Social Distance Modeling
You can run this model in your browser.
I was interested in the fact that there are multiple dimensions of social distancing, and most Covid-19 models weren't accounting for this. The two that I looked into were:
How many people are social distancing
How aggressively these people were isolating
Basically, I'm curious about questions like:
What's better? To have 50% of the population isolating very aggressively, or 75% of the population moderately isolating? This model allows you to adjust these variables, and a handful of others. It also gives a rough estimate of the economic consequences of your policy decisions. Check the readme file for details about how assumptions were made.
In part 2, I modified the code created for part 1 to attempt to create a self-regulating system. Is it possible, in theory, to dynamically increase and decrease levels of social distancing in such a way as to have a stable level of currently infected persons?
Why does this matter?
As of writing this (early April 2020), there’s a lot of discussion around the world about “re-opening economies”, and although I think this is often the result of misunderstanding the risk of the virus, it does raise an interesting question: can partial quarantines be effective? Can we slowly ease out of social distancing measures? Or will any easing result in another big peak?
For this simulation, I used three variables to control the level of social distancing:
[prop-infected]: the proportion of people infected
[daily-delta]: the daily change in number of infected people
[threshold]: a proportion of the population infected above which healthcare systems become overwhelmed. In the simulation I am using 10% as the percentage of the population ill at one time that the healthcare system can accommodate.
If the [prop-infected] rises above the threshold, or [daily-delta] is too high (indicating that cases are rapidly growing), the proportion of the population taking social distancing measures increases. So, for example, if 11% of the population is infected, the proportion of the population taking social distancing measures would increase by x amount every day until prop-infected falls below 10%.
Conversely, if the [prop-infected] is below 5% (threshold/2), and [daily-delta] is negative, we can decrease the proportion of people socially distancing by x amount.
How much is x amount? That’s a good question. The granularity with which a society can adjust how many of its citizens are social distancing unclear and subject to political pressures. On one end of the spectrum, we could imagine a government announcing every morning which birthdays were allowed to leave the house. On the other end of the spectrum, we could imagine a government announcing at the start of the month that everyone must stay inside, and at the end of the month, letting everybody out. The most realistic course of action is probably somewhere in the middle. I think most citizens would get awfully fed up with a government micromanaging and making frequent adjustments, however, we probably want something more attentive than the second scenario. This is an added challenge — we want a self-balancing system that takes large enough steps so as not to require super frequent adjustments, but also keeps the virus at acceptable levels. To start, I’ve set the [distancing-step-ups] (by what percentage of the population do we increase the total number of people distancing) at 10%. I’ve done the same for [distancing-step-downs] (by how much do we decrease the number of people social distancing). We can imagine city governments being able to adjust social distancing behavior with this sort of granularity by taking steps such as expanding and contracting the list of “essential businesses”. (Note: I am well aware of the fact that opening and shuttering businesses adds a whole new level of economic stress and greatly impacts these business’s ability to plan. That being said, I think what we’re interested in here is the effect of slowly opening or closing the economy on the spread of a virus, not the economic difficulties and feasibility of opening and closing the economy.)
Here’s an example of the results:
This is a fairly typical result, even when we vary the population size and other factors. There’s a lot we can dive into here, but I think the biggest takeaway is the difficulty of returning to old social behaviors and not having another outbreak. Even when social distancing is very slowly eased (which, as we discussed above, would be difficult to do), there is often a rebound outbreak, which, although smaller than the first, still requires a rapid return to distancing to contain.