Some Promising (or Misleading?) Coronavirus Plots?
I decided to practice my webscraping skills by pulling COVID-19-related death data from the web archives for worldometer.info (mainly because it's an easy site to mine), collecting the number of recorded cases at time points going back two weeks. The plots I got surprisingly seemed a bit encouraging, though of course trying to infer trends from a few days worth of data points (the data is updated every few hours so there are actually a few points per day) is risky. In any case there is something of a clear trend. Let's look at total COVID-19 related deaths over over the last couple weeks (worldometer only has state-level data going back to March 18), or since the first recorded case, in the largest and most affected states:
There seem to be decelerations in the curves starting about 2-3 days ago in most large states. The red lines, I should add, are logistic growth curves fitted to the data. The logistic curves fitted to the current data probably aren't very useful for predictive purposes, as the estimates for the asymptote - and how long it will take to reach it - vary wildly depending on the day. Somewhat puzzlingly, though, the country as a whole doesn't show of a deceleration:
Data source: https://www.worldometers.info/coronavirus/country/us/)
There seem to be decelerations in the curves starting about 2-3 days ago in most large states. The red lines, I should add, are logistic growth curves fitted to the data. The logistic curves fitted to the current data probably aren't very useful for predictive purposes, as the estimates for the asymptote - and how long it will take to reach it - vary wildly depending on the day. Somewhat puzzlingly, though, the country as a whole doesn't show of a deceleration:
It's possible that the smaller, thus far less affected states are starting to see more infections, cancelling out the deceleration in the already severely affected states. There also appears to be something of a lag in the attribution of cases to individual states in the available data (that is, country totals seem to be ahead of the sum of the state totals), perhaps because states release their data to the federal government before they release it to the public. In any case, there is some suggestion that many states are starting to deviate significantly from their curves, indicating that these states are responding constructively to their dire situations. It is of course possible that these apparent abatements will be temporary, and deaths will pick up again. Many states show irregular inflection points that caution against being too trustful of simple models.
Another curiosity, to me at least, is how low the estimated asymptotes are for the logistic fits. The national curve, for example, though highly variable, tends to average around 20,000 deaths as its asymptote for the current outbreak, with the country reaching that point in roughly one month. The most current fit, for example:
This of course seems extremely optimistic, and contradicts most of the expert predictions. The federal government just predicted a best case scenario of 100,000-240,000 deaths (https://www.washingtonpost.com/politics/trump-white-house-projects-up-to-240000-coronavirus-deaths-in-us-even-with-mitigation-efforts/2020/03/31/62df5344-7367-11ea-87da-77a8136c1a6d_story.html). Annoyingly, none of the news sources reporting on the prediction say what the time frame for these deaths are, so I'd guess that's how many are expected within the next year. That doesn't seem consistent with only 20,000 people dying by summer, since a second outbreak in fall would probably be less severe than the current one. Just to illustrate how variable best-fitting models can be from day to day, a fit from a couple days earlier anticipated an asymptote of 30,000 cumulative deaths.:
That's still optimistic compared to what is being predicted though. More complex models must be reaching far less sanguine conclusions. Over the course of the next few weeks it will be interesting to see how accurate extrapolations from previous timepoints prove to be. We might expect periodic decelerations and re-accelerations in the death rate in the next few months, causing marked deviations from the simple logistic model, and if people respond to the declining death rate by being less cautious (and/or as restrictions are lifted), we would likely see some resurgences in the death rate. As it stands, though, it is difficult to reconcile logistic growth models with the predictions of epidemiologists. If the growth rate is highly variable the data we have up to now may be fairly useless in predicting future trajectories, but this would cast more than just simple logistic models into questions. Or perhaps epidemiologists have reason to expect the growth rate to increase sharply in the next two weeks, or to expect that it will decelerate much more slowly (which strikes me as the more likely scenario). Inasmuch as these models do fail in the next several weeks, it will raise the question of why the local epidemics undergo periodic decelerations as they burn through the population. Is it an artifact of the healthcare system? Do cities oscillate in how intensively they engage in 'social distancing? Though we should never be so naive as to expect reality to neatly fit simple models, but irregularities also demand explanations. Obviously, it would be wonderful if it turns out that many places are indeed past the inflection point and mortality rates will decelerate going forward, but the consensus is leaning heavily in the opposite direction.
Data source: https://www.worldometers.info/coronavirus/country/us/)
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