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AA3-3 team exploration of COVID 19 cloned 1/19/2021

Last updated about 4 years ago
12 questions
In this investigation, we are going to explore the spread of COVID-19 in Multnomah County. The numbers I am using are based on real data, but due to rounding and other assumptions we must make, it is a hypothetical mathematical exploration more than a scientific or statistical exploration.

In other words, learn from this, but don't cite these numbers in a debate.

We are going to look at weekly data. This seems to make sense because people are infectious for approximately that long. For our purposes there are two things we need to know. First, the number of people who are infectious that week. For simplification, we will call these people carriers. Second, the infection rate, the average number of people each person infects.
1

If we have an infection rate of 2. Does that mean that each carrier infects exactly 2 people? Explain.

The spread of COVID 19 is exponential because we assume that each new carrier will go on to infect more people, those new carriers will do the same, on and on.
1

Hypothetical #1:
The last day of school was March 13. On that day, Multnomah County had 2 carriers. The infection rate was 1.85. This was about 32 weeks ago. If that infection rate continued, calculate, how many people would become infected this week.
To use Desmos as a calculator put 32 as the exponent and it will give you the answer.

1

Your calculation should have shown about 708,800,000 people. This is over 708 million.

Remember, exponential equations do not tell us the total number of people that have been infected, but the number that would become infected that week. If Multnomah County has 825,000 people, graph your equation above and estimate in which week a number equal to the entire population would become infected.
An easier way to do this is to add y=825000 and look for the point of intersection.

1

Fortunately, that infection rate did not continue. One month later, mid-April, there were 160 carriers and an infection rate of 1. If that infection rate continued, how many people would become infected this week (28 weeks later)?

1

How many newly infected?

1

Describe the shape of the graph. Why?

1

We didn't stop there. In mid-May there were 140 carriers and an infection rate of 0.9. How many new infections would we have this week (23 weeks later) if this rate had continued? Use Desmos to calculate.

1

How many newly infected?

1

Graph your equation above. If this continued, when would there be 0 new cases? Explain.

1

The rate climbed again during the summer, but when school started we had an infection rate of 0.95 and about 280 carriers. To open schools, we must have less than 10 new cases for three weeks in a row. If that infection rate had continued, would we be able to open schools this year? (There are 52 weeks in a year, 40 in the school year.)

1

Would we be able to open schools?

1

Sadly, the number of infected continues to rise. Today we have about 600 carriers and an infection rate of 1.1. This is almost exactly the same as at our peak in mid-July.

Based upon what you have seen abov e, what do you think the term "flatten the curve" means.