Vaidya, PG
(1999)
The Geometry and Nonlinear Dynamics of pathogenesis.
Sadhana, 24 (1-2).
pp. 53-71.
| Abstract: |
This paper is an extension of previous work on the dynamics of the competition of normal cells
and cancer cells for food supply. In this paper, we deal with pathogenesis (development of illness)
in general. In addition to cancer, other pathogens (disease causing agents) such as those which
attack normal cells directly and those which have a very low metabolic rate, are considered.
The paper differs from our previous work in another significant way. The entire presentation
has been based on a geometric perspective. It has been shown that this perspective, not only
greatly simplifies the analysis but also helps as a cogitation and communication tool. Two new
theorems about the stability of the rest points have been stated, and extensively used. One of the
fundamental questions of pathogenesis is this: why is it that sometimes a little bit of the disease
gets completely cured, on its own, and why is it that at times it grows a lot? Mathematically
it has been shown that the results depend crucially on two "upheavals" in the system caused
by changes in the parameters of the system. These upheavals cause "bifurcations". There are
bad bifurcations which are triggered by lowering the immune system below a dangerous level,
and good bifurcations which results when the food supply is significantly reduced. Using this
analysis, we now have a possibility for developing a firm quantitative foundation for the problem.
We have also shown that the famous ecological principle of "competitive exclusion" is not always
valid in these cases. In fact, we often get a "critical mass" of pathogen which must be present
for the disease to become viable.
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| Item Type: |
Journal Paper
|
| Additional Information: |
The Copyright belongs to Indian Academy of Sciences. |
| Subjects: |
School of Natural and Engineering Sciences > Mathematical Modeling |
| Date Deposited: |
19 May 2006 |
| Last Modified: |
07 Jul 2007 15:48 |
| Official URL: |
http://www.ias.ac.in/j_archive/sadhana/24/1and2/53... |
| Related URLs: |
|
| Funders: |
UNSPECIFIED |
| Projects: |
UNSPECIFIED |
| DOI: |
|
| URI: |
http://eprints.nias.res.in/id/eprint/76 |
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