Math Modeling: Day 32

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Announcements:
- During class time I'll be on Zoom, at https://nku.zoom.us/j/7057440907.
- You have an assignment due today: three things related to the Fletcher data.
  If you're loading in the data to Mathematica, one tip is how to deal with missing values (some of the maxes or mins are missing):
  LinearModelFit[Cases[data, {_?NumericQ ..}], {x}, x]
  Runs linear regression on only those cases of data that are not missing -- only on those cases that are numeric data.
- You have a lab due Tuesday: your final InsightMaker lab, the third in a series of three for SIR models (thinking especially of the Covid-19 virus).
- I think that I'm up to date on the grading. Your graded work is in the directories that I set up for each of you. If you still can't access that, let me know.
- Fletcher model reconstruction key:
  These are the sinusoidal models of BG Climate Normals, by month (max, mean, min temperatures), plus a model for all the 1893-1992 record temperatures taken from the Fletcher data.
  - Sean's versions
  - And now, for more than you probably want to see... :)
    1. FletcherMinMaxMeanSinusoids.nb
    2. FletcherMinMaxMeanSinusoids.pdf
- Lab "keys":
  - Predator/Prey:
    1. Lab 1: logistic and intro to InsightMaker
    2. Lab 2:
      1. Basic predator/prey model (Lotka-Volterra)
    3. Lab 3:
      1. Tyson et al. Lynx and Hare
      2. Samuel did a nice job on PP3
  - SIR models:
- We do have an exam Friday. That will cover non-linear regression stuff, predator/prey, and SIR modeling.
  Fletcher stuff may appear as well. You should try to be up to speed on everything we've been doing, especially since Spring Break. I know that it's been rougher for some of you than for others.
  There may be an InsightMaker component. That would seem reasonable, given all we've done.
Last time:
- I had you try your hand at a third and final SIR lab: Covid-19 in Italy
  This is an interesting one. When I started looking for Covid-19 models, I found this one InsightMaker, and it incorporated real data.
  As applied math modelers, we need to try to make sense of real data (e.g. the Fletcher data). In this lab we examine how some modelers tried to make sense of real data (and make important predictions); then, how we need to make changes to their model, to reflect the real world, which intruded upon their theories....
Today:
- I think for today I'll do a little video survey of the labs that we've just engaged in, with a bit of a "big picture" of each. You can check out my "keys" above, but it seems hard for me to write things up in a way that is to my liking. Maybe it will be easier to follow along in video format....
  At this point, I've got the predator/prey video summaries done:
  Here are the SIR lab summaries:
  1. Lab SIR1: Basic dynamics
  2. Lab SIR2: Flatten the curve
  3. Lab SIR3: Corona in Italy
- Then Wednesday I'll do some reviewing of the material (especially non-linear regression) in preparation for the exam.
  Again, I'll try to do some video summaries to emphasize and clarify some things.
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
- Our final mini-project will be to work on infectious disease models (e.g. Susceptible/Infected/Recovered models of disease).
  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. 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.
  8. A nice R-based introduction to infectious diseases and nonlinear differential equations.
  9. 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."

Website maintained by Andy Long. Comments appreciated.