SIR Lab III

Sadly each of these cases represents a real person, a real Italian. Our job is to help those fighting this disease understand better how it is behaving, and make intelligent moves to keep it from infecting (and killing) more Italians -- and everyone around the world.

Now let's get started....

Big picture:

1. Someone (Gabo HN) collected data on Total Italian Covid-19 cases, March 3 through March 14, and built a (pretty good) InsightMaker SIR model to fit the data. From that model, we can make predictions, about total cases, etc. into the future.
2. I collected data on Total Italian Covid-19 cases, February 24th through April 9th, from Harvard. We can test the Gabo HN model against the more recent data. Their model doesn't do very well.
3. We can improve their model. Our goal is to tune their model, and hopefully learn something more about the disease.

1. The original model:

   Visit this Italian SIR model that includes death and real data. You'll need to "Clone Insight".

   Hit Simulate. You should see something like this:

   

   and you'll notice several things:

   1. In that graphic, there is an "actual" data: it's 12 real numbers of Total cases in all of Italy, from March 3rd to the 14th (0 to 11). And their model for Total cases is doing a pretty good job of fitting the data.

   2. This is an SIRD -- each of the stocks is there. However, there are additional stocks, such as the invulnerable "Quarantined", and a sort of half-way house between susceptible and infected -- "Exposed". The "Surviving/Survived" gives one the sense that they could die, but there's no flow in that direction.

   3. You might notice some of the other features of this model:
      • Incubation rate -- how long does it take to get infectious, once you're exposed? (This is really important in real epidemiology, because "contact tracing" is a good way to stamp out an epidemic -- finding out whom you might have infected, based on how many days ago you started shedding virus).

      • This model has an explicit $R_0$ -- the intrinsic reproductive number. If it's below 1, the epidemic will die out on its own. Basically it means how many you infect, given that you're infected. If you infect 1 person, then the epidemic will just walk through the population; but if you infect 2, and then they infect 2 each, and so on, you can see the "exponential growth" that everyone keeps talking about.

      • They introduce "social distancing" in explicit fashion: the "lockdown" isolates people in place, so they are cut off from spreading (possibly from treatment, as well), and from getting infected (if they're not already). In this model, you see that the Quarantined are not contributing to any other category, so we're just isolating off some susceptibles (so they're not susceptible anymore). These are modeled after the actual lockdowns that Italy implemented.

      • The flows from infectious send all the infectious off every day -- which seems kind of weird, especially because they're feeding back into the "exposed" population. People aren't infectious for just a single day.

        If you look at the flow equations from the "Infectious" stock, what are they? (report these in your word document)

   4. Change settings, and simulate for 37 days (until the 9th of April).
      1. Simulate, and include this in your report. Also:
      2. How many Total cases are expected on the 9th of April?
      3. How many deaths are expected on the 9th of April?

      These are predictions, which health care professionals and government officials may use. It would be nice if they were accurate!

      (status as of April 9th, 2020)

   5. Comment on how well the model has done.

2. Now I'd like you to visit a slightly new and improved version of that model: my version that includes data through April 9th.
   1. Simulate, and include this in your report. Describe what is going on.

      Our objective: to modify the model to fit the data.

   2. It took me a fair amount of playing around, but I managed to get a decent fit to the data through April 9th:
      

      by making certain modifications and (dare I say) improvements on their model.

      I'm going to have you reconstruct my model, which is pictured here:

      

      So let's start with "what's new". I've added a "deathrate" and a "recoveryrate": I've short-circuited the process from the Infectious to the Dead and Recovered -- I'm not using the "Surviving Rate" anymore). I've also added the Infectious stock to the Total reported cases.

      There are links from these new rates to the appropriate Flows, and from the Infectious to the "Total reported cases" variable.

      There are also a few changes to things that you can't see, so I'll report them here; you should set up your model the same way, as follows:

      Incubation rate:  .025
      R0: 3
      First Lockdown: IfThenElse(Days() == 5, 16000000, 0)
      Total Lockdown: IfThenElse(Days() >= 7, 0.7,0)
      

      (I didn't want to assume that the "Total Lockdown" wasn't leaky! So it gets successively tighter, but people are sloppy, so it simply goes to 0 exponentially, rather than completely all at once.)

      As I noted earlier, these are modelled on lockdowns that the Italians actually implemented.

      deathrate: .01
      recoveryrate: .03
      
      "Death flow": [deathrate]*[Infectious]
      "Recovery flow": [recoveryrate]*[Infectious]
      
      Total Reported Cases: [Dead]+[Surviving / Survived]+[Infectious]
      

      1. Reproduce my figure, my better simulation results, but include your name in the Display (configure allows you to rename a display).

      2. How well does this model predict deaths and recovered on April 9th?

   3. Extend the simulation from the 9th of April to the 9th of May.

      1. Include your model graph.

      2. What would you predict for Total recorded cases, deaths, and infectious on the 9th of May?

      3. It is the sum of the recoveryrate and deathrate that determines how much "attrition" the infected population suffers. Can you "tune" these parameters to get the Dead and the Recovered to fall more in line with the data for their status as of April 9th,

3. Comment in your report on what was changed from the original Italian model. When the parameters of the model are changed -- or when the model undergoes surgery, as what happened here -- you want to ask "Is the model better?" "Does it do a more realistic job of modeling the situation?" Those kinds of things.

   I'll give you a couple examples of my own criticisms.

   1. I moved the date of the first lockdown up a day. If you look into that, you'll see that there's a little wiggle-room in that (check Wikipedia -- Italian for "Web Encyclopedia" -- on that). But I think that I'm early....

   2. I added the "Infectious" to the "Total reported cases". In the first model, as soon as the Infectious were in the model for a day, they were divided into "Surviving/Survived" and "Dead" - because they'd been identified as problematic, and stopped by the authorities from further infecting people. I kept them in, still infecting people (partly because they infect those in nursing homes, hospitals, their families, etc. -- in fact, they could be the most dangerous infectors!),

      But an alternative would have been to make the Exposed do much of the infecting, while asymptomatic; and calling the infectious "Symptomatic" -- and hence quickly removed (yet still dangerous, and still infectious).