Queueing models of potentially lethal damage repair in irradiated cells.

Some of the ideas arising in queueing theory are applied to describe the repair mechanisms responsible for recovery of cells from potentially lethal radiation damage. Two alternative versions are presented of a queueing model of damage repair after a single dose of irradiation. The first version represents a linear misrepair model, and the second invokes the idea of spontaneous lesion fixation.

A distribution of tumor size at detection and its limiting form.

A distribution of tumor size at detection is derived within the framework of a mechanistic model of carcinogenesis with the object of estimating biologically meaningful parameters of tumor latency. Its limiting form appears to be a generalization of the distribution that arises in the length-biased sampling from stationary point processes. The model renders the associated estimation problems tractable.

A bivariate limiting distribution of tumor latency time.

The model of radiation carcinogenesis, proposed earlier by Klebanov, Rachev, and Yakovlev [8] substantiates the employment of limiting forms of the latent time distribution at high dose values. Such distributions arise within the random minima framework, the two-parameter Weibull distribution being a special case. This model, in its present form, does not allow for carcinogenesis at multiple sites.

A stochastic model of radiation carcinogenesis: latent time distributions and their properties.

A stochastic model of radiation carcinogenesis is proposed that has much in common with the ideas suggested by M. Pike as early as 1966. The model allows us to obtain a parametric family of substochastic-type distributions for the time of tumor latency that provides a description of the rate of tumor development and the number of affected individuals.