On Measuring COVID-19 Infection Growth
While most of my blog posts have been capturing the daily total counts of confirmed COVID-19 cases in the DC area, I haven't published too much with respect to growth rates. Growth rates are naturally intriguing, because it shows how quickly the disease is spreading in the area (as well as a function of testing capacity, which I don't plan on getting into). Without further ado, I'm going to jump into a discussion on the various ways one can measure growth, specifically total counts, percentage increase, and doubling time.
Total Count- This method is very simple to calculate and intuitive. I post this figure in my daily updates, and it's simply the difference between yesterday's top-line figure and today's top-line figure. From a recent example, total cases in the DC area grew by 448, from 3,389 to 3,837. This figure is the best way to quickly get an idea about the magnitude of growth - a total case increase of x is the same magnitude in any context. That said, the impact of the increase x depends heavily on local settings - total population, hospital capacity, etc. As you can see in the chart below, the increase in total new cases has been increasing on a gradual, if intermittent, basis.
Percentage Increase- Also simple to calculate, and also quite intuitive. This merely takes the total cases from day n and expresses it as a percentage increase from day n-1. This removes the issue of magnitude when looking at growth; a 448-case increase when you had 600 to begin with (i.e. a 75.67%) increase is a whole lot different than a 448-case increase from 3,389 cases (i.e. a 13.22% increase). Thus early in the outbreak of COVID-19, percentage increase wasn't particularly useful - as such, you can see the fluctuations early on due to the low total cases (i.e. a low denominator) and hence the outsized impact of changes in the new cases (i.e. the numerator). The daily percentage increase doesn't really "settle down" until late March, as shown in the chart below. To take out some of the daily noise, I included a 4-day moving average line to help smooth the curves a bit.
Doubling Time- Effectively a function of percentage increase, but expressed in a different way. This is apparently very useful for public health officials to take diagnostics of local healthcare capacity. I hadn't really read much about doubling time before the Coronavirus outbreak, so mostly my knowledge about its calculations comes from the Wikipedia page on it. Suffice it to say that the calculation for our purposes is (ln 2)/(ln 1+(r/100)), where r is the percentage increase (discussed above).
Total Count- This method is very simple to calculate and intuitive. I post this figure in my daily updates, and it's simply the difference between yesterday's top-line figure and today's top-line figure. From a recent example, total cases in the DC area grew by 448, from 3,389 to 3,837. This figure is the best way to quickly get an idea about the magnitude of growth - a total case increase of x is the same magnitude in any context. That said, the impact of the increase x depends heavily on local settings - total population, hospital capacity, etc. As you can see in the chart below, the increase in total new cases has been increasing on a gradual, if intermittent, basis.
Percentage Increase- Also simple to calculate, and also quite intuitive. This merely takes the total cases from day n and expresses it as a percentage increase from day n-1. This removes the issue of magnitude when looking at growth; a 448-case increase when you had 600 to begin with (i.e. a 75.67%) increase is a whole lot different than a 448-case increase from 3,389 cases (i.e. a 13.22% increase). Thus early in the outbreak of COVID-19, percentage increase wasn't particularly useful - as such, you can see the fluctuations early on due to the low total cases (i.e. a low denominator) and hence the outsized impact of changes in the new cases (i.e. the numerator). The daily percentage increase doesn't really "settle down" until late March, as shown in the chart below. To take out some of the daily noise, I included a 4-day moving average line to help smooth the curves a bit.
Doubling Time- Effectively a function of percentage increase, but expressed in a different way. This is apparently very useful for public health officials to take diagnostics of local healthcare capacity. I hadn't really read much about doubling time before the Coronavirus outbreak, so mostly my knowledge about its calculations comes from the Wikipedia page on it. Suffice it to say that the calculation for our purposes is (ln 2)/(ln 1+(r/100)), where r is the percentage increase (discussed above).
Summary - Clearly we can observe changes in the three statistics since early March. I'm not surewhat public health or epidemiological conclusions one can draw, but these figures do help keep things in perspective. I'll try to include these figures in the daily updates of new infections.
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