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# What is a logistic growth curve?

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A logistic growth curve is a sigmoidal, or S-shaped, curve used to map functions of initially gradual increase, rapid increase in the middle growth period and a slow leveling off to a maximum value at the end. Typically, a logistic growth curve will be used to model patterns of biological growth, such as population or ecology.

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The exponential, or geometric, growth of populations is rapid at first but always slowed by their environment's carrying capacity, which is the availability of food and other resources. Other factors will also slow population growth, such as predation and disease.

The logistic growth curve has also been used to model the rate of AIDS infection over a period of time. In the United States, the rate of AIDS infection between 1981 and 1992 followed a classic logistic curve, leveling off at around 47,500 cases each year. Since the logistic growth curve dictates that this leveling off occurs at more or less of a maximum value, as with the maximum population permitted by a given environment's carrying capacity, the results of the study could be extrapolated through to 1995. However, researchers point out that only the infection rate can be reliably plotted as a logistic growth curve because the morbidity rate is affected by advances in AIDS medicine and healthcare.

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