Monday, June 22, 2020

What is happening in North Carolina?

We have been working on using our model for North Carolina, where hospitalizations have been increasing consistently. We will be sharing a summary of our results soon with a paper but here are two figures which provide some idea as to what we see.
North Carolina is set to move to Phase 3 on June 26 but there is a possibility that Governor Cooper might decide to extend Phase 2. In the figure above, we are looking at three possibilities: the state moves to Phase 3 starting with June 26, stays at Phase 2, or moves back to Phase 1 until the end of the year. I do not think there is a serious possibility of going back to Phase 1 or staying in any one of the phases until the end of the year but they are useful for understanding the impact of different decisions. The figure strongly suggests that moving on to Phase 3 will be disastrous. In fact, even staying in Phase 2 will likely result in a significant increase in the number of deaths and hospitalizations peaking some time in Fall.

The figure above assumes a testing capacity of 30,000 per day, which is a little more than the maximum number of tests performed on a given day so far in North Carolina. If we double the testing capacity, it certainly helps but moving on to Phase 3 or staying on course in Phase 2 will again result in major increases in deaths and hospitalizations over the course of a few months. You can see that in the following figure.
More to come soon...

Monday, June 15, 2020

Ways to reopen

Here are predictions of the trajectory of the pandemic in NYC under different approaches for reopening. The charts show daily deaths, with the total death count at the every end. In each chart, we repeated the data series under different levels of testing capacity per day. After June 1, we switch to different levels of relaxation in social distancing norms -- as measured against the NY Pause measures. In particular, 0% means keeping the social distancing norms as in NY Pause, 100% means going back to pre-NY Pause norms. According to our model, to put it extremely vaguely, we cannot afford to be relaxed more than somewhere halfway between pre- and in-Pause norms. Otherwise, a bad second wave looms. Naturally, one wonders what does it mean to be halfway between pre- and in-NY Pause social distancing norms.

3 phases:

4 phases:

2 phases:

Saturday, June 13, 2020

Tradeoffs between social distancing norms and casualties

Below are efficient frontiers that show the tradeoff between the total number of deaths in NYC by September and the relaxation in social distancing norms. The efficient frontiers are repeated under different levels of testing capacity. To interpret the social distancing norms, 0% relaxation means keeping the norms as in NY Pause, whereas 100% relaxation means going back to pre-NY Pause norms as in before March 22. The efficient frontiers are constructed under the assumption that all new social distancing norms come into effect on June 1. Before that, we stick to NY Pause social distancing norms. Whenever we adopt a social distancing norm, we stick to it until September. Some analysis on gradually relaxing social distancing norms will follow.

Total deaths by the end of September

Wednesday, June 10, 2020

A few plots comparing the predictions of the model with history

Here are a few plots that compare the predictions of the model against the actual trajectory of the pandemic so far. In these plots, we stopped calibrating the model on April 15 and let it run its course in late April and May period, during which NYC was in NY-Pause. The model seems to be doing a decent job of predicting the course of the pandemic. As the City reopens, we will need to re-estimate the R-naught value corresponding to the current level of social distancing norms. It will be interesting  to see what we will predict for what is to come in late late June and the rest of the summer. All plots focus on NYC -- 5 boroughs.

Cumulative deaths
Note that the historical data reports both deaths from Covid and probable deaths from Covid.

Cumulative infected
The historical data only provides the known infected. One nice thing about having a model is that  we can see the number of people infected and know that they are infected, as well as then umber of people infected and do not know that they are infected. The green plot shows the total number of infected people who do and do not know that they are actually infected. The predicted fraction of the infected population appears to be lower than what is anecdotally discussed. 

Daily hospitalizations

Daily deaths
We are a bit off in terms of daily deaths, but we over-predict earlier and later deaths, whereas we under-predict peak deaths, as a result of which cumulative deaths is captured by our model reasonably well. This could be because we do not explicitly model hospital capacities.

Daily tested positive
The number of people tested positive comes out endogenously through the inner workings of the model. In other words, we do not have something like an exogenously-specified probability of testing positive. We fixed the testing capacity at 30,000 starting on June 1. For the other days, the number of people tested is what is in the historical data.

Can we flatten the curve in North Carolina?

Our paper on North Carolina is now available here . My last few posts essentially give a summary of the paper but all the details including ...