How dangerous is Covid ?  

It looks like the high fatality rates observed in NY and Italy
are linked to stress on their health care systems at the
height of their infections. There also seems to be a
correlation with the state of urban decay in the big cites in
each state. Neither of these should come as a  surprise, but
of course correlation does not necessarily mean causality.

Depends on health care stress

For obvious reasons, the mortality of Covid is a critical
property that affects the entire response to the virus.  In the
early stages of an infection, a popular  measure is the ratio
of Deaths to Cases called the  Case Fatality Rate (CFR)
(see https://ourworldindata.org/coronavirus).  CFR values
have ranged from  0.5% in  Iceland to  14% in  Italy with a
world  average of 7%.  In the US, the variation is from 1% in
Nebraska,  to 10%  in Michigan, with a US average of  4%.  
In general, these variations have been blamed on non-
uniformities in  detection, classification and reporting.

To see if these variations might be real,  I made a sorted
table of CFR for the states based on the data from (https:
//www.worldometers.info/coronavirus/country/us),  and all
the states that were hit hardest (NY, NJ, MI, LA) have the
highest CFR. This clearly suggests that the loading on the
health care system is a factor. Stress on the hospitals,
particularly the ICU should be related to the daily death
count, and the greatest demand will occur at the peak of the
infection.  I plotted the Maximum daily Deaths per Million
(MDM) as a proxy for health care stress against CFR and
found a statistically significant (>99%, R = 0.64) trend. The
correlation is better with deaths than cases, suggesting that
it is ICU pressure that is the problem. There was less or no
correlation with other metrics of health care availability such
as number of doctors, hospital bed count, the head room
between deaths and beds, whether the state was infected
early or late benefiting from health care learning etc. The
caution is that correlation does not mean causality, so this
might be just a useful indicator of a problem.

My first take away from the graph is that the peak daily
death count (MDM) needs to be less than 10 deaths per
day per million to keep CFR around 4%, greater than 10
and the fatality rate (CFR) starts to rise.  The second take
away is that what happened in NY with a CFR of 8% was
probably a serious step towards health care collapse. In full
collapse, presumably the roughly 20% of cases who need
hospitalization will die. The Region of Lombardy in Italy had
a CFR of 14% so it was getting close to complete collapse.  

After removing the correlation with  health care stress, the
states with  largest residual (also graphed)  were MI & LA for
high values, and NE & SD for low values. The infection in MI
is centered on Detroit which  has an unfortunate status as
the poster child for what can go wrong in inner cities like
Detroit; poverty, homelessness, drug abuse, poor health,
poor health care  all focused on minority communities.




Depends on urban decay

The second factor that seems to correlate with high  fatality
rate is urban decay,  with MI as the key State and Detroit
being the hot spot.   After removing the effect of health care
stress, the states with  largest residual  MI  for high values,
and corn belt states NE & SD for low values.  

MI and Detriot  could just be a unique case, but there are
multiple reports of poor and minority communities being
over-represented as victims of Covid so it is more likely that
it is the worst case example of a trend. There is data at the
US Census on the poverty level in the largest city in each
state,  and the states for those without big cities.  I am
using  poverty as a proxy for all the ills of urban decay.

After removing the correlation with  health care stress, the
residuals, highlighted that  the states with  largest residual
were urban decay states MI & LA for high values, and corn
belt states NE & SD for low values. The infection in MI is
centered on Detroit which  has an unfortunate status as the
poster child for what can go wrong in inner cities; poverty,
homelessness, drug abuse, poor health, poor health care  
all focused on minority communities. It is not surprising that
these issues combined with Covid would affect mortality.
To try to see if there is a statistically valid correlation across
all States, I went looking for appropriate proxy data sets. It
turned out that urban decay seems to depend on many
factors which is one reason why it been so hard to fix !
Gruesome measures of Detroit’s problems include; first in %
poverty,  second only to New Orleans in murder rate, first in
population decline from 1950-2100, first in drug problems.  
(https://en.wikipedia.org/wiki/Decline_of_Detroit).  

