In my classroom: Mathematical modeling of Influenza spread (and comparison to Coronavirus COVID-19)

Every biology classroom is likely teeming with discussions about COVID-19. This offers a unique opportunity to share real-time data and situations with students. Each day brings new developments in this world public health crisis. How are the epidemiologists working to temper the spread?

This week, I adapted a lesson plan which I co-developed for high school students as part of the CDC.gov Science Fellowship program in 2014 (1). The plan is “Have You Herd” and is available for free, in its entirety, on the CDC website. Here is the pdf link: https://www.cdc.gov/careerpaths/scienceambassador/documents/hs-have-you-herd-modeling-influenza-2014.pdf which is also listed in references below (2). The lesson has links to NGSS standards on page 14 of the pdf (page 11 if printed hardcopy of lesson).

SEMANTICS NOTE: The novel coronavirus, which is central to the current outbreak, is notated as SARS-CoV2. This virus causes coronavirus disease, identified in 2019, which is notated COVID-19 (3).

Time estimate: 90 minutes-ish, depending on length of discussion and if you assign the pre-lab the night before or have students complete in class.

Why use an influenza lesson to teach about COVID-19? From the CDC website: “the newly emerged coronavirus disease 2019 (COVID-19) is a respiratory disease that seems to be spreading much like flu. Guidance and tools developed for pandemic influenza planning and preparedness can serve as appropriate resources for health departments in the event the current COVID-19 outbreak triggers a pandemic” (4).

Learning Objectives:

After completing this lesson, students should be able to (coronavirus addendums are in parentheses):
• employ mathematical models for influenza (SARS-CoV2) outbreak scenarios to calculate measures of disease spread and intervention effectiveness.
• synthesize effects of physical (e.g., social distancing or non-pharmaceutical interventions) and medical (e.g., vaccines) countermeasures for influenza outbreak scenarios. What are COVID-19 physical countermeasures which can be employed (especially since a vaccine is currently unavailable)?
• identify public health countermeasures that restrict the spread of an influenza (SARS-CoV2) outbreak.
• IF PART 2 OF LESSON IS USED: explain the importance of vaccinations and monitoring cases of infectious diseases. Since there is currently no vaccine is available for COVID-19, this part of the lesson really only works if using only influenza as written. You can discuss that there is a race to create a vaccine to SARS-CoV2.

Overview: I taught the lesson plan as it was written, but added the following components:

  • Opening: Make it clear to students that this lab is about influenza, however when appropriate, COVID-19 data will be discussed as a comparison.
  • Prelab: Assigned students to make a chart to compare flu to COVID-19. I did this ad hoc, but you could take the basic chart from Appendix 1A and have the students make a second column for COVID-19. I especially like the “misconceptions” line – they could list anything they heard early on about COVID-19. Note that at this time, seasonality of SARS-CoV2 is unknown, so that part of the chart students would leave blank. Another column of “cause” would be helpful to distinguish the difference between COVID-19 to SARS-CoV2 (as noted in the semantics note/paragraph 3, above) versus. influenza to influenza virus A, B or C.
  • Worksheet 1: Note that there are three different demographic scenarios to this activity, A-C. One-third of your class should each be given their corresponding version of Worksheet 1. For reference, A = urban/dense population; B = suburban/moderate population density; C= rural/low population density. Wetlab opening – Perform as written in lesson. Point out that the wetlab simulation of rapid influenza test is a nasopharyngeal swab (long Q-tip thing which makes you gag – they will relate). The CDC SARS-CoV2 test kit uses a similar collection method, plus may also collect sputum (6). Tests are described on the CDC website (6). Discussion questions & R0 calculations – Calculate as written. I like to work through this worksheet as a whole class but allowing each group (A-C) to work together to perform their calculations and double check each other. Then we discuss questions as a class. Helpful R0 information is listed in references below (7). Something which struck me as this lesson was developed was that although small towns have less people, therefore less opportunity for interactions with an infected person, the folks an infected person encounters is more likely to be someone they know (closer contact). It is more likely they will hug, shake hands, hug, etc. if they know the person. Thus, your students will see that the scenario C is not too far off from R0 of scenario A. As you conclude the calculations (discussion questions 1-9), compare the various R0 for your three different populations to the R0 value for COVID-19. One source that I found reported R0 for COVID-19 to be anywhere from 1.4 to 4.08 (8). I’ve seen the number in various places and, situationally, it varies, which makes sense. Examples to discuss are a cruise ship vs. various providences in China. Check out the description in that source (8) with a nice comparison of R0 for different diseases. If you are not familiar with R0 and are Googling around, note that it is different than RE (effective reproduction number). RE is addressed in Worksheet 2.
  • Worksheet 2: Although optional for the purpose of COVID-19 knowledge (because there currently isn’t a vaccine), I went ahead and had the students work through Worksheet 2 where they calculate herd immunity threshold (Ic) and the critical vaccination level (Vc). We discussed the effective reproduction number (RE) of influenza and who is appearing to be susceptible to COVID-19. CDC has a rapidly changing risk assessment description available on their website (9).
  • Assessment (Appendix 4A): I love the figure of genetic evolution of influenza virus H7N9. It really shows how genetic shift occurred in a possible bird/poultry market to generate a novel virus which affected humans in 2013 China. Relate this to the source and spread of SARS-CoV2 (10). Make sure your students know what zoonotic diseases/zoonoses are! Merck Manual online (source 3) is my go-to for animal related information (I teach a veterinary medicine course). Search “zoonotic diseases” on Merck Manual or any credible source.

