Math Modeling: Day 29

Last time

Next time

Announcements:
- During class time I'll be on Zoom, at https://nku.zoom.us/j/7057440907.
- You also have a lab due today -- concerning the beginning SIR model.
- I created a "key" for the first SIR lab.
- A reminder that I have a preliminary a version (1.0) of our paper, which I've linked to the Fletcher page. Please take a look at it soon. We'll be working on it exclusively, once we finish with this SIR unit.
Last time:
- We started SIR models. This seems particularly appropriate given the moment in time we're living through. Usually it's all theoretical, but this time we're in the middle of the biggest SIR of my life, and yours too, I hope!
- We worked on a first lab (in a series of three) in InsightMaker, related to Susceptible, Infected, Recovered (SIR) problems (e.g. the Coronavirus). We're obviously a little more interested in those at the moment. We'll be adding Death to the models, unfortunately (this Covid-19 situation is more suited to a SIRDs model (with disease-induced death)).
Today:
- Today we're going to talk about a trilogy of things:
  1. Flattening the curve with social distancing
  2. The impact on death rates
  3. Surprising implications of doing too good a job....
  Carry out the second SIR lab
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."

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