In any biological system, if you put a living organism into an environment where it can thrive, with unlimited resources and no predators or competitors, it will always grow in the same fashion: exponentially.
As long as those conditions are met, everything from wolves to parasitic wasps to yeast cells will grow exponentially, up until one of those assumptions fails to be true. Only that that point will growth become slower, and that holds the key to understanding how to mitigate the present pandemic.
In the case of the coronavirus COVID-19, exponential growth will occur in the disease rate in humans so long as:
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