Understanding WUHAN Coronavirus (COVID19) Growth Rate

The growth of a pandemic seems to follow a certain pattern. The growth rate is rapid and graphically is very alarming. But there is a certain mathematical pattern to all such growths. You might have heard the term “Exponential Growth Rate.” What does that mean? Essentially it is the number of the initial infection multiplied to its exponent. Or simply if the growth rate is from 200 on day 1 and that changes to 350 the next day then, the change number is 150 over the previous day. If that number grows to 480 the next day and 660 the next, then 200350480->660 indicates a rise of 150 on day 2 and 130 on day 3 hence the exponent (150/130) is 1.15. Using the 1.15 exponent rate of growth, further projections can be made which on Day 5 would be (660 *1.15) 759. And if the exponent reduces to 1.08 then the infection on day 5 will be 712. If the future number is higher or lower the exponent can be recalculated. The rise and fall of the exponent determine the rise and fall of the spread of the pandemic and whether the peak has been reached and the curve flattened.

Example of how to calculate the exponent and whether it is increasing or decreasing:

Assumed data for the graph below:

         Numbers  Rate increase Exponent
Day 1 200
Day 2 350          150
Day 3 480          130               1.15
Day 4 660          120               1.08

Graph 1

Now let us look at how we can determine and do a look back after noting the first tested individual who is shown to be positive and who has died. There are a few assumptions that will have to be taken to make such a determination. Simple mathematics makes it quite easy to understand.

Assumption #1: The Death Rate is 0.6%

Assumption #2: The Doubling Rate is 5 days

Assumption #3: The Time from Infection to Death is 20 days.

(These assumptions are based on the facts available from data on COVID19 from China and other countries where Social Distancing and other Hygiene measures are in full force).

Using assumption #1 in association with #3 suggests that for every 6 deaths there were 1000 cases 20 days ago. Next, since the doubling rate is 5 days (assumption #2), that would indicate that there will be 2000 cases 15 days ago, 4000 cases 10 days ago and 8000 cases 5 days ago and today the number would be 16,000 cases. These cases are actual infected cases and these will add to the death burden as time goes on, calculated below. Essentially one can do the look back of the potential infected based on current data and then based on the exponent, probabilistically show what to expect in the future if nothing else changes.

Graph 2

Data assumed Past Infections and Future Deaths based on an exponent of 1.53 would be:
Days    Future Deaths    Present Infections    

1            6                              1000
2            9                              2000
3            14                            4000
4            21                            8000
5            33                            16000

Graph 3

The current data from China, South Korea, and Japan shows that the actual infection rate in those countries is diminishing, and the diminished exponent reduces the peak infection rate and hence the flattening of the curve as explained above. We can IF WE follow the basic principles outlined below flatten the curve fairly quickly in the United States as well.

As I write this the total number of actual cases in the entire globe is 214,480 and total deaths equal 8,803 with 84,521 fully recovered. The Mortality rate in this larger picture is 4.1% and that includes the excessive death rates in countries where measures are less than expected. The full recovery rate is 39% as of this moment in time.  Additionally, as has been discussed, since new deaths are being reported, these reports suggest the implications of the tested sickest/infirmed patients first and the data will be skewed temporarily towards a higher Mortality Rate in the beginning but then the numbers will diminish to the expected mortality rate. Once the testing gets underway for a larger subset of individuals with symptoms, the rate normalizes eventually to the expected norm. In this case at or around 0.6%-08%.

Stay Safe and follow these simple Hygiene Principles:
1. Wash hands with Soap and Water
2. Do Not shake hands with others
3. Do Not touch your face with unclean hands
4. Clean the surfaces that can transmit infections (fomites).
5. Go out for walks but do not congregate.