Extensions:

  • Worksheet 1, before question 3, have actress Kate Winslet from 2011 movie, Contagion, introduce the concept of R0 in about 10 seconds: https://www.youtube.com/watch?v=VrATMF_FB9M
  • Do some epidemiological studies. There is a great module on the CDC website, complete with slides for teacher use (11).
  • Have students choose a section to research from the JAMA article, Characteristics of and Important Lessons from the Coronavirus Disease 2019 (COVID-19) Outbreak in China (12). Then, report back to the whole class in jigsaw style.
  • Deconstruct the epidemic curve (“epi curve”) of that same article (12).
  • Show some video clips about herd immunity (13 & 14), especially if you had the students complete Worksheet 2.
  • Have students compare COVID-19 to MERS and SARS. Compare and contrast. Ask them to look into the zoonotic origin. What are zoonoses/zoonotic diseases (15 and 3)?
  • Some more fabulous resources to share with your students in references (16 & 17). Check in back in with those resources periodically as a class.

REFERENCES

  1. CDC.gov Science Fellowship program: https://www.cdc.gov/careerpaths/scienceambassador/index.html
  2. “Have You Herd” lesson plan: https://www.cdc.gov/careerpaths/scienceambassador/documents/hs-have-you-herd-modeling-influenza-2014.pdf
  3. COVID-19 vs. SARS-CoV2, and description of coronaviruses: https://www.merckmanuals.com/professional/infectious-diseases/respiratory-viruses/coronaviruses-and-acute-respiratory-syndromes-covid-19,-mers,-and-sars
  4. Why use an influenza lesson to teach about COVID-19? How is the United States preparing for a pandemic? https://www.cdc.gov/coronavirus/2019-ncov/php/pandemic-preparedness-resources.html
  5. Nasopharengeal samples for COVID-19 testing, described in “Specimen Type and Priority” section at https://www.cdc.gov/coronavirus/2019-nCoV/lab/guidelines-clinical-specimens.html
  6. Tests for COVID-19 described at https://www.cdc.gov/coronavirus/2019-ncov/about/testing.html
  7. R0 information – 9:00 min video for the teacher if you’ve never calculated “R-naught” AKA “basic reproductive number”: https://www.youtube.com/watch?v=jKUGZvW99os
  8. R0 for COVID-19: https://sph.umich.edu/pursuit/2020posts/how-scientists-quantify-outbreaks.html
  9. COVID-19 CDC Risk Assessment: https://www.cdc.gov/coronavirus/2019-nCoV/summary.html#risk-assessment
  10. Source and spread of SARS-CoV2: https://www.cdc.gov/coronavirus/2019-nCoV/summary.html#source-spread
  11. Introduction to Epidemiology: https://www.cdc.gov/publichealth101/epidemiology.html#anchor_topics
  12. JAMA Network article synthesizing CDC data: https://jamanetwork.com/journals/jama/fullarticle/2762130?guestAccessKey=bdcca6fa-a48c-4028-8406-7f3d04a3e932&utm_source=For_The_Media&utm_medium=referral&utm_campaign=ftm_links&utm_content=tfl&utm_term=022420
  13. Herd immunity –  3:31 min video:  https://kcpt.pbslearningmedia.org/resource/nvvs-sci-herdimmune/herd-immunity/
  14. Herd immunity – 2:17 min video: https://www.youtube.com/watch?v=oAJDoLbrNRE
  15. Zoonotic Diseases/Zoonoses – why are they so deadly? https://bionexuskc.org/coronavirus-outbreak-raises-questions-why-are-bat-viruses-so-deadly/
  16. Current situation report, compiled by the World Health Organization: https://www.who.int/emergencies/diseases/novel-coronavirus-2019/situation-reports
  17. Rolling updates on Coronavirus from World Health Organization: https://www.who.int/emergencies/diseases/novel-coronavirus-2019/events-as-they-happen

