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 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: 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.


  • Worksheet 1, before question 3, have actress Kate Winslet from 2011 movie, Contagion, introduce the concept of R0 in about 10 seconds:
  • 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.


  1. Science Fellowship program:
  2. “Have You Herd” lesson plan:
  3. COVID-19 vs. SARS-CoV2, and description of coronaviruses:,-mers,-and-sars
  4. Why use an influenza lesson to teach about COVID-19? How is the United States preparing for a pandemic?
  5. Nasopharengeal samples for COVID-19 testing, described in “Specimen Type and Priority” section at
  6. Tests for COVID-19 described at
  7. R0 information – 9:00 min video for the teacher if you’ve never calculated “R-naught” AKA “basic reproductive number”:
  8. R0 for COVID-19:
  9. COVID-19 CDC Risk Assessment:
  10. Source and spread of SARS-CoV2:
  11. Introduction to Epidemiology:
  12. JAMA Network article synthesizing CDC data:
  13. Herd immunity –  3:31 min video:
  14. Herd immunity – 2:17 min video:
  15. Zoonotic Diseases/Zoonoses – why are they so deadly?
  16. Current situation report, compiled by the World Health Organization:
  17. Rolling updates on Coronavirus from World Health Organization:

2020 Ecosystems of Kansas Summer Institute

Several universities across this great state are working together on a massive interdisciplinary project (MAPS – Microbiomes of Aquatic, Plant and Soil Systems). As part of this project, they are holding annual Summer Institutes for teachers interested in the ecosystems of Kansas. This summer is the third edition, being held 8-12 June 2020 at the University of Kansas Field Station. Participants are given travel allowances and a stipend, and anyone with a commute >1 hour driving time from Lawrence will be provided with lodging.

If you are interested in applying, click here.

If you have any questions, contact one of the project leaders, Dr. Peggy Schultz (

KABT Members Drew Ising, Michael Ralph, Marylee Ramsay, Andrew Davis and Bill Welch were participants or organizers for the first summer institute and can also help.

2019 Summer PD – Ecosystems Across Kansas (Konza Prairie)

Several universities across this great state have partnered together on a massive interdisciplinary project (MAPS – Microbiomes of Aquatic, Plant and Soil Systems). As part of this project, they are holding annual Summer Institutes for teachers interested in these fields. This summer is the second edition, being held 17-21 June 2019 at the Konza Prairie Biological Station. Participants are given travel allowances and a stipend, and anyone with a commute >1 hour driving time from Konza will be provided with lodging.

If you are interested in applying, click here.

If you have any questions, contact one of the project leaders, Dr. Peggy Schultz ( KABT Members Drew Ising, Michael Ralph, Marylee Ramsay, Andrew Davis and Bill Welch were participants or organizers for the first summer institute and can also help.

KABT 2018 Fall Conference

The 2018 fall professional development conference will be held at the KU Field Station’s Armitage Education Center from 9:00 AM to 5 PM on Saturday, September 22nd. There is a $15 on-site registration fee and an optional year-long KABT membership for an additional $15. Yellow Sub sandwiches will be provided for lunch. Please view the attached flier for the schedule and contact with any additional questions.

A Thematic Approach to Anatomy and Physiology


I recently had an exchange with some area teachers about how we approach the curriculum of a high school anatomy and physiology course. My course (and entire practice) is always undergoing change and revision. That said, I’ve created an outline for my course that might be helpful for others who are considering an attempt to escape the vocabulary grind of a legacy A&P classroom.

The students and I work the entire semester at developing their competency at telling the ‘story’ of a single anatomical theme instead of grinding through a linear sequence of discrete curricular units and a series of independent point-driven tasks.  While not strictly PBL as it is commonly described, students are accountable for developing and presenting a cohesive, thematic schema for what they know as a result of our work together.

So here is an outline of what we’ll be attempting this year. If you’re walking a similar path in your classroom, be sure to share out your questions, suggestions, and comments.


Fall Semester – Thematic Development of Curricular Standards

Theme: Environmental Interactions – Your Brain is a Survival Organ

Your heart pumps blood.  Your lungs breathe air.  Your skeleton provides structure, support and protection.  Your muscles produce movement.  But what about your brain?

Your brain is a survival organ that regulates your internal physiology within relatively narrow limits and guides your environmental interactions to maximize homeostasis (health).  Biologically, humans are habit-driven, emotional beings who have the capacity for cognition (thinking, self-awareness).  Our brain’s function is to continually respond to the dynamic environment in which we live enabling us to avoid threats, seek opportunities, and utilize cognition so that we may assert greater levels of control within that environment.  We are a bundle of habits, emotions and thoughts, and we can act in response to all three.

