Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-23T02:05:16.343Z Has data issue: false hasContentIssue false
  • English
  • Français

Certain state-dependent processes for dichotomised parasite populations

Published online by Cambridge University Press:  14 July 2016

A. W. Kemp  and
J. Newton
A. W. Kemp
Affiliation:
University of St Andrews
J. Newton*
Affiliation:
University of St Andrews
*
∗Postal address for both authors: Department of Mathematical Sciences, North Haugh, University of St Andrews, St Andrews KY16 9SS, Scotland.
Get access Rights & Permissions [Opens in a new window]

Abstract

The paper re-examines Quinn and MacGillivray's (1986) stationary birth-death process for a population of fixed size N consisting of two types of parasite, active and passive, and sets up a more elaborate model for the dichotomy between parasites on hosts with and without open wounds resulting from previous parasite attacks. The probability generating functions for the stationary count distributions are obtained, allowing limiting forms of the distributions to be investigated.

Keywords

BIRTH-DEATH PROCESSCONFLUENT HYPERGEOMETRIC DISTRIBUTIONQ-BINOMIAL ANALOGUEQ-POISSON ANALOGUESTRONGLY UNIMODAL DISTRIBUTIONSLIMITING NORMALITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 2 , June 1990 , pp. 251 - 258
Copyright
Copyright © Applied Probability Trust 1990 

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

Barbour, A. D. (1974) On a functional central limit theorem for Markov population processes. Adv. Appl. Prob. 6, 21–39.Google Scholar
Diamond, P. M. (1983) Functional response and some stationary distributions of searching parasites. Pure Mathematics Preprint 70, University of Queensland.Google Scholar
Erdélyi, A. (1953) Higher Transcendental Functions, Vol. 1. McGraw-Hill, New York.Google Scholar
Exton, H. (1983) q-Hyper geometric Functions and Applications. Ellis Horwood, Chichester.Google Scholar
Kapur, J. N. (1978a) On generalised birth and death processes and generalised hypergeometric functions. Indian J. Math. 20, 57–69.Google Scholar
Kapur, J. N. (1978b) Application of generalized hypergeometric functions to generalized birth and death processes. Indian J. Pure Appl. Math. 9, 1059–1069.Google Scholar
Kemp, A. W. (1968a) Studies in Discrete Distribution Theory Based on the Generalized Hypergeometric Function and Associated Differential Equations. Ph.D. Thesis, Queen's University, Belfast.Google Scholar
Kemp, A. W. (1968b) A wide class of discrete distributions and the associated differential equations. Sankhya A 30, 401–410.Google Scholar
Kemp, A. W. (1987) A Poissonian binomial model with constrained parameters. Naval Res. Logist. Quart. 34, 853–858.Google Scholar
Kemp, A. W. and Kemp, C. D. (1988) Weldon's dice data revisited. (Submitted).Google Scholar
Mcneil, D. R. and Schach, S. (1973) Central limit analogues for Markov population processes. J. R. Statist. Soc. B 35, 1–23.Google Scholar
Quinn, B. G. and Macgillivray, H. L. (1986) Normal approximations to discrete unimodal distributions. J. Appl. Prob. 23, 1013–1018.Google Scholar
Slater, L. J. (1960) Confluent Hypergeometric Functions. Cambridge University Press.Google Scholar
Srivastava, H. M. and Kashyap, B. R. K. (1982). Special Functions in Queueing Theory. Academic Press, New York.Google Scholar