Math Modeling: Day 23

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Special Announcements:
- Welcome back video -- sorry about the sound quality.
- Obviously things are going to be a little different going forward. I'm sorry that this has happened, for lots of reasons; but especially for the anxiety and fear that this has caused.
  Let us continue our work in this class, in order to maintain some sense of the normal.
- There have been a few changes to your syllabus. The new improved version is here.
- Most importantly, we're going to be reducing the workload a little. We've lost a week, and so I'm winnowing down the material. Check the assignments page to see exactly how things have changed.
  The schedule is now complete, and we have a week of Hares and Lynx, a week or so of SIR models (e.g. Coronavirus), an exam, and then two weeks to complete our major project. The last week will be for review and "presentation of our results" -- not yet sure exactly what that will look like!
  In particular, our next exam has been pushed back a week, to 4/10.
- Material will also be delivered a little differently, however. You will have to put up with my video presentations of our material (if you wish): I will continue to walk you through the material.
- You will continue to do your assignments, but will have to turn them in electronically. Our exams will be a little more interesting, as well. These will be timed exams, to take place during your usual class time. More on those as they approach.
  Let me know if it will be a hardship to take the exams during our scheduled class time.
Announcements:
- Your midterm grades were based on whatever I had at the moment (three homeworks, and three mini projects, plus your exams).
- Your revised Keeling reports are graded. There are still some issues that I will want to discuss.
- Your computational homework is also graded, and that included some Mathematica (or at least I had hoped it would).
  Here are files illustrating what I was hoping you might do.
- You have a major project-related homework due Monday, 3/23.
  We are going to continue with our major project, and this is one of the first salvos. In effect, the answer to this question determines whether we continue, or bail! If we saw nothing, then we might say it appears to be unaffected by climate change.
  Our department chair suggests using Microsoft Lens (getting started) to scan your homework to pdfs.
  My son just installed the app on his android phone, fired it up, scanned a letter, and sent it to me as a pdf in about two minutes. And he wasn't sweating. So I think that it's doable.
  Some of you may actually have a scanner!
  At any rate, I'll probably not have any trouble with this audience figuring out how you'll get me your homework. Please do your best to make scans legible, however!
  Please, please: put MAT375 (as one word (i.e. not "MAT 375"), as well as assignment info) in the subject line of your message -- I'll be routing all messages using the tag MAT375. It will really help.
- On a related note, right after class on Friday before break I came across this article: Nenana Ice Classic Is the Great Alaskan Guessing Game
  Look at those break-up dates...
Last time:
- We had our introduction to "InsightMaker" for Logistic Growth. (You'll need to set up an account, if you haven't done so yet.)
  Last time I had you "clone" my "insight" about logistics. Once you own an insight, you can begin altering parameters, population values, connections (flows and links); adding new elements, and introducing flows between them; etc.
  You are modeling! The objective is to do it well, of course....
- InsightMaker is a way of modeling visually (called Compartment modeling): it gives you some good insight as you build a model.
- Next we compared our work in InsightMaker with a Mathematica file to do what the InsightMaker example of Logistic Regression is doing.
  Mathematica is much more powerful (in particular, the "Manipulate" command allows us to gain some really neat and quick insights; but InsightMaker allows us to create a model system, and then figure out how to write down the equations. I think that it's a little more user-friendly for the beginning modeler.
Today:
- For this next mini-project, Hares and Lynx, we'll continue to work with InsightMaker, advancing to the results highlighted in the paper by Tyson, et al.: Modelling the Canada lynx and snowshoe hare population cycle: The role of specialist predators
  I've prepared a lab, of sorts, for you to carry out in InsightMaker.
- If you want to get ahead, our next (and final) mini-project will be to work on SIR (Susceptible/Infected/Recovered) models of disease. We're obviously a little more interested in those at the moment. We'll be adding Death to the models, unfortunately (SIRD models)....
  Some good links that I'll expect you to visit:
  1. 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.
  2. 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.
  3. 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?
  4. This Covid-19 situation is probably more suited to a SIRDs model (with disease-induced death).
  5. An on-line model developed by Ashleigh Tuite and David Fisman, Dalla Lana School of Public Health, University of Toronto
  6. This one incorporates space into the model. These models are called "agent-based models".
  7. 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.
Links:
- The Bestiary of functions, from Ben Bolker's Ecological Models and Data in R
- My "DEs in a Day" page.
- Mathematica version of the Tyson, et al. basic model

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