2. Introduction

By using sequences and the mathematics associated with the concept of half-life you will develop a simple mathematical model to explore Drug Levels in the Human Body.

Consider the following:

Imagine that you have a headache, and wish to take a pain-relieving drug. One dose of the drug is 1 pill with 400 mg of active medical ingredient. The drug's container directs you to take 1 dose every 4 hours. Since your headache is not relieved in 4 hours, you decide to take another dose, and in another 4 hours, you take another dose. Suppose this process continues, with doses being taken at regular time intervals; in this case, every 4 hours.

A few questions that aries immediately:

  1. Will the maximum amount of drug in the body continue to rise if the medication is taken regularly?
    1. If so, will the drug level in the body become toxic?
    2. If not, what will happen? Will the drug reach some steady state? Is it possible to predict the drug level over a prolonged period?
  2. Can we ensure that the drug is present in a high enough quantity so that it will be effective? A low enough quantity so that it will not be toxic?
  3. Suppose a patient decides to double the dose (take twice as many pills), but only half as often (say, every 2 hours instead of 4). Does this make any difference to the long-term levels?

In the coming sections, we will learn the mathematical background required to develop a simple discrete model which we can use to answer the questions above!