Key Concepts
Biology
Bacteria
Health
Medicine
Mathematics
Probability

Introduction
Have you ever had to take antibiotics? Your doctor or nurse probably told you to finish taking every dose of the medication—even if you start to feel better before you finish it. But why is that? You might be surprised to learn that if you stop taking antibiotics early, you might contribute to the creation of antibiotic-resistant "superbugs," which can make our medicine less effective—and illnesses harder to treat. In this activity you will find out why these superbugs are so difficult to treat by rolling dice to see how bacteria respond to antibiotics.

Background
Bacteria are microscopic organisms that are everywhere. Even when we are healthy, trillions of them live on and in our bodies. Most bacteria are harmless to humans—and many are beneficial. But some can make us sick. Antibiotics are drugs that treat bacterial infections, such as strep throat or ear infections, by killing bacteria. Before antibiotics became widely used in the mid-20th century people sometimes died from minor wounds and infections (perhaps injuries we might think of as trivial, such as a scraped knee).

Over time many antibiotics, however, have lost their effectiveness because bacteria have become more resistant to them. This means some bacteria can survive the antibiotics that were supposed to kill them. These bacteria are known as antibiotic-resistant bacteria, or "superbugs."

This happens because not all bacteria are the same: some bacteria can be more resistant to an antibiotic than others. If some bacteria are not as susceptible to the antibiotic, they can survive—and even multiply.

Scientists agree that taking antibiotics for too short of a time increases the risk of creating antibiotic resistance in surviving bacteria. Other actions that can lead to antibiotic-resistant bacteria are taking antibiotics when they aren't necessary (such as when you are sick with a virus), not disposing of antibiotics properly or taking antibiotics for too long. In this activity you will model the development of antibiotic-resistant bacteria with dice. How many doses do you think it will take to wipe out all of them?

Materials

• Twenty dice (six-sided: 15 of one color and five of another color) or access to an online dice-roller or dice roller app
• Paper
• Pen
• Large, flat work area where you can roll all the dice (if you are using physical dice)
• Additional dice of each color (optional)
• Graphing paper (optional)

Preparation

• Divide the dice by color. In your model each die will represent one bacterium, with the five dice of the same color representing the more-resistant bacteria and the 15 dice of the other color representing the less-resistant bacteria. (In nature, luckily, the less-resistant bacteria are still the most abundant.)
• Write on your paper which color represents which bacteria.
• In your simulation each roll of the dice will correspond to taking one dose of antibiotics. The more-resistant bacteria will survive the antibiotics when their roll is a 2, 3, 4, 5 or 6. Less-resistant bacteria only survive when their roll is a 6. How are the survival probabilities different for the less-resistant versus the more-resistant bacteria?

Procedure

• Mix all your dice together and roll them to represent the first dose of antibiotics.
• Separate the rolled dice into a "surviving" pile and a "died" pile based on the rules for the less-resistant and more-resistant bacteria. How did the first dose of antibiotics do in killing off bacteria?
• Set all the dice in the "died" pile aside. They will not be used anymore. Count how many dice of each color are in the "surviving" pile, and record your results on a piece of paper. How many bacteria survived? How many of the more-resistant or less-resistant bacteria died?
• Repeat these steps until no dice are left. Record your results every time you roll the dice. How many rolls does it take to kill all of the more-resistant bacteria? Do the more-resistant bacteria survive longer or for less time compared with the less-resistant ones? Why do you think this is the case?
• Extra: Increase the number of dice for each bacteria group or change the ratio of more-resistant versus less-resistant bacteria. How does this change your results? What happens if you start out with a larger proportion of more-resistant bacteria?
• Extra: Use graphing paper to graph your results. On the horizontal axis write the number of doses (how many times you roll the dice), and on the vertical axis graph the number of survived bacteria after each dose. How do your graphs for the more-resistant versus less-resistant bacteria compare?
• Extra: In the real world, live bacteria can multiply, creating more of their own type of bacterium. What do you think will happen if you allow each bacterium to multiply over time? Go through two doses of antibiotics (rolls of the dice), removing the "dead" bacteria each time. After the second dose remove the "dead" bacteria as usual, but this time add in a die of the same color for each bacterium that survived. What did that do to the ratio of more-resistant and less-resistant bacteria? Continue to do this after every two rolls of the dice. What happens to the ratio of bacteria? Are you able to wipe out the more-resistant bacteria eventually? Can you think about why it is important to avoid the presence of more-resistant bacteria in the first place?
• Extra: Antibiotics only work to kill off bacteria. What happens if you have a virus, which is caused by a different type of infection, such as the common cold? Let's find out. Gather the 15 dice of the same color; this time these will be the virus cells. Now roll all of the dice, representing one dose of antibiotics. Remove any die that landed on a 7. Did the antibiotic kill any of the virus cells?

Observations and Results
Were you able to kill all the bacteria? Probably yes, but it might have taken you many rounds of rolling the dice to do so. You probably noticed that the "normal," or less-resistant bacteria got killed off pretty quickly. As they only survived in your model when the roll outcome was a 6, and with six possible numbers on the die the probability for them surviving one roll (representing one dose of antibiotics) was only one out of six, which is 16.6 percent. It likely took only a few rolls to eliminate all less-resistant bacteria.

The more-resistant bacteria in this model, however, have a survival probability of five out of six, or 83.3 percent for each roll (or dose), as they survive when a 2, 3, 4, 5 or 6 is rolled. This means that it should have taken much longer to kill all the more-resistant bacteria. Even though they start out at a much lower number than the less-resistant bacteria, after a few rolls they were probably the only ones alive. It might have taken you up to 10—or even more—doses of antibiotics (or dice rolls) to wipe out all of them.

This is what happens in real life with bacteria. One dose of antibiotics is very efficient in killing off a lot of bacteria that can't resist the effects of the drug. Bacteria that can defend themselves against the antibiotics, however, are able to survive the first dose, and it will take several doses of treatment to kill them. If you tried the additional activity of allowing the surviving bacteria to multiply, you probably saw that it was extremely difficult to kill off the more-resistant bacteria. This is why we try to avoid having more of these bugs in the first place. And if you tried to kill off viruses with antibiotic doses, you of course saw that it didn't work at all! So keep this in mind for the next time you are sick. Take any prescribed antibiotics exactly as your doctor or nurse instructs—so you can do your part and help avoid the creation of superbugs.

More to Explore
What About Antibiotics?, from Kids' Health at the Women's and Children's Health Network
Antibiotic Resistance Questions and Answers, from the Centers for Disease Control and Prevention
Combating Antibiotic Resistance, from the U.S. Food and Drug Administration
Color-Changing Dots, a Bring Science Home activity from Scientific American
STEM Activities for Kids, from Science Buddies

This activity brought to you in partnership with Science Buddies