Bang-Bang Optimal Control for a Cancer Therapy Model
by Mike Martin

This page generates a plot of the input (or control) and the output (or response) of a simple model for the population of tumor cells (as measured in volume). Consider a population of cells that change at a rate given by

where

The function u(t) is defined on an interval of length 2T units; on the first half of the interval u is turned on and has a value of one (then multiplied by the dosage factor - D) and on the second half of that interval there is no treatment (the value of u there is zero).   Nmax represents the size the tumor would level off at if there were no treatment.   N0 is the initial size of the tumor.   r is a growth/decay parameter. The first graph that is generated is for the input, D u(t), and the second graph is that of the response as measured by the tumor size. In the second graph, the dashed-red graph is the tumor size if there had been no treatment.

Enter in the values of the non-negative parameters Nmax, N0, r, D, and T and select the plotting bounds, then press the "Evaluate" button.

Nmax =  

N0 =  

r =  

D =  

T =  

  ≤   t   ≤  


References:

Mackenzie, D. (2004). Mathematical Modeling and Cancer. SIAM News, 37:1.

Byrne, H., Cancer Modeling and Simulation, Chapman & Hall/CRC, Boca Raton, FL, 2003.