BioRender

Imagine for me, if you would, this scenario: you are trying to make a diagram for a lab report (or assessment or poster or whatever) but you can’t find the right figure. So you draw something that resembles what you want, or you use an image you found online that is similar to what you want, but then you spend almost as much time identifying and discussing the weaknesses of the model as you do working with the model itself.

Diffusion Diagram

[ESPN Documentary Narrator Voice] What if I told you there was a free way to make high-quality, detailed models with your students?

My wife’s uncle shared BioRender with me this week, and I knew I needed to share this ASAP.  Watch this intro video you’ll see when you sign up for a free account, and try to act cool… I’ll wait.

DID YOU FREAK OUT A LITTLE BIT?! I did. (OK, maybe more than a little bit.) There is a lot to explore with this, but here are some highlights for me. Not only are there 1000s of icons you can add to your figure, but you can control the color scheme for many of them and add labels to make your models even more robust.
It has some built-in support to pull models from the Protein Databank. When you have the EXACT protein you want to use, you can control how your protein is visualized and rotate the protein so you show the exact part of interest. After Andrew Taylor’s Fall Conference presentation on 3D-printed models, I went looking for the proteins associated with the pharmaceutical product Gleevec.  

I encourage you to go check this out. Visit https://biorender.io/ and create an account. Once you start creating, share your best figures with us here or on social media. I may be speaking for myself here, but I can’t wait to start using and making these models with my students!

KABT: Facebook Group  or   Twitter
BioRender: Twitter

edited to fix a capitalization mistake 8/13

In Praise of Collecting

One of the old standby activities of biology class is collecting, labeling, and classifying insects. I remember this was one of the true highlights of my life. When I was a young child I began collecting insects. The night before our collection was due several cute giggling girls in my ninth grade class showed up at my house asking if they could have some of my collection. The next week when we had our collections graded mine stood out among other less ambitious attempts which looked more like they had been collected with a shoe than a net. It was a rare moment where my nerdy habits were celebrated.

Rightly, insect collections have fallen out of favor in modern biology education. Bug collecting and classifying is hard to justify as a 21st century skill. 

Still, I think we shouldn’t forget about the value collections can have. Catching the bugs is a great way to compare and analyze biological forms.I think that there are two significant ways collections can be used in our evolution unit. 

First, collections allow students to consider the obscure insight of variation in a population.

consider how Alfred Russell Wallace arrived at his insight about natural selection. David Quammen explains in his book Song of the Dodo: Biogeography in the Age of Extinction  he explains,

“ Wallace had reason to notice such variation more clearly than most other naturalists. As a commercial collector, he collected redundantly- taking not just one specimen  each of this parrot ant that butterfly but sometimes a dozen or more individuals of a single species. Lovely dead creatures were his stock-in-trade, literally, and he grabbed what he could for the market. But after grabbing, he preserved, inspected, and packed his creatures with a keen eye, so he saw infraspecific variation laid out before him in a way that other field biologists ( including even the best of the wealthy ones, like Darwin) generally didn’t. it was a trail of clues that Wallace would follow to great profit.” (pg 65) 

This summer, I collected 133 Green June Bugs Cotinis nitida and then put them in a collection together.

