Day 2, MAT115

Last Time

Next Time

Announcements:
- Welcome back, masked students!
- This session will be captured on Zoom, if I remember to turn it on, and record it. Please help me to remember.
  Of course I forgot to hit the record button...:( Argh!:)
  So here's the day02 play-by-play. I had to redo what we did in class, but it might be good to see it again.
- Roll (if I don't have a note card for you, let me know.)
Questions from last time?
So let's get to today's "Question of the day":

How might a mathematician model Covid?
- You'll notice that I've brought my friends Tetrahedron 1 and Tetrahedron 2 back again! We'll be using them some more.
- We'll need some definitions: in fact that's one of the things I want you to pay attention to most.
  I've created a Graph Terminology page for you. You should learn those definitions. I'll be using some of them today, and will give you some definitions as we go.
  When you do your reading for next time (Chapter 3 in our text), try to describe each graph you see using the terminology.
- So let's get to the modelling! (I'll be using the Whiteboard, and will save the work we do on it to a file which I'll post here.)
  A couple of things to look for as we go:
  1. Linear relationships: if I double one quantity does it double another?
    1. If I double the gasoline in my car, I double the miles I can travel (roughly!).
    2. If I double my time of travel, I can double my distance (roughly!). The "DiRT" formula: $D=RT$ (distance = rate * time).
      Double the time, double the distance.
  2. How do masking, quarantining, and vaccinating figure in the model?
  3. Can we get waves of infection?
- We're going to start by drawing some pictures of the situation -- the SIR model for Covid.
  Caveat: this is a very simple model! It is not intended to completely and accurately reflect the disease (we might call it a "toy model").
- To get at the grubby details, we'll imagine an SIR simulation where we have
  - 100 Susceptibles (susceptible to infection with Covid),
  - 2 Infected (and infectious) with Covid, and
  - 0 Recovered people.
  Suppose that
  - the "R_o" of this strain of Covid is 2 -- meaning that an infected person will infect two more people, on average, in a week.
  - A week is a good unit of time, because we might assume that infected folks are only infectious for about a week.
  - We'll assume that 1 in 20 recovered people (on average) loses their immunity each week.
- Then we'll check out a simulation of our Covid model: Our Covid simulation from InsightMaker
- Where in the model will
  - masking have an impact?
  - quarantining have an impact?
  - vaccination have an impact?
  - treatment for those with Covid have an impact?
Links:
- Graph Terminology
- Our Covid simulation from InsightMaker
- Gotta catch those sneezes!
- Wear a good mask
- Boardwork from today

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