similar type of approximation and he derives explicit results to the same order. Bailey uses an eigenfunction approach whereas Weiss's method is more direct and perhaps easier to generalise. However, in attempting to extend the method to the case of a closed epidemic with removals Weiss is led to intractable difference equations.

Type
III. Results on the General Stochastic Epidemic
Information
Advances in Applied Probability , Volume 3 , Issue 2 , Autumn 1971 , pp. 214 - 218
Copyright
Copyright © Applied Probability Trust 1971 

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References

Bailey, N. T. J. (1968) A perturbation approach to the simple stochastic epidemic in a large population. Biometrika 55, 199–209.Google Scholar
Daniels, H. E. (1960) Approximate solutions of Green's type for univariate stochastic processes. J. R. Statist. Soc. B 22, 376–401.Google Scholar
Weiss, G. H. (1970) On a perturbation method for the theory of epidemics. (WHO Symposium).Google Scholar
Whittle, P. (1957) On the use of the normal approximation in the treatment of stochastic processes. J. R. Statist. Soc. B 19, 268–281.Google Scholar