Lesson Ideas

The Spread of Infectious Diseases, Exponential Growth, and Social Distancing

With so many schools ordered to shut down, students find themselves at home all day. Many of them worry about viruses and other infectious diseases and don’t quite understand the reasons why they are staying home. This is the perfect time for an interdisciplinary math and biology lesson about exponential (vs. linear) growth, immunity, infection rates, quarantines, social distancing, and social responsibility.  

This lesson is based on this excellent article in the Washington Post.  

Lesson Plan

Begin with a provocation: “I am fed up with staying at home. I want to go watch a movie, go to the gym. How bad can this virus be? After all, most people have only light symptoms.” 

Let’s examine the scientific principles at play during a pandemic! It will be the students’ job to persuade the teacher that staying at home instead of going to the movies is a smart idea.  

Begin with a review of the important scientific terms.  

(If these are new to the students, have them complete the first part of this online assignment before class.) 

  • What is an infectious disease? – a disease which can be transmitted from one person to another 
  • Give some examples.
  • What about cancer and asthma? Are they infectious diseases? Introduce the term “non-infectious disease.”  
  • What causes infectious diseases? – viruses, bacteria, fungi and others (collectively called pathogens
  • What is our immune system‘s job?  
  • How can you acquire immunity against a disease? – after recovering from the infection or after vaccination. (See here for more detailed classification of the types of immunity.) 
  • So how fast do diseases spread in the population? – It depends on the disease: how many people does one sick person infect?  

The Lily Pad Riddle

Take a break here to pose a riddle to the students: “There’s a lily pad in a pond. The lily pad doubles in size every day and after 30 days it completely covers the pond.  On what day does the lily pad cover half the pond?”

Most students will guess day 15, thinking of linear growth.  

The big aha! moment comes when somebody realizes the right answer is day 29. Show them this graph and point out how small the lily pad was on day 15.  

(Source

This is what we call exponential growth – not merely fast growth, but growth that keeps speeding up.  

How does exponential growth work with the spread of the virus causing the current pandemic?  

Show this interactive graph (found here) about the number of cases in the U.S. Point out how the number of cases doubles every few days. Just like the lily pad! 

(Source)

Exponential Growth Simulator

Show the Washington Post article and walk the students through each step of the simulation.

Each colored dot represents a person who is either healthy, sick or recovered (i.e. immune).

What happens if we continue business as usual?

Go to the source for a live simulation.

What about if we try to quarantine (cut off and completely isolate) the sick people?

Go to the source for a live simulation.

This strategy obviously cannot work in the connected world we live in.

Replay the first scenario and let the students brainstorm ways to SLOW DOWN the spread of the disease. Some may realize that the dots (people) move very fast and interact too much, so we should try and see what happens if we reduced that.

Now, show the scenario in which SOME of the people (3/4 in this model) stay at home and avoid interacting with other people – both healthy and sick! That’s part of the #SocialDistancing strategy.

Seeing how this strategy flattens the curve and slows down the spread of the infection should really serve as a light-bulb moment.

Now ask: “So is it a good idea to stay at home from a scientific point of view?” Students should overwhelmingly answer yes.

Misconceptions

  • Some may wonder if wearing a mask while going to the movie theater might also be effective. Remind them that with an aggressively spreading virus, a mask does not provide as much protection as isolation.
  • Sometimes students ask “Can’t you just avoid contact with only the people who are sick?” This is a good moment to talk about the incubation period – the time between getting sick (and being able to pass on the disease) and showing symptoms.
  • Remind the students that the likelihood of them personally getting the disease is low. Even if they did, their symptoms are likely to be mild. However, we are all staying home in order to protect each other and, most importantly, the people who are most vulnerable and likely to die if infected (that is, the elderly and/or sick with other diseases).

Endgame

We certainly can’t remain permanently in isolation at home. The global goal is to curb the infection growth rate, as China has already done.

For most recent data on the spread of the virus world-wide, check here.

Follow the World Health Organization for other updates.

Other Resources

Our site offers hundreds of scientific articles about infectious diseasesoutbreaksdisease control and health and medical topics. Everything is free to download! Use the filter to find the ones you need!

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