Searching Out a Matter: The Effect of Population Density

It is the glory of God to conceal things, but the glory of kings is to search things out.
(Proverbs 25:2 ESV)

Living in Missouri, I got curious about how population density affects the number of cases of COVID-19 per million people. So looking up case data from the John Hopkins website and demographic data from the census bureau I put together some graphs.

Figure 1

Figure 1 show the case density vs population density for counties in Missouri. It appears that case density does not take off until you reach a population density > 100 people per square mile. Two outliers are Saline county and Perry county, both of which have populations of ~20,000 and ~40 cases of COVID-19 (as of 4-14-20).

Breaking the data into 2 sets of PD < 100/sqmi and PD > 100/sqmi we have Figures 2 & 3.

Figure 2 PD < 100/sqmi
Figure 3 PD > 100/sqmi

Missouri has few real high population density areas, so let’s pull the data from the Top 50 counties in the country on the John Hopkins website and add it to Missouri.

Figure 4 Missouri + Top 50–Linear y axis

Figure 4 makes it look like you don’t really take off in case density until around 400-500/sqmi. So let’s convert it to a log-log scale.

Figure 5. Missouri + Top 50–Log-Log scale

Figure 5 shows there is a definite trend toward increasing case density as population density increases. Around 62% of case density can be explained as a result of population density. Other factors affecting this are probably local culture, climate, politics, etc. For Phelps county Missouri, PD = 67 and population is 44,573. The equation in Figure 5 implies that Phelps county’s case load should be 27.448 x 67^0.6305 = ~389 per million population. For 44,573 population that implies there should be ~17 cases of COVID-19. There has only been 1 as of April 14, so Phelps county is doing fairly well. (Phelps county actually has the lowest case density in Missouri at 22/million.)

The point of all this is that efforts at containment (aka lockdown) should be focused on high case density areas–major cities, not the entire country.

#Stopthe Madness



Searching Out a Matter: How Far has COVID-19 Progressed?

It is the glory of God to conceal things, but the glory of kings is to search things out.
(Proverbs 25:2 ESV)

One of the big uncertainties about COVID-19 is how many people have actually had the disease. Because that number is used to calculate the death rate of the disease. Based on official cases COVID-19 looks to be much more deadly than the flu.

Let’s search it out.

Early on the WHO said the R0 value for COVID-19 was between 2 and 2.8. R0 is the basic reproduction number. It means that on average an infected person will infect that number of other people during the time that they are contagious. So that an R0 of 2.0-2.8 means each person will on average infect roughly 2-3 other people. This is over the time that the infected person is contagious. It also assumes that the infected person does nothing to isolate themselves from other people and that people do nothing to protect themselves from infected people. The contagious period for COVID-19 is said to be around 14 days. So, an infected person will infect 2-3 other people during a 14 day period.

Another way to look at this is to use the R0 number to estimate a daily growth factor. Since

where G is the daily growth factor and T is the number of days a person is contagious, then for R0 = 2 and T = 14, then G = 1.05075663865 or G = ~1.051.

Wikipedia says that R0 for COVID-19 is between 3.8 and 8.9 so this implies that 1.10 < G < 1.17. John Hopkins website says that as of today (April 9, 2020), there are 454,304 cases of COVID-19 in the US. The date of the first confirmed case was Jan 20, 2020–80 days ago. We can use those numbers to estimate the growth factor in the US and it comes out to G = 1.17683840302 or G = ~1.18. This in turn corresponds to an R0 of ~10 in the US. This would put the disease at being roughly as contagious as chickenpox.

The question is are there really 454,304 cases in the US or is the number higher. This number is low, probably quite low, because in most places people are only actually being tested when they show signs of respiratory distress. So the growth rate number, G, could be low.

What effect does it have if G is higher than 1.18? Well, for instance, the apparent death rate for COVID-19 in the US is 16,267/454,304 = 3.58%, where 16,267 is the current number of deaths according to John Hopkins. But is G is > 1.18 and Jan 20 is the date of the first case then,

G = 1.19–the total number of cases is actually 1.11 million and the death rate is 16,267/1110000 = ~1.47%.

G= 1.20–the total number of cases is actually 2.16 million and the death rate is 16,267/2,160,000 = ~0.75%.

G = 1.21–the total number of cases is actually 4.2 million and the death rate is 16,267/4,200,000 = ~0.39%.

G = 1.22–the total number of cases is actually 8.1 million and the death rate is 16,267/8,100,000 = ~0.20%.

G = 1.23–the total number of cases is actually 15.6 million and the death rate is 16,267/15,600,000 = ~0.10%.

Ok, you get the picture–it is highly likely that a lot of people that have the disease were not tested so the real growth rate is higher and it only takes a 4.24% increase in the growth rate to balloon the real total number of cases by a factor of 34x and reduce the death rate by the same amount.

Also, given that the disease origin date in China is November and tens of thousands of Chinese were traveling to the US everyday until the travel ban, it is highly likely that the first case was way before Jan 20. So what effect does an earlier date have on the numbers. We’ll assume that G = 1.18.

Start date Jan 13–real number of cases is 1.79 million, so death rate is 16,267/1,790,000 = ~0.91%.

Start date Jan 6–real number of cases is 5.7 million, so death rate is 16,267/5,700,000 = ~0.29%.

Start date Jan 1–real number of cases is 15.4 million so death rate is 16,267/15,400,000 = ~0.11%.

Start date Dec 25, 2019–real number of cases is 49.1 million so death rate is 16,267/49,100,000 = ~0.033%.

Let’s stretch it out to Dec 1st, 2019. Real number of cases is 2.61 billion…in other words everyone that can get it in the country has already had it.

Ok, let’s take a fairly conservative look at both types of numbers, the growth rate and the start date. Let’s assume G is slightly higher than 1.18, say 1.19. And let’s assume a start date of Jan 1, 2020. Then what does it look like?

A total of ~36 million people have had the disease, which gives a death rate of 16,267/36,000,000 = ~0.045%.

What does that look like? It looks like the flu.