The dynamics of a nonlinear model of signal transduction in human under impulsive depressant drug treatment

Abstract

A mathematical model of the signal transduction process, involving hormone coupled receptors and an inhibiting enzyme, under impulsive depressant treatment, is proposed and analyzed. We show that there is a stable periodic solution, at the vanishing density of the ligand bound receptors on the cell membrane and plasmalemma, when the impulsive period is less than some critical value. The conditions for permanence of the system are then given. Finally, it is shown that as the impulsive period increases beyond a certain critical value, the emergence of stable positive periodic solution may be observed under appropriate conditions on the system parameters. © Dynamic Publishers, Inc.