- Spread of infectious disease from person to person in a population can result in an exponential increase in the number of infected people.
- Similarly, when population size doubles repeatedly, this results in exponential growth.
- Population growth is limited by the availability of resources.
- The maximum population size that an environment can sustain is called the carrying capacity.
- As population size approaches the carrying capacity, the rate of growth in population size decreases, resulting in a logistic growth curve.
In accordance with A Framework for K-12 Science Education, students will:
- Gain an understanding of two crosscutting concepts (stability and change; patterns) and one disciplinary core idea (ecosystem dynamics, functioning, and resilience)
- Engage in scientific practices (developing and using models; using mathematics; analyzing and interpreting data; constructing explanations).
The Spread of an Infectious Disease
Equipment and Supplies
- Small Dixie cups (3-5 oz; 2 cups per student)
- Chemical (such as Calgon water softener or NaOH) to mix with water to produce a clear solution with a basic pH of 10 or above
- Phenolphthalein pH indicator (Available from Carolina Biological: Phenolphthalein Indicator Solution, item 879993, $4.95 for 100 mL or item 879995, $6.50 for 500 mL)
You can substitute any basic indicator that is clear until in a basic solution.
- Small container with an eyedropper or pipet for phenolphthalein
- Container for mixing the basic solution
1. Prepare a basic solution to be used as the infected solution. Make sure the solution is concentrated enough that your indicator will still change color when added to a solution that has been diluted to 1/8 strength.
2. Prepare two sets of cups (each with one cup per student) for the two sets of interactions (instructions 1-3 and 4 on page 1 of the Student Handout). For each set, fill one of the cups one-quarter full with the infected solution. Fill all the other cups one-quarter full with plain water.
3. Explain that each student will receive a cup containing a clear solution. Tell the students that the solutions represent bodily fluids. Explain that after they receive their solutions each of them should first interact with one other student. The interaction is accomplished by one student pouring all of their solutions into the partner's cup. Then, that partner will pour all of the solution back into the empty cup. Then the two partners each take half of the solution in their cups and move to a different part of the room to interact with different students during the second round of interactions. When they are ready, give the signal for the second interaction.
4. After students have completed these two rounds of interactions, have them go back to their seats and predict the number of infected people. Go around the classroom and drop the phenolphthalein indicator in the cups; as you’re doing so, tell the students that you are putting an infection indicator into their cups. If they have exchanged solutions with the original infected person in the class or someone who came into contact with the infected person, they are now infected and their solution will turn pink. If they have not exchanged solutions with anyone who was infected, their solution will not turn color. Have a show of hands to determine the number of people who were infected.
5. Now repeat the process, but have three interactions instead of just two.
6. If you have enough time and your class size is large enough, it may be helpful to have another round with four interactions (you will need another set of Dixie cups and your infected solution will need to react with the indicator when the solution is at 1/16 strength).
7. Dispose of the liquid by rinsing it down the sink with plenty of water.
Suggestions for Discussing Infectious Disease Questions in Student Handout
7. In order to predict the subsequent spread of the disease, students should notice the approximate doubling of the number of infected people after each round of interactions. The following graphic may help your students to understand this process.
The doubling of the number of infected people after each round of interactions results in exponential growth. The term, exponential growth, is introduced in the second half of the activity when we discuss population growth in an environment with abundant resources. When resources become limiting, as population size approaches the carrying capacity of the environment, population growth slows. The result is logistic growth (see figure comparing exponential and logistic growth on the next page).
In this activity, a round of interactions will result in less than a doubling in the number of infected people if two infected people interact with each other. This is increasingly likely as more of the students in the class have been infected. However, it can also occur in earlier rounds of interactions, particularly if the students do not move to other parts of the room with different students after each interaction. In answering question 7, students should anticipate that the rate of increase in infected people will slow as the number of infected people approaches the total number of people in their class.
This figure shows the exponential growth curve that would be observed if the number of infected people doubled during each interaction. The logistic growth curve takes into account the likelihood of interactions between already infected people as the number of infected people increases.
8. Why is the spread of infection slower in real life?
The rate of interactions with other people is typically much less than one interaction every couple of minutes. Also, even when you have contact, you don't always transmit any germs or enough germs to start an infection. If a person does get enough germs to start an infection, it takes a while for the germs to reproduce to high enough levels for that person to become contagious. Notice that this last point links real-life spread of infections to the time it takes for the growth of a population of germs inside a person's body. You may want to relate this to the discussion of bacterial population growth in the second half of this activity.
Optional Additional Questions on Infectious Disease
You can add some or all of the following questions on the top of page 3 of the Student Handout if you would like to reinforce student learning about the ways that infectious diseases spread, ways to prevent the spread of infection, and/or the body’s defenses against infection.
- What are some ways that infectious diseases are transmitted from one person to another?
- What are some ways you can prevent the spread of an infectious disease?
- Our simulation showed the way a disease could spread if the spread of disease depends on person-to-person contact. Examples of this kind of disease include pink eye, chickenpox, and herpes (lip sores). Other diseases, such as colds and tuberculosis, can be spread by germs in the air. How might the spread of these diseases differ from the spread of diseases that depend on person-to-person contact?
- In addition to exposure to germs (bacteria or viruses), what other factors influence your risk of getting an infectious disease? What defenses does your body have that can prevent you from getting sick, even when you have been exposed to germs?