Here you see the variation in Cotinis nitida as they go from bronze (left) to vivid green (right)

This gives students a vivid example of variation in a population. Most of the general public hasn’t seen the slight differences between individuals of the same species. Analyzing these collections can help them see the ingredient of variation that is necessary for of natural selection.

Shells can show this property as well, plus students can manipulate shells without breaking them. 

Shells can also help students to interact with the concept of biological variation. Students can manipulate them on their tables and sort them according to the variation that they see. (plus they’re fun to collect)

Secondly, collections allow students to very vividly see homologous traits and fossil evidence.

Last year I got out several of my collections and I had students move from station to station examining evidence for evolution. At each station I had either a fossil, a collection showing homologous traits/variation, a map for biogeography, a specimen with a vestigial trait/atavism, or a diagram showing comparative DNA.

Here students examine cowrie shells and find their “tooth like” structure. my goal is that they recognize that these similar species have a common structure due to a common ancestor. Looks like they’re having fun!

The students then had to apply what they knew about each evidence for evolution to a novel case. This proved to be a really fun experience for me because it forced me to apply what I was teaching in class to the world around me.

If that sounds like a whole lot to chew start with this; collect several pine cones from different species of firs, spruces, and pine. Challenge students with questions about why different species have similar structures.

At this station students were asked to consider why pine cones are so similar even though they are from different trees. In the physical examination of these structures homologous traits go from being an abstract idea to a physical reality.

Have your students examine these biological forms and identifying them helps you to move them from defining terms to analyzing and applying their knowledge.

Students comparing fossil ammonites to an extant Nautilus. I like that the evidence is in their hands not on a piece of paper. This allows them a more real chance to engage with the concept of evolution.

In My Classroom: Going Bananas for Phenomenon Based Teaching

I originally drafted this “In my classroom” as a way to talk about this cool lab that I used to begin talking about the role of biological molecules in living things.  I originally intended to end this with talk of how it was a great lab experience for my students and made for a good model to explain how living things utilize biological molecules.  This was all before the recent NABT conference when I learned about the work being done by teachers in Illinois to create phenomenon based storylines as a way to teach concepts and practices from the NGSS.  I still intend to say all of those things, but the ending has really just sparked a thousand new fires in my head.  Brad’s use of the lighting of the beacons from The Return of the King is in full effect, and I am seemingly humming the score as I type away.

A few years ago, an inquiry idea got posted in the October 2015 ABT about utilizing bananas as a model for learning about biochemistry.  This year, I decided to utilize the model in my classroom as a way to introduce biological molecules and begin talking about cells and cellular processes.  I started with the bananas in class, giving groups of my students (both AP and General) very ripe, somewhat ripe, and unripe bananas.  I asked them to use their chalk markers and record as many observations as they could, comparing and contrasting the bananas.  I got some predictable responses like their coloration was different, but most made great observations about the texture, mass, and taste of the bananas.  My favorite interaction was when one adventurous student informed the class of the taste and consistency of all the banana peels, pointing out that the unripe banana appeared to have a higher water content in the peel compared to the riper specimens.

So after all these observations and in class discussion, I directed students to use the two chemicals I had provided them (iodine and Benedict’s solution) and create an assay to observe how they affected the various bananas.  We made some observations, and recorded our qualitative data from what we saw.  This lead to me revealing that Iodine serves as an indicator for starches and Benedict’s for sugars.  At this point we talked about carbohydrates and their overall structure, pointing out that polysaccharides like starches are formed from sugar monomers like glucose.  We could see clearly that one banana was strongly positive for the presence of starches while the other was more strongly positive for sugars.  This lead to me posing a question.  How did all those starches seemingly disappear, and the sugars replace them?  

My students sat on this for a second.  I had to prove that I had not injected them with sugar.  Students teetered around an answer, but I eventually had a student in each class suggest that the starches are being digested.  I had one student go so far as to name drop amylase.  This lead to us talking about chemical reaction that are occurring to break these polymers up into simpler pieces.  We modeled what they looked like and investigated the role and structure of proteins, particularly amylase.  With the last few minutes of class, we broke out the microscopes and identified cells that had been stained with iodine to indicate the location of starches in the cells.  My students were super engaged with the whole process.  We had a small writeup to summarize and model the processes we had observed.  But that was kind of the end. We still talked about these things in class, but I left a pretty cool phenomenon just hanging there.

