This was prepared for a mathematical literate (honors) young teenage girl. This introduces risk assessment and risk mitigation using Public Health Measures. Also includes a mathematical tuitorial.

1. A Lesson In Mathematics
A Lesson Is Risk Assessment
The Coronavirus Pandemic
James K. Orr
A Gift To My Granddaughter
March 14, 2020

2. Disclaimers
This presentation is:
• Targeted to a mathematically literate 13 year
old.
• The is a lesson in risk assessment and risk
management packaged within a tutorial in
mathematics
• If you are reading this and do not understand
the math, just listen to your public health
authorities for direction.

3. Teaching Risk Assessment
In “Out of Control” Times
• For a typical 13 year old on Spring Break in
Houston Texas, messages are overwhelming
shouting “panic”
– Daily reports of rapidly rising coronavirus case, with
cases number “suddenly” alarming growing in the US
– Houston Rodeo abruptly canceled and shut down
– School re-start delayed at least a week
– Travel from all of Europe shut down
– Grocery store shelves bare
– Stock Market in record plunge

4. A Grandfather’s Assessment
Exactly As Expected
• Analysis of case per day in Mainland China, South Korea, Italy,
and Iran established a solid model for expected case growth
over next two weeks on March 7, 2020.
• https://www.slideshare.net/JamesOrr4/coronavirus-case-growth-by-country-jkorr-2020-0307
• Case growth would reach public (and investor) panic
levels in the following week (just simple mathematics).
• Worldwide, in Washington state, New York state and
Houston, coronavirus cases numbers grew as expected
• Houston, Texas taking early, appropriate Public Health
measures in face of early reports of cases from
returning international travelers and later intra-United
States travelers (in specific to California).

5. United States Coronavirus Risks
# Description Qualitative Risk
1
U.S. Medical System Collapse Due To
Cases
Very High
2
U.S. Medical Staff Simultaneously
Infected
High
3
Total Number of Individuals Infected
and Unable To Work Causes Inability To
Produce and Distribute
Medium
4 Death of Patients at High Risk Medium
5 Loss of paycheck due to work absence High
6 Bankruptcy for individual companies Low
7 Effect on typical Patient if infected Low

6. Public Health Roles (1 of 2)
• Federal and state government
– Receive advice from Public Health professionals,
weight risks and what the public will accept, and
make best case trades between available actions
• Public Health Professionals
– Protect the health of the overall population
– Protect the health care system ability to function
– Provide advice on public health mitigations to
minimize the rate of spread of coronavirus cases

7. Public Health Roles (2 of 2)
• Medical Care Professionals
– Treat patients
– Keep self well (if Doctors are sick, no one to help)
• High Risk General Public
– Pay maximum heed to advice to minimize
exposure
• Low Risk General Public
– Per direction from Public Health, take as drastic
measures to avoid spreading the disease

8. Public Health Mitigation
The goal of community mitigation, (1) delay outbreak peak (2)
decompress peak burden on healthcare, known as flattening the
curve (3) diminish overall cases and health impact.[203][204]
Source: Consistently Reliable: Reference 1

9. Qualitative Risk Assessment
• What is the expected rate of new cases?
• What are the sources of the new cases?
• What are possible Public Health Measures that
can be implements to slow the growth of new
cases?
• What Public Health Measure will the general
public be willing to tolerate and agree to follow
as directed
• What Public Health Measures will the
government be willing to implement and enforce
including with physical police actions

10. Quantitative Risk Assessment
• What Quantifiable Information Is Needed?
– With Current Public Health Measures
implemented
• Total Cases By Day (which implies new Cases Per Day)
• Percent of Low Risk Public
• Percent of High Risk Public expected to die if infected
with coronavirus.
• Number of available hospital beds
– Bottom Line: Define a Critical Metric
• Percent of Beds Needed By Hospitalized Coronavirus
Patients

11. Mathematical Tutorial
• Growth of coronavirus cases can be approximated by a
simple model of growth as percent of current cases
each day
• The next two pages illustrate this with use of Microsoft
Excel functions.
– First case uses brute force numerical integration and then
show how this can be approximately reversed for number
of day for total case ratio
• This is a method later used when growth per day is not constant
– Second case generalizes to function that can be used to
assess exactly number of days to a certain growth for
constant percent growth in prior cases per day

12. Brute Force Numerical Integration
Just Counter
Input - B2
(B2 is cell #)
=INT(C2*(1+B2)) =C2-C1
Input - E2
(E2 is cell #)
Input - F2
(F2 is cell #)
=1/LN(1.5) =G2*LN(E2/F2)
Just Counter Constant y=x*(1+constant)
difference of
current and
prior ys
Input y Constant 225 Constant
=constant*(Natural
Log) of (y/225)
Day
Growth Per Day
Percent Per Day
Total Cases Cases Per Day Y A B X
0 50% 225 225 225 2.466303462 0.000
1 50% 337 112 337 225 2.466303462 0.996
2 50% 505 168 505 225 2.466303462 1.994
3 50% 757 252 757 225 2.466303462 2.992
4 50% 1,135 378 1,135 225 2.466303462 3.991
5 50% 1,702 567 1,702 225 2.466303462 4.990
6 50% 2,553 851 2,553 225 2.466303462 5.990
7 50% 3,829 1,276 3,829 225 2.466303462 6.990
8 50% 5,743 1,914 5,743 225 2.466303462 7.990
9 50% 8,614 2,871 8,614 225 2.466303462 8.990
10 50% 12,921 4,307 12,921 225 2.466303462 9.990
Numerical Integration Example
Excel Formula Usage
Reverse Engineer Numerical Integration
Excel Formula Usage
Mathematical Excel Formula Usage

