Classical one population models
Population theory, with its long history, dates back to the Malthus model, formulated for economic reasons in the early nineteenth century, predicting the population problems due to an exponential growth not supported by unlimited resources. The basic equation was then corrected by Verhulst (1845; 1847) to compensate for the shortcomings of the earlier model. The logistic equation states instead the existence of a horizontal asymptote to which the population tends as time ﬂows. This asymptote has a biological interpretation, namely the carrying capacity the environment possesses, to support the population described by the model.