A student slide of unripe banana stained with iodine to highlight the presence of starch (in this case amylose).

As previously stated, I got to see some awesome phenomenon based teaching from my experiences at NABT, and am looking at next steps with my students.  Jason Crean from the Illinois Association of Biology Teachers has formulated these NGSS storylines in his class following specific organisms and phenomena.  His phenomena are very heavily focused on real data from collaborations with zoologists and some of his work can be found at http://www.xy-zoo.com/.   His focus is on how all of the content standards in the NGSS connect to each other in an engaging and coherent storyline, all sparked by an investigation into a particular phenomenon.  

While thinking about writing this post, it occurred to me that the banana lab seems like a great piece in the puzzle to start my own conceptual storyline unit on how “We are what we eat.” In my head, this will be something that delves into why some people have trouble processing certain foods and how malnutrition affects us.  I have shared a little bit about this idea already on a Facebook post, and am now looking into a collaboration to produce some conceptual storylines that follow phenomenon, not just the order the standards are packaged and delivered to us.  I realize there is safety there, but safety has never been fun.

Data Analysis in a Natural Selection Simulation

+/-1 SEM bars added

I really like the HHMI Biointeractive activity “Battling Beetles”. I have used it, in some iteration (see below), for the last 6 years to model certain aspects of natural selection. There is an extension where you can explore genetic drift and Hardy-Weinberg equilibrium calculations, though I have never done that with my 9th graders. If you stop at that point, the lab is lacking a bit in quantitative analysis. Students calculate phenotypic frequencies, but there is so much more you can do.  I used the lab to introduce the idea of a null hypothesis and standard error to my students this year, and I may never go back!

 

We set up our lab notebooks with a title, purpose/objective statements, and a data table. I provided students with an initial hypothesis (the null hypothesis), and ask them to generate an alternate hypothesis to mine (alternative hypothesis). I didn’t initially use the terms ‘null’ and ‘alternative’ for the hypotheses because, honestly, it wouldn’t have an impact on their success, and those are vocabulary words we can visit after demonstrating the main focus of the lesson. When you’re 14, and you’re trying to remember information from 6 other classes, even simple jargon can bog things down.  I had students take a random sample of 10 “male beetles” of each shell color, we smashed them together according the HHMI procedure, and students reported the surviving frequencies to me.

Once I had the sample frequencies, I used a Google Sheet to find averages and standard error, and reported those to my students. Having earlier emphasized “good” science as falsifiable, tentative and fallible, we began to talk about “confidence” and “significance” in research. What really seemed to work was this analogy: if your parents give you a curfew of 10:30 and you get home at 10:31, were you home on time? It isn’t a perfect comparison, and it is definitely something I’ll regret when my daughter is a few years older, but that seemed to click for most students. 10:31 isn’t 10:30, but if we’re being honest with each other, there isn’t a real difference between the two. After all, most people would unconsciously round 10:31 down to 10:30 without thinking. We calculated the average frequency changed from 0.5 for blue M&M’s to 0.53, and orange conversely moved from 0.5 to 0.47. So I asked them again: Does blue have an advantage? Is our result significant?

Error bars represent 95% C.I. (+/- 0.044) for our data.

Short story, no; we failed to reject the null hypothesis. Unless you are using a 70% confidence interval, our result is not significantly different based on 36 samples. But it was neat to see the interval shrink during the day. After each class period, we added a few more samples, and the standard error measurement moved from 0.05 to 0.03 to 0.02. It was a really powerful way to emphasize the importance of sample size in scientific endeavors. 

Should the pattern (cross-cutting concept!) hold across 20 more samples, the intervals would no longer overlap, and we could start to see something interesting. So if anyone has a giant bag of M&M’s lying around and you want to contribute to our data set, copy this sheet, add your results, and share it back my way. Hope we can collaborate!

Email results, comments, questions to Drew Ising at aising@usd348.com or drewising@gmail.com

–Versions of Battling Beetles Lab I’ve Tried–

HHMI Original

My “Student Worksheet” Edit

Lab Instructions Google Doc

Lab Notebook Intro. from 2017-18

Lab Notebook Data from 2017-18