A surge function is a function of the form
f (t) = Atne(−bt)
The values A, n, and b are the parameters of the function.
This function accurately represents the way a drug interacts in the bloodstream. Studying
this function is essential to doctors and pharmacists because it allows them to administer
dosages of medicine correctly.1
A drug dose is being designed for a 90kg male patient. The amount of the drug in the
patient’s bloodstream after t hours, measured in nanograms per milliliter (ng/ml) is given
by a surge function.
Any positive value of A can be achieved by increasing or decreasing the amount of
medicine given. However, depending on the type of delayed release mechanism selected
there are choices possible for the value of the pair (n,b): The achievable pairs are listed in
the table below.
Delay Type n value b value
Extended 2 0.3
Medium 3 0.5
Rapid 3 0.7
The medical requirements for the treatment are:
• The dose (in ng/ml) may not exceed 100 at any time.
• The dose must fall to be at or below 20 ng/ml by 24 hours.
Within these parameters, the treatment effect will be measured in ng/ml-hours. (1
ng/ml concentration for 1 hour is 1 ng/ml-hour of treatment). The objective is to obtain
the maximum possible treatment effect while ensuring the requirements are met.
1Tarko, Olta (2021) ”Surge Functions and Drug Interactions,” Undergraduate Journal of Mathematical
Modeling: One + Two: Vol. 12: Iss. 1, Article 7