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## What is the Math?

The curve used to model this situation is called a logistic curve, an S-shaped curve that describes population growth—of both viruses and people—as well as other phenomena in economics and science.

### Interesting Facts about the Logistic Curve

The point of inflection is the point where the curve changes from increasing faster to increasing slower. It also marks some symmetries for the curve.

• Half of the people are accounted for below the point of inflection, and half are accounted for above the point of inflection.
• Half of the time is accounted for to the left of the point of inflection, and half of the time is accounted for to the right of the point of inflection.

Once the point of inflection is known, it is possible to estimate:

• How long a pandemic will last. Since half the time occurs to either side of the point of inflection, the point of inflection is the midpoint of the curve. Therefore, if a pandemic has lasted x days in getting to the point of inflection, it will likely continue for another x days.
• The total number of people that will be infected. Because half of the people are infected on either side of the point of inflection, it gives the midpoint. Therefore, the number of people who will be infected after the point of inflection is roughly equal to the number infected up to the point of inflection.

Before the point of inflection is known, it is not easy to make accurate predictions.

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