13. Generalizes Function
Input Constant =INT($C$2*(1+$C$3)^($A7)) =BN-B(N-1) =LN($B7/$C$2)/LN(1+$C$3)
Independent
Variable
Computed Parameter Reference Delta
Recreate Independent
Variable From Total Cases
Day Total Cases Cases Per Day Days
0 225 0
1 337 112 1
2 506 169 2
3 759 253 3
4 1,139 380 4
5 1,708 569 5
6 2,562 854 6
7 3,844 1,282 7
8 5,766 1,922 8
9 8,649 2,883 9
10 12,974 4,325 10
Number Of Cases Day 0 - $C$2 225
General Case Using Excel Functions
Growth Per Day, %/Day - $C$3 50%

14. Illustrate No Public Health Measures
• Total hospital beds in United States is 790,000
US hospitals will run out of beds if coronavirus cases spike
https://www.usatoday.com/in-depth/news/investigations/2020/03/13/us-hospitals-
overwhlemed-coronavirus-cases-result-in-too-few-beds/5002942002/
• The United States had 2092 cases on March
13,2020
• 81 % Cases Mild, Only 19 % need hospital bed
• 1/3 beds available now
• 2/3 needed beds put hospital in severe stress

15. No Public Health Measures
20 % Per Day Case Growth
Number Of Cases Day 225
Growth Per Day, 20%
=INT($C$2*(1+$C$3)^($A7)) =LN($B7/$C$2)/LN(1+$C$3)
Computed Parameter
Recreate Independent
Variable From Total Cases
Total Cases Days
225 0 Reference
2,092 12 3/13/2020
1,385,789 48 4/17/2020
2,766,842 52 4/21/2020
General Case Using Excel Functions
Date

16. No Public Health Measures
50 % Per Day Case Growth
Number Of Cases Day 225
Growth Per Day, 50%
=INT($C$2*(1+$C$3)^($A7)) =LN($B7/$C$2)/LN(1+$C$3)
Computed Parameter
Recreate Independent
Variable From Total Cases
Total Cases Days
225 0 Reference
2,092 5 3/13/2020
1,385,789 22 3/29/2020
2,766,842 23 3/30/2020
Date

17. No Public Health Measures
Number Of Hospital Beds
Total Cases
19% Need Hospital Bed
Growth Per Day, %/Day Days
Date
Reference 2,092 50% 5 3/13/2020
253,300 1,385,789 50% 22 3/29/2020
525,799 2,766,842 50% 23 3/30/2020
Reference 2,092 40% 7 3/13/2020
253,300 1,385,789 40% 26 4/1/2020
525,799 2,766,842 40% 28 4/3/2020
Reference 2,092 30% 8 3/13/2020
253,300 1,385,789 30% 33 4/6/2020
525,799 2,766,842 30% 36 4/9/2020
Reference 2,092 20% 12 3/13/2020
253,300 1,385,789 20% 48 4/17/2020
525,799 2,766,842 20% 52 4/21/2020
Reference 2,092 10% 23 3/13/2020
253,300 1,385,789 10% 92 5/20/2020
525,799 2,766,842 10% 99 5/27/2020
Reference 2,092 5% 46 3/13/2020
253,300 1,385,789 5% 179 7/24/2020
525,799 2,766,842 5% 193 8/7/2020

18. No Public Health Measures
KEY MESSAGE
With No Change In Growth
Rate, System is
overwhelmed once 1/3
hospital Beds filled

19. Need Public Health Measures
• The above illustration shows dramatically that
drastic Public Health Measures are needed.
• We have longer term examples from four
countries where longer Term health measures
were implemented.
• Consistent pattern is that the percent of new
cases per day drops steadily.
• Next, lets look at data to see what this drop
looks like over time.

20. In Search Of Data
KEY MESSAGE
With Public Health
Measures, US growth
per day should match
Model III values

21. Corresponding Cases Per Day

22. Same Data, Logarithmic Scale

23. U.S. Projected Coronavirus Cases
Using Model III Case Growth Rate

24. U.S. Projected Coronavirus Cases
Using Model III Case Growth Rate

25. Current Public Health Measures
• May Not Be Adequate To Drive Case Growth
Rate to the Model III levels
• Due to the multiple geographic dispersed
clusters of cases, the “single country model”
may not match future data. There may be a
need to model each outbreak area separately
and add to total for United States
• Public Health Measured Needed NOW

26. Consistently Reliable
1. 2019–20 coronavirus pandemic, updated
constantly
– https://en.wikipedia.org/wiki/2019–20_coronavirus_pandemic
2.Coronavirus Case Growth Per Day After A
Country Reaches 225 Cases, March 7, 2020
– https://www.slideshare.net/JamesOrr4/coronavirus-case-growth-by-country-jkorr-2020-0307
3.Exponential Function
– https://en.wikipedia.org/wiki/Exponential_function

27. Gather Relevant Data
US hospitals will run out of beds if coronavirus cases spike
https://www.usatoday.com/in-depth/news/investigations/2020/03/13/us-hospitals-overwhlemed-coronavirus-
cases-result-in-too-few-beds/5002942002/
Ignore the attention grabbing. Hard facts::
• US Has 790,000 hospital beds
• Normally about 2/3 of the beds are in use at any one time
2019–20 coronavirus pandemic
https://en.wikipedia.org/wiki/2019–20_coronavirus_pandemic
This has been a rigorously consistent source. Information is the best available from government health
services.
• 81 % cases Mild
• 14 % cases Severe
• 5 % cases Critical