Difference equations like in Example 4.5.3 of the textbook are widely used to model the dynamics of drug concentration in patients. The animation below allows you to explore the predictions of this model graphically for different choices of the daily dosing (labeled ‘d’ in the animation) and the metabolism rate (labeled ‘k’ in the animation). The concentration starts at C0=0 and the simulation runs for 2 weeks. In the example of textbook d=0.3 and k=0.2.
Experiments have been conducted to see how well such models predict actual drug dynamics. In the animation below data from such an experiment is plotted (blue dots), along with the simulation output (black dots). You can explore different choices for d and k in the model. The data is for the pain relief drug acetaminophen, which was administered every 6 hours at a dose of 1000 mg for 2 days.
References
Data are from the FDA at the website http://www.fda.gov/ohrms/dockets/ac/02/briefing/3882b1_13_mcneil-acetaminophen.htm