- Once you have caught a cold or flu, you do not stay sick forever. How does your body eventually get rid of the viruses that cause a cold or flu?
- In almost every case, a person who becomes infected with the HIV virus is infected for the rest of his or her life. With highly effective modern medical treatment, a person may survive a long time with an HIV infection. However, an untreated HIV-infected individual is very likely to eventually develop AIDS and die. Why is a person with an HIV infection unable to get rid of this infection the way a person can get rid of an infection with a cold or flu virus?
Background Information for These Optional Questions:
1. Ways that diseases are transmitted from one person to another:
- Droplets in the air (e.g. cold, flu, tuberculosis)
- Via food or water (e.g. Salmonella, food poisoning)
- Via mosquitoes, ticks (e.g. malaria, West Nile virus, Lyme disease)
- Physical contact (e.g. pinkeye, herpes, chickenpox, sexually transmitted diseases)
You can catch an infectious disease due to a virus by getting it on your hands and then touching your mouth or eyes or eating food you have touched with unwashed hands. The AIDS virus is NOT spread this way.
Ways that HIV/AIDS is transmitted from one person to another:
- By having vaginal or anal intercourse with a person who is infected with HIV
- By sharing needles with someone who is infected with HIV
- From an infected mother to her baby during pregnancy, birth or nursing
2. Ways to prevent infection:
- Avoid close contact with people who are infected.
- Use tissues if you have a cold or flu and throw them away.
- Wash hands especially before eating, after using the toilet, or after contact with someone who has an infection.
- Don’t touch other people’s blood or body fluids (e.g. soiled tissues from someone who has a cold).
- Don't share toothbrushes, eating utensils, etc.
- Eat nutritious food to keep the body healthy.
Some ways to prevent HIV infection:
- Abstain from sexual contact (or reduce risk by a monogamous mutually faithful relationship and use of condoms).
- Don't use intravenous drugs.
- Treatment of a pregnant woman can reduce the risk that her baby will be infected with HIV.
3. Differences in the spread of airborne vs. person-to-person contact diseases:
Airborne diseases can be spread to multiple people at the same time and can be spread to people who are nearby but not in direct contact.
4. What other factors influence your risk of getting an infectious disease?
Susceptibility to infection can be reduced by good hygiene practices, such as washing your hands after possible exposure to pathogens before touching your eyes, mouth, or mucous membranes where infection may occur. Susceptibility may be increased by a weak immune system due to age, previous illness, inadequate nutrition, etc. Resistance to a specific infectious disease can be increased if you have had this infectious disease previously or been vaccinated against this disease (see 5 below).
What defenses does your body have that can prevent you from getting sick, even when you have been exposed to a pathogen?
Important defenses include barriers such as the skin and mucous membranes, chemicals such as acid in the stomach, inflammation, and phagocytic cells. The specific immune system also contributes to defenses against infection, but more slowly, as discussed in 5 below. Any good biology text will provide additional information.
5. How does your body eventually get rid of the viruses that cause a cold or flu?
If a cold or flu virus gets past the first set of defenses (such as the skin and mucous membranes) and infects your body, your immune system is stimulated to produce specific immune system cells (B cells and T cells) that can effectively fight the particular virus that has infected your body. This response takes time, especially the first time you are exposed to a specific virus, so you are sick with a cold or flu until the specific immune cells become effective enough to rid your body of the virus.
After an infection, your body will have memory cells which can produce a rapid defense if you are exposed to the same virus a second time, so you are able to fight off a second infection rapidly and effectively, so the level of viruses is kept low and you may never even feel sick. A vaccination induces the production of memory cells which can mount a rapid defense against that particular infection.
6. Why is a person with an HIV infection unable to get rid of this infection the way a person can get rid of an infection with a cold or flu virus?
There are many reasons why our bodies are unable to get rid of an HIV infection. One important reason is that HIV infects an important type of T cell, the Helper T cell, which is crucial in mobilizing other immune cells to fight infection. As more and more Helper T cells are killed by HIV infection, the body becomes less and less able to fight infections, including HIV infection. Another reason why the body cannot get rid of HIV infection is that the genetic material of the HIV virus is incorporated in the DNA of infected cells, and some of these infected cells can survive undetected by the immune system over long periods of time. (Scientists are very interested in the genetic and immune system differences of the tiny number of people whose bodies appear to be able to control or eliminate HIV infection.)
If the population of bacteria doubles every 30 minutes, there should be 512 bacteria after 4 hours and 30 minutes and 1024 bacteria by 5 hours. The increasingly rapid increase in the number of bacteria is characteristic of exponential growth. Researchers have found that under optimal conditions bacteria can divide as often as every 20 minutes for even more rapid population growth. Question 13 prompts students to relate the increasing slope of the exponential growth curve to the observation that, since population size doubles every 30 minutes, the rate of increase in population size is proportional to the size of the population.
Eventually, population growth will slow due to increasing competition for resources. Population size will level off at the carrying capacity of the environment, i.e. the maximum number of individuals environment can support. This leveling off is shown in the logistic growth curve.
In the real world, population growth often does not follow either an exponential or a logistic growth curve. Examples and explanations of these discrepancies, as well as a more sophisticated introduction to exponential and logistic population growth models are provided in "Population Growth – Exponential and Logistic Models vs. Complex Reality", available at http://serendip.brynmawr.edu/exchange/bioactivities/pop.