Abstract
Let X(t) be the number of tumor cells at time t, and Pr{X(t) = n} = pn(t) is the density of X. A “birth”, i.e., an increase of one of the total population of cancer cells, can occur either by mutation of a normal cell caused by the action of the carcinogen, consisting of randomly (Poisson) distributed hits, or by reproduction of existing cancer cells. A death of a tumor cell occurs as an additive combination of non-immunological and immunological elements. Once a tumor is initiated by carcinogenic action, it undergoes a birth and death process with infinitesimal birth rate linear and infinitesimal death rate composed of a linear and a nonlinear term, the former due to non-immunological deaths, the latter to immunological feedback. The death rate per tumor cell due to immunological response is proportional to the total number of antigen-producing (tumor) cells; thus, the total death rate is quadratic. Although this assumes a very simple mechanism for the action of immunological feedback, it is nevertheless a first step.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1976 Springer-Verlag Berlin · Heidelberg
About this chapter
Cite this chapter
Dubin, N. (1976). The Mathematical Model. In: A Stochastic Model for Immunological Feedback in Carcinogenesis: Analysis and Approximations. Lecture Notes in Biomathematics, vol 9. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46338-9_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-46338-9_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-07786-2
Online ISBN: 978-3-642-46338-9
eBook Packages: Springer Book Archive