The U.S.A. Census Bureau's Statistical Abstract of the
United States: 2012 has data on poverty in the 72 largest
cities in Table 708. I took  that list and selected the largest
city in each state, based on the fact that most Covid
infections occur in population centers. I used the state  
poverty level for the 20 states with no city that qualified for
the list. There was a statistically significant correlation  
>99% between poverty level and residual. The random
variation left after removing the poverty effect had a 3 sigma
of 2%, with no outliers.




The data suggests a simple equation for the CFR
CFR% = 1.6+ 0.11*(Max. Daily Deaths per Million) + 0.13*(%
Poverty)

For a state with the minimal urban decay and low health
care stress the CFR could be as low as 1.6%. I created the
bar graph that shows how parts of the observed case
fatality rate can be assigned to health  care stress and
urban decay.


My takeaway from this is that focusing  resources on
centers of poverty and urban decay in any COVID hot
spots, and by avoiding overloading the health care system,
we  could have a real impact on mortality.











As the infection progresses, it has become clear that Covid
preys on the old and infirm. On Texas Covid web site there
is demographic details on both cases and deaths up to
4/20/20, shown on the right. The cases generally follow the
age profile of the general population but, as you might
expect, with the very young under represented.

The CFR within each age group follows the well known  
trend of increasing deaths with age, and for the 80's Covid
is very dangerous. The CFR for the total population was
3.3%.

Dividing the population into over and under 60, the under
60's had a CFR of 0.8%, and the over 60's a CFR of 11.8%.
Therefore CFR may give some insight into the
demographics of the infected population. If the infection is
proceeding through the general population, then the CFR
will be around 3%. If the infection is being passed through
the under 60's, the CFR will be around 1.0%. If the infection
is being passed from oldie to oldie within the over 60
community, the CFR will be 12%. The % of >60's infected =
(CFR%-1)*10.

This is a additional explanation for  the wide variation in
CFR that has been observed around the world; Health care
stress, poverty and age,

Time evolution of CFR

It is also useful to look at the evolution of CFR over time. I
calculated the CFR from the ratio of the 7 day average for
daily Deaths(d+3)/Cases(d). The 3 day lag reflects the time
shift in maxima of the 2 metrics. Finally, to avoid aliasing
around weekly variation, I calculated the 9 day rolling
average.  NY shows the maximum in CFR that I previously
assigned to health care stress. There is a second peak
about a month later, that Gov. Cuomo has assigned to
additional fatalities in closed communities of at risk
individuals such as nursing homes. Using the age model, at
a CFR 8%, the over 60's were 70% of the infected
population, consistent with Cuomo's observation













Florida publishes and archive of their daily dashboard that
includes a histogram of cumulative cases by age group. By
subtracting histograms a week apart, I obtained a snap shot
of the demographics over time.


During June there has been a 3x improvement in CFR for
the over 85 crowd. This is very significant. At the same time
hospitalization rates have remained constant, showing that
infections rates are not changing, but survival has become
a lot better, probably due to health care improvements.
Case Fatality Rate (CFR) plotted against the maximum in deaths per day per million as
a proxy for health care stress. The correlation suggests that overloading the health
care system, may result in poorer outcomes. The high fatality rates in Italy and NY
suggest that the health care system was headed to collapse. A safe loading appears to
be <10 deaths per day per million.
Residual CFR after removal of health care effect. MI is a high outlier, WY and NE
a low outlier.
Residual CFR after removal of health care effect plotted against the poverty% in
the largest city in the state, suggesting the communities with urban decay have a
higher fatality rate.
An assignment of the Case Fatality Rate in NY, MI and TX to health care stress
and urban decay at the maximum in daily deaths.
Time line of the evolution of CFR, from the 3 day lag of 7 day average  daily
deaths to cases. The CFR is a 9 day rolling average to eliminated aliasing.