Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-23T11:04:11.239Z Has data issue: false hasContentIssue false
  • English
  • Français

A state-dependent lifetime process of individuals subject to external perturbations

Published online by Cambridge University Press:  14 July 2016

Wolfgang Mergenthaler
Wolfgang Mergenthaler*
Affiliation:
Strahlenbiologisches Institut der Universität München
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider an individual which ultimately dies or divides, and whose state is subject to drift and jumps caused by external perturbations. The mortality and division rates being state-dependent, the present paper deals with the time-dependent distribution of the individual's position in the state-space and with its lifetime distribution. The results are applied to a model of a biological cell which is exposed to ionizing radiation. Under certain conditions on the parameters of the type of perturbation one can show that the division probability decreases and the mean regeneration time increases with increasing frequency and ‘effect' of the perturbations.

Keywords

LIFETIME DISTRIBUTIONDIVISION PROBABILITYMEAN REGENERATION TIMEIRRADIATED BIOLOGICAL CELLS
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 4 , December 1980 , pp. 922 - 938
Copyright
Copyright © Applied Probability Trust 

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

Bartlett, M. S. (1960) An Introduction to Stochastic Processes. Cambridge University Press.Google Scholar
Feller, W. (1937) Zur Theorie der stochastischen Prozesse. Math. Ann. 113, 113–160.Google Scholar
Feller, W. (1952) The parabolic differential equations and the associated semi-group of transformations. Ann. Math. 55, 468–519.CrossRefGoogle Scholar
Feller, W. (1954) Diffusion processes in one dimension. Trans. Amer. Math. Soc. 77, 1–31.CrossRefGoogle Scholar
Mergenthaler, W. (1979) A sufficient criterion for particles performing a diffusive motion with state-dependent death-rate to die with probability one. Adv. Appl. Prob. 11, 510–526.Google Scholar
Trott, K. R. (1974) Das Proliferationsmuster unbestrahlter und röntgenbestrahlter Säugetierzellen in vitro. GSF-Bericht B 553, Gesellschaft für Strahlen- und Umweltforschung, Neuherberg bei München.Google Scholar