Thematic Development: Lower Order and Higher Order Interrelationships

The lower order and higher order parts of the brain do not operate independently of one another.  The brain stem, diencephalon, basal nuclei, limbic system, and cerebral cortex have established numerous neural and hormonal interconnections through which they influence one another in such a way that they are able to warn of potential threats in the environment and reward successful interactions with the environment. The amygdala (warning) and the septal region (reward) play a significant role in learning and knowing, the amygdala at the beginning of the process (learning) and the septal nuclei and nucleus accumbens at the back end (knowing).

Thematic Development: Learning and Knowing are NOT the Same Thing

The functional interrelationships between higher order regions of the brain are such that learning and knowing take place as related, but distinctly different, processes.  An individual’s cognitive belief system and self-concept impact every aspect of the learning and knowing processes.  Mindset, in particular, functions as a ‘system override’ that acts to habitually accept or reject new learning in ways that can either enhance the receptivity to new information, or dramatically close off access to the learning and knowing pathways within the brain.

Thematic Development: Motivation

Humans don’t have to be motivated to learn, learning is the motivation.  Cognition is a powerful survival adaptation for interacting with one’s environment.  Our brains contain an internal frame of reference, so that success in thought leads to heightened levels of control which we ultimately experience as competency and gratification.  The brain has evolved to learn, and so it should be no surprise that cognition leading to greater control is ‘hardwired’ into the brain’s internal reward system.  All motivation can be explained in terms of environmental interactions that lead to the feeling of well-being and competency.

Thematic Development: Joints and Movement – Bones, Muscles and Nerves

Moveable joints have fundamental structural and functional characteristics in common with each other along with skeletal and soft tissue adaptations to provide for the unique stability and range of motion possible at each joint.  Bones, bone markings, bone tissues, articular surfaces, cartilages, ligaments, tendons and skeletal muscles work in combination to provide humans with the ability to respond in rich and varied ways to their environment.

The biochemical and mechanical pathways through which sensory input enters the central nervous system is integrated into the brain’s existing schema for responding in a manner that maximizes homeostasis.  A motor impulse originating in the brain results in the contraction of a motor unit that is part of a muscle that acts with other muscles in groups at a specific joint.

By focusing on the names, origins, insertions and actions of the muscles that act on the knee to move the leg and that act on the shoulder to move the arm it is possible to develop a schema for knowing how any number of muscles (3, 30 or 300) act at joints without having to depend on the serious limitations that come with attempts to rote memorize new information, especially when that information is conceptually challenging and there is a lot of it.


Spring Semester – Thematic Development of Curricular Standards

Theme: Regulation and Maintenance – Organ Systems at Work

The cells throughout your body are not capable of carrying out all the functions necessary for survival by themselves.  They cannot obtain nutrients, rid themselves of wastes, exchange essential gases, protect themselves from toxicity and temperature variations, or other necessary tasks.  Blood and interstitial fluid serve as the exchange medium between systemic cells and the various organ systems of your body through which those cells maintain homeostasis.  The human body functions physiologically through the operation of pressure, temperature and concentration gradients, and those gradients result in blood flow, respiration, digestion and absorption, liver function, and renal processing.

Thematic Development: Cardiac Cycle

The cardiac cycle is the sequence of electrical events, mechanical events, pressure changes and volume changes that occur during one heartbeat.  Muscle contractions, pressure gradients and valve operation initiate and maintain productive blood flow through the heart and throughout the pulmonary and systemic circulation.

Thematic Development: Pulmonary and Systemic Circulation

Oxygenated air entering your respiratory system and deoxygenated blood returning to your heart must reach each other at the respiratory membrane where concentration gradients facilitate the exchange of O2 and CO2.  Blood that is oxygenated at the respiratory membrane must reach the systemic microcirculation and interstitial fluid throughout your body where concentration gradients facilitate the exchange of O2 and CO2.

Thematic Development: Cardiovascular and Digestive Systems

Ingested food that enters the GI tract and oxygenated blood that enters the abdominal viscera must reach each other at the GI mucosa where the products of digestion enter the systemic microcirculation through the operation of concentration gradients and active transport.  Deoxygenated, nutrient-rich, xenobiotic-rich blood must pass through the hepatic portal system so that it can be processed in the microcirculation of the liver and then returned to the systemic circulation.

Thematic Development: Blood as a Transport Medium

Blood is composed of various formed elements and plasma, through which blood gases and solutes are transported throughout the body.

Thematic Development: Systemic Circulation and the Lymphatic System

The lymphatic system is closely associated with the cardiovascular system, since it returns fluids that have leaked from the vascular capillary beds back into the blood.  It consists of three parts: the lymphatic vessels that parallel the blood vessels; the fluid in those vessels, called lymph; and lymph nodes that cleanse the lymph as it passes through the lymphatic vessels prior to re-entering the vascular system as plasma.

