Effect of time delay in a physiological process containing both a positive and negative feedback response

Abstract

A mathematic model for any physiological process which requires three variables, one of which experiences a positive feedback response and another one which experiences a negative feedback response is proposed. A time delay is incorporated into the positive feedback loop. A bifurcation analysis of the three nonlinear autonomous first order differential equations comprising the model is done. It is found that the model allows for a bifurcation to a limit cycle behavior as the delay time is varied. It is seen that the model describes process call erythropoiesis, the production of red blood cells. Numerical solutions agree with behaviors predicted by the mathematical analysis.