Discrete Model for Periodic Hematopoiesis
by Mike Martin

This page allows you to iterate a difference equation model, given explicitly below, for N steps using selected values of the parameters. The xt variable represents the number of red blood cells (in billions) on day t. τ is a parameter giving the time for cell development in days and γ gives the fraction of cells that die each day. F(x), also given below, is a hill function that gives the cell production as a function of the current number of cells. For the the function F(x), F0 is the maximum production of cells, θ represents the cell level where the cell production is halved, and n is a shape parameter for the function. Finally, x0 is the initial red blood cell count. typical parameter values for healthy individuals are listed when the page is first loaded. Different dynamic and observed behaviors can be obtained as parameters are varied.

The model equations are:



Enter in the value of the parameters and select the plotting bounds, then press the "Plot" button.

τ =  

γ =  

F0 =  

θ =  

n =  

x0 =  

N =  


References:

Adler, F. R. Modeling the Dynamics of Life: Calculus and Probability for Life Scientists. Brooks/Cole, Pacific Grove, CA, 1998.

Glass, L. and M. C. Mackey From Clocks to Chaos: The Rhythms of Life. Princeton University Press, Princeton, N.J., 1988.

Othmer, H. G., F. R. Adler, M. A. Lewis, and J. C. Dallon Case Studies in Mathematical Modeling: Ecology, Physiology, and Cell Biology, Prentice Hall, Upper Saddle River, N.J., 1997.