The Mathematics of Pandemics: From the Spread of Infections to Cost-Benefit Analyses of Responses (tentatively Math 119/312, offering at two different levels)

Steven Miller: sjm1@williams.edu

Tentative Schedule (~33 classes), highlighted in blue are tentative.

1. Introduction to the class and previous pandemics throughout history.

   1. Syllabus

   2. At what point in human history did disease become a major concern? When humans shifted to agrarian lifestyles 10,000 years ago, putting humans into closer contact with each other.

   3. The origins of diseases, how they spread to become pandemics, what the responses were and the long term effects: Leprosy, the Black Plague, smallpox (spread to the Americas via the Columbian Exchange), Cholera (the first global pandemic?), the Spanish Flu, HIV/AIDS, SARS, Ebola, and now COVID-19.

2. Simple Mathematical Systems

   1. Bacteria growth and rabbits.

3. Introduction/review of Statistics

   1. Means, standard deviations, central limit theorem, confidence intervals, and hypothesis testing.

   2. Issues with statistics: shoe size/spelling example.

   3. Example: Won three of last four….

   4. What is the right statistic: The notion of a mean

4. Advanced Mathematical Systems

   1. Solving differential equations and models for infections.

5. Advanced Mathematical Systems 2

   1. Solving different kinds of differential equations.Introduction to Measurement

   2. What are we measuring and why? Why do we choose some quantities over others? 

6. “Flattening the Curve”

   1. What does it really mean? Where did the curve come from? What model was used to make this assumption/prediction?

   2. Was the U.S. able to achieve it? What part of the curve are we on right now?

7. Introduction to Chaos and Parameter Sensitivity

   1. The notion of chaos in modeling weather and finding roots of polynomials.

   2. How climate change models can produce very different predictions based on small changes in input parameters.

8. Biology speaker to talk about disease and models.

9. Discussion: Individuals vs. the State

   1. Where is the line between individuals’ rights and the power of the state to force its citizens to take certain actions?

   2. Possible topics: free speech, abortion, genetic engineering, gun control, seat bels and motorcycle helmets and bakeries.

   3. At what level of government should policy (and restriction) be set: federal, state or city/local?

10. Have a philosophy professor come in to talk about individuality vs. public good and facilitate a discussion with the class

11. Have someone from law discuss  (COULD BE WHAT I LISTED AS ‘C’ ABOVE...OR SOME COMBO OR B AND C)

12. Midterm I Placeholder (if we have a midterm -- likely we will be doing papers)

13. COVID-19 and the economy.

    1. The impacts that COVID-19 has had on the economy due to lockdowns and social distancing.

    2. The idea of unemployment in economics: structural and cyclical unemployment. What type was caused by COVID-19?

    3. Comparison of current unemployment levels to those of the Great Depression. What can we expect to see in the global economy in the coming years?

    4. The economics of working from home: Are there any productivity boosts/decreases? Is working from home lowering costs? Which industries can work from home and which can’t? How does that impact wealth distribution?

14. Economics speaker

    1. Highlight the impacts of covid globally, as well.

    2. Contrast the varied policy decisions made around the world and how they have worked out to date.

    3. Implications on a macro and micro level.

15. COVID-19 and the Media

    1. How does the media influence how we perceive the pandemic? How does the media shape discussions around it?

    2. The media as gatekeepers of what the public gets to know regarding the pandemic.

16. Journalist Speaker I’D COMBINE 15 AND 16 USING THE SPEAKER OR TWO PJ

    1. What are they reporting and why? Does bias influence the coverage?

17. Medical frontline worker speaker 

    1. How has healthcare changed in the face of COVID-19? 

    2. What is it like to be in the frontlines of covid?

    3. What medical conditions have not been treated, or have been under-treated, during the focus on COVID-19 cases? 

    4. What kinds of lasting impacts will COVID-19 have on the healthcare industry? How will we prepare for a future pandemic? MIGHT CONSIDER A PUBLIC HEALTH OFFICIAL, AS WELL--DIFFERENT FROM A FRONTLINE WORKER

18. Introduction/review of cost-benefit analyses.

    1. How do we quantify benefits and costs into a number? How do we make sure all benefits and costs are accounted for? How do we quantify moral concerns?

    2. How do we maximize benefit and minimize cost? How can we do such an analysis objectively?

    3. How do we decide how many deaths are “acceptable.” 

19. Midterm II Placeholder (?)

20. Establishing COVID-19 Baselines

    1. What was the state of the world pre-COVID-19? 

    2. What are parameters/response variables we are interested in studying for comparison of pre and post COVID-19?

    3. Is it practical to study these parameters? Will we be able to get accurate data for these parameters?

21. The short term effects of COVID-19.

    1. Deaths and infections. Change in mortality rate?

22. The long term effects of COVID-19 and the effects of policies resulting from COVID-19.

    1. Also, long-term psychological effects?

23. Agendas and Hindsight (speaker?)

    1. In hindsight, we can analyze the actions taken and whether or not they were appropriate? 

    2. Can you detect the agendas of people who pushed for various responses to the pandemic?

    3. Expanding on the notion of  “acceptable losses,” how do we make the hard decisions, especially considering people who are at a higher risk from the virus, such as those who are older or immuno-compromised.

24. Effects of Lockdowns

    1. Did they work? How many lives did they save? Were they worth the widespread job loss? What have been the costs and benefits?

    2. Are lockdowns constitutional? Do they infringe on the rights of citizens?

    3. The case study of masks: How and why did recommendations relating to them evolve? Is being required to wear a mask an infringement on personal liberties? Why are some unwilling to wear it? Were U.S. residents far more resistant than their counterparts in other countries? 

25. Contact Tracing: Cost-Benefit Analysis

    1. Cost: people lose a degree of privacy as the government tracks where every single person goes on a daily basis.

    2. Benefit: Reduces the spread of the virus.

    3. How to quantify these costs and benefits? 

    4. South Korea’s contact tracing.

26. Educational Institutions

    1. Costs and benefits of an educational institution being open vs. offering online classes. Is the situation different for high school vs. college level education?

    2. In hindsight, should colleges have closed campuses in March?

27. Comparison of different policies taken by countries worldwide

    1. Costs and Benefits of each approach.

    2. China, Italy, Sweden, Brazil, U.S.

28. Political Science Speaker

    1. Global implications of our response and the new normal.

    2. China relations: the conspiracy theory that covid was man-made in a lab in China. AGAIN, SEE MY MEMO TO COME, pl

    3. The political realities and how things are done.

29. Personal Responses to COVID-19

    1. If I am a doctor/nurse, should I continue working without hazard pay? Am I morally obligated to do so?

    2. Is it okay for me to continue going outside? Maintaining in-person social relationships?

    3. Who did we decide were essential workers and what were the pressures on them? Ex. food delivery services, meatpacking plants

    4. Cost-benefit analyses on a personal level.

30. Midterm III Placeholder (?)

31. Presentations

32. Presentations

33. Presentations