Math Modeling: Day 26

This is mathematical modeling: of course there has to be a thing or things that you're modeling (in this case, a population, and how it grows and changes in time) and then we see how mathematical tools allow us to capture or predict the thing's behavior.

It really helps if you invest yourself in the thing you're modeling, because then your curious mind takes over, and you start to mull over how we can make a model give us the

1. behavior
2. answers
3. insight
4. whatever

Or at least it helps to be invested! So, even if you really don't have much reason to think about hares and lynx, it really pays if, for the exercise, you'll take a moment or two to reflect on how they might behave, and how that behavior will show up in their populations.

If you didn't get an email that looks like this,

let me know, and I'll try to resend.

If that works the way I hope, then we can simply use that folder as a place for uploading your work, and then for me to grade it.

Let me know if you're having any problems or issues with that.

1. I thought that you should read Fletcher's descriptions of the decades relevant to our data set. There is a key in there as to why the data didn't look quite right.

2. The second reading is about our expectations of the impacts of climate change. This, too, was motivated by the graphics (and their failure to agree with expectations.

   I asked you to choose any paper from this conference proceedings ( Asymetric Change of Daily Temperature Range, Proceedings of the International MINIMAX WORKSHOP Held Under the Auspices of NOAA National Environmental Watch and the DOE Global Change Research Program), an to submit a (typed) two-page "book report" about the implications of what we might expect to see in our maximum and minimum temperature data, based on what others have seen due to climate change. Base your conclusions on what you've read in your chosen article (due Monday, 3/30).

Some good links that I might recommend (a few of which we'll focus on):

1. A great intro to many of the most important question: "When a new virus emerges, no one is immune. A highly transmissible virus, like the coronavirus behind the current pandemic, can spread like wildfire, quickly burning through the dry kindling of a totally naive population. But once enough people are immune, the virus runs into walls of immunity, and the pandemic peters out instead of raging ahead. Scientists call that the herd immunity threshold."

2. How epidemics like covid-19 end (and how to end them faster): A coronavirus causing a disease called covid-19 has infected more than 70,000 people since it was first reported in late 2019. To predict how big the epidemic could get, researchers are working to determine how contagious the virus is.

3. The SIR Model for Spread of Disease - Introduction (from the MAA).

   In particular, we will implement The SIR Model for Spread of Disease - The Differential Equation Model in InsightMaker.

4. Mathematics of the Corona outbreak, with Professor Tim Britton

   (An excellent introduction to SIR models, from both the infectious disease and mathematical sides)

   Questions:

   1. Where is the "calculus moment" in this video?

   2. How does Britton suggest breaking $R_0$ down into "actionable" pieces?

5. This Covid-19 situation is probably more suited to a SIRDs model (with disease-induced death).

6. An on-line model developed by Ashleigh Tuite and David Fisman, Dalla Lana School of Public Health, University of Toronto

7. This one incorporates space into the model. These models are called "agent-based models".

8. Could Coronavirus Cause as Many Deaths as Cancer in the U.S.? Putting Estimates in Context

   This on-line estimator (i.e., a model!) allows one to estimate deaths, as well as death by age-category.

9. A nice R-based introduction to infectious diseases and nonlinear differential equations.

10. Use of a log-scale (which they take pains to explain) to illustrate deaths by country, updated daily. There is even a separate page at the New York Times to explain log plots: "A Different Way to Chart the Spread of Coronavirus: Those skyrocketing curves tell an alarming story. But logarithmic graphs can help reveal when the pandemic begins to slow."