Dubey2007 - A mathematical model for the effect of toxicant on the immune system (without toxicant effect) Model1

In this paper, a nonlinear mathematical model is proposed and analyzed to study the
effect of environmental toxicant on the immune response of the body. Criteria for local
stability, instability and global stability are obtained. It is shown that the immune
response of the body decreases as the concentration of environmental toxicant increases,
and certain criteria are obtained under which it settles down at its equilibrium level.
In the absence of toxicant, an oscillatory behavior of immune system and pathogenic
growth is observed. However, in the presence of toxicant, oscillatory behavior is not
observed. These studies show that the toxicant may have a grave effect on our body’s
defense mechanism.
Keywords: Pathogen; Immune Response; Toxicant; Stability.