Stochastic processes often pose the difficulty that, as soon as a model devi ates from the simplest kinds of assumptions, the differential equations obtained for the density and the generating functions become mathematically formidable. Worse still, one is very often led to equations which have no known solution and don't yield to standard analytical methods for differential equations. In the model considered here, one for tumor growth with an immunological re sponse from the normal tissue, a nonlinear term in the transition probability for the death of a tumor cell leads to the above-mentioned complications. Despite the mathematical disadvantages of this nonlinearity, we are able to consider a more sophisticated model biologically. Ultimately, in order to achieve a more realistic representation of a complicated phenomenon, it is necessary to examine mechanisms which allow the model to deviate from the more mathematically tractable linear format. Thus far, stochastic models for tumor growth have almost exclusively considered linear transition probabilities.
Product Identifiers
Publisher
Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
ISBN-13
9783540077862
eBay Product ID (ePID)
190212995
Product Key Features
Author
Neil Dubin
Publication Name
A Stochastic Model for Immunological Feedback in Carcinogenesis: Analysis and Approximations
Format
Paperback
Language
English
Subject
Mathematics
Publication Year
1976
Type
Textbook
Number of Pages
165 Pages
Dimensions
Item Height
244mm
Item Width
170mm
Volume
9
Item Weight
370g
Additional Product Features
Title_Author
Neil Dubin
Series Title
Lecture Notes in Biomathematics
Country/Region of Manufacture
Germany
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