The Geometry and Nonlinear Dynamics of pathogenesis

Publication Type:

Journal Articles

Authors:

PG Vaidya

Source:

Sadhana, Volume 24, Number 1-2, p.53–71 (1999)

URL:

http://eprints.nias.res.in/76/

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.

Notes:

The Copyright belongs to Indian Academy of Sciences.