Thematic Development: Cardiovascular and Urinary Systems

A nephron is comprised of both vascular and tubular structures that are involved in the renal processing of whole blood through the operation of filtration, concentration gradients and active transport.  The various components of blood (formed elements, plasma, desirable plasma solutes, and undesirable plasma solutes) enter the kidney, undergo processing by the nephrons, and are either returned to the systemic circulation or are removed from the body as urine.


Thematic Development of Curricular Standards – Semester Grade Determination

Academic success is commonly framed as something that results from ongoing task completion, the purpose of which is to accumulate points toward reaching an arbitrary percentage benchmark that represents a particular grade.  Learning is thought to arise intuitively in direct proportion to the number of points acquired, and so it is often a secondary consideration at best.  Our approach to Anatomy and Physiology will be structured so that students are empowered to concentrate exclusively on learning and knowing, instead of chasing points, and each student’s grade will represent the level of competency he or she has developed through that effort.

Students establish a grade in Anatomy based on how they are progressing in their response to one question, the one question that drives EVERY class period, “What do you know?”  There are NO assignments, NO homework grades, NO quizzes, NO high-stakes projects or tests, NO points, and NO percentages.  Students are NEVER penalized for mistakes they make as they struggle deliberately at ‘coming to know’, and we DON’T have to resort to curving test scores, awarding extra credit points for routine tasks, or rounding percentages to make up for any perceived ‘hits’ against a student’s grade.

There is nothing permanent about a grade in Anatomy.  Since the sole focus of our time in class is ‘students making progress in what they know’ relative to a single semester-long theme, as opposed to accumulating points by completing an ongoing series of discrete tasks, we have no need for multiple gradebook entries and arbitrary mathematical averages to determine a grade.  There will never be more than one item in the gradebook.  That item will be titled as the theme for the semester, and it will be subject to revision at any time throughout the semester

Each student’s Anatomy grade is simply a notification of how far that student has progressed, or regressed, in knowing at the time the grade is updated.  Students NEVER have to carry the weight of a bad grade as part of their quarter or semester average (since we do not calculate averages), nor do they have to struggle unproductively through a punitive makeup or retake process to amend an undesirable grade.  We are always working forward to better develop our curricular theme and each student’s understanding of that theme by starting wherever the student is ‘at’ at any given time and helping that student grow his or her understanding to the highest level possible.

The ONLY grade that counts toward GPA, and is reported on transcripts, is the semester grade.  And for Anatomy, that semester grade represents the progress a student has made in developing competency at accessing anatomy and physiology content in meaningful ways so that it can be understood and known as a durable network of long-term memories.  That semester grade represents what the student demonstrates that he or she knows about our thematic focus due to his or her purposeful, ongoing effort at ‘practicing knowing’.  In class.  Every day.  Throughout the semester.

Grading practices that serve to enforce compliance with teacher directives by awarding points for various forms of task completion are not compatible with an instructional approach that is geared solely toward engaging students in a persistent effort to develop what they know about a broad curricular theme.  Students who have been conditioned to care more about points and percentages than about learning will only commit to the struggle of knowing if they are confident that their progress in knowing will result in the grade they expect.  Therefore, the points-driven, percentage-based grading scale that is common in many classes has been replaced in our Anatomy class with the growth-oriented competency rubric that can be found below.  The rubric has been intentionally developed to ensure that when students invest in deliberately knowing more each day, the grade will take care of itself.


Demonstrates a thorough command of the curricular theme.  Has developed a factually-accurate, meaningful thematic schema…can tell a rich, fully-developed ‘story’ that ties relevant details to big ideas to convey depth of understanding.

Symbol = ACM                   ParentVue/StudentVue Numerical Equivalent = 5               Grade = A


Conveys a coherent understanding of the curricular theme.  Has developed a thematic schema that is reasonably accurate and makes sense…but a truly comprehensive understanding that demonstrates mastery of the details and how they contribute to the big ideas is not yet obvious.

Symbol = EST                      ParentVue/StudentVue Numerical Equivalent = 4               Grade = B


Presents the essential features of the curricular theme.  Beginning to combine thematic concepts into a working schema…knows some, but not all, of the parts of the ‘story’, and is still working to describe how all those parts fit together in a meaningful way.

Symbol = FND                    ParentVue/StudentVue Numerical Equivalent = 3               Grade = C


Recognizes the basic elements of the curricular theme.  Can articulate a few of the concepts that are necessary to a growing schema…but there are significant gaps in what is known relative to what has been developed in class.

Symbol = PRG                    ParentVue/StudentVue Numerical Equivalent = 2               Grade = D


Unfamiliar with the basic elements of an anatomical schema related to the curricular theme that has been developed in class.

Symbol = BEG                    ParentVue/StudentVue Numerical Equivalent = 1               Grade = F


Has not provided recent evidence of competency.                                                                             

Symbol = INC                     ParentVue/StudentVue Numerical Equivalent = 0               Grade = F