A Stochastic Model for Immunological Feedback in Carcinogenesis: Analysis and Approximations (1976) (Lecture Notes in Biomathematics #9)
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- Synopsis
- Stochastic processes often pose the difficulty that, as soon as a model deviĀ 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 reĀ 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.
- Copyright:
- 1976
Book Details
- Book Quality:
- Publisher Quality
- ISBN-13:
- 9783642463389
- Related ISBNs:
- 9783540077862
- Publisher:
- Springer Berlin Heidelberg
- Date of Addition:
- 06/23/22
- Copyrighted By:
- N/A
- Adult content:
- No
- Language:
- English
- Has Image Descriptions:
- No
- Categories:
- Nonfiction, Mathematics and Statistics
- Submitted By:
- Bookshare Staff
- Usage Restrictions:
- This is a copyrighted book.