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On variation in birth processes

  • M. J. Faddy (a1)

Abstract

Birth processes with piecewise linear birth rates are analysed, and numerical results suggest that, relative to the linear case, convex birth rates increase variability and concave birth rates decrease variability.

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Copyright

Corresponding author

Postal address: Department of Mathematics and Statistics, University of Otago, PO Box 56, Dunedin, New Zealand.

References

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Abramowitz, M. and Stegun, I. A. (1972) Handbook of Mathematical Functions. Dover, New York.
Bailey, N. T. J. (1975) The Mathematical Theory of Infectious Diseases and its Applications. Griffin, London.
Ball, F. and Donnelly, P. (1987) Inter-particle correlation in death processes with application to variability in compartmental models. Adv. Appl. Prob. 19, 755766.
Cox, D. R. and Miller, H. D. (1965) The Theory of Stochastic Processes. Methuen, London.
Faddy, M. J. (1977) Stochastic compartmental models as approximations to more general stochastic systems with the general stochastic epidemic as an example. Adv. Appl. Prob. 9, 448461.
Faddy, M. J. (1985) Nonlinear stochastic compartmental models. IMA J. Math. Appl. Med. Biol. 2, 287297.
Morgan, B. J. T. and Hinde, J. P. (1976) On an approximation made when analysing stochastic processes. J. Appl. Prob. 13, 672683.

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On variation in birth processes

  • M. J. Faddy (a1)

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