Verhulst derived his logistic equation to describe the self-limiting growth of a biological population.

Application of law of mass action to microbial populations results in the linear logistic equation.

The simplest way to model harvesting is to modify the logistic equation so that a certain number of individuals is continuously removed:

The logistic equation assumes that density dependence takes the form of negative feedback.

The Piotrowski law is a case of the so-called logistic model (cf. logistic equation).

The logistic equation which allows us to calculate the p value is:

This representation exploits the linear property of the logistic differential equation:

First, one assumes that the growth of the prey population is determined by the logistic equation.

For the competition equations, the logistic equation is the basis.

Using these techniques, Malthus' population principle of growth was later transformed into a mathematical model known